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Appendices - Springer LINK

Jan 03, 2023

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Page 1: Appendices - Springer LINK

Appendices

Page 2: Appendices - Springer LINK

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Page 3: Appendices - Springer LINK

Tabl

e A

-l-l

S

atu

rate

d S

team

: T

emp

erat

ure

Tab

le (

51)

Spe

cifi

c V

olum

e. m

3/k

g E

nth

alp

y.

kJ/k

g E

ntr

op

y.

kJ/k

goK

T

emp

A

bs.

Pre

ss.

Sat

. S

at.

Sat

. S

at.

Sat

. S

at.

Tem

p

C

kPa

Liq

. E

vap.

V

apor

L

iqu

id

Eva

p.

Vap

or

Liq

uid

E

vap.

V

apor

C

T

P

v,

V,.

V •

h,

h,.

h.

S,

Sf"

S

. T

0.0

1

0.6

11

2*

0

.00

10

00

2

20

6.1

6

20

6.1

6

0.0

0

25

01

.6

25

01

.6

0.0

00

0

9.1

57

5

9.1

57

5

0.0

1

1.0

0

.65

66

0

.00

10

00

1

19

2.6

1

19

2.6

1

4.1

7

24

99

.2

25

03

.4

0.0

15

3

9.1

15

8

9.1

31

1

1.0

2

.0

0.7

05

5

0.0

01

00

01

1

79

.92

1

79

.92

8

.39

2

49

6.8

2

50

5.2

0

.03

06

9

.07

41

9

.10

47

2

.0

3.0

0

.75

75

0

.00

10

00

1

16

8.1

7

16

8.1

7

12

.60

2

49

4.5

2

50

7.1

0

.04

59

9

.03

26

9

.07

85

3

.0

4.0

0

.81

29

0

.00

10

00

0

15

7.2

7

15

7.2

7

16

.80

2

49

2.1

2

50

8.9

0

.06

11

8

.99

15

9

.05

26

4

.0

5.0

0

.87

18

0

.00

10

00

0

14

7.1

6

14

7.1

6

21

.01

2

48

9.7

2

51

0.7

0

.07

62

8

.95

07

9

.02

69

5

.0

6.0

0

.93

45

0

.00

10

00

0

13

7.7

8

13

7.7

8

25

.21

2

48

7.4

2

51

2.6

0

.01

93

8

.91

02

9

.00

15

6

.0

7.0

1

.00

12

0

.00

10

00

1

12

9.0

6

12

9.0

6

29

.41

2

48

5.0

2

51

4.4

O.

3

8.8

69

9

8.9

76

2

7.0

8

.0

1.0

72

0

0.0

01

00

01

1

20

.96

1

20

.97

3

3.6

0

24

82

.6

25

16

.2

0.1

21

3

8.8

30

0

8.9

51

3

8.0

9

.0

1.1

47

2

0.0

01

00

02

1

13

.43

1

13

.44

3

7.8

0

24

80

.3

25

18

.1

0.1

36

2

8.7

90

3

.92

65

9

.0

10

.0

1.2

27

0

0.0

01

00

03

1

06

.43

1

06

.43

4

1.9

9

24

77

.9

25

19

.9

0.1

51

0

8.7

51

0

8.9

02

0

10

.0

12

.0

1.4

01

4

0.0

01

00

04

9

3.8

3

93

.84

5

0.3

8

24

73

.2

25

23

.6

0.1

80

5

8.6

73

1

8.8

53

6

12

.0

14

.0

1.5

97

3

0.0

01

00

07

8

2.9

0

82

.90

5

8.7

5

24

68

.5

25

27

.2

0.2

09

8

8.5

96

3

8.8

06

0

14

.0

16

.0

1.8

16

8

0.0

01

00

10

7

3.3

8

73

.38

6

7.1

3

24

63

.8

25

30

.9

0.2

38

8

8.5

20

5

8.7

59

3

16

.0

18

.0

2.0

62

4

0.0

01

00

13

6

5.0

9

65

.09

7

5.5

0

24

59

.0

25

34

.5

0.2

67

7

8.4

45

8

8.7

13

5

18

.0

20

.0

2.3

37

0

.00

10

01

7

57

.84

5

7.8

4

83

.86

2

45

4.3

2

53

8.2

0

.29

63

8

.37

21

8

.66

84

2

0.0

2

2.0

2

.64

2

0.0

01

00

22

5

1.4

9

51

.49

9

2.2

3

24

49

.6

25

41

.8

0.3

24

7

8.2

99

4

8.6

24

1

22

.0

24

.0

2.9

82

0

.00

10

02

6

45

.92

4

5.9

3

10

0.5

9

24

44

.9

25

45

.5

0.3

53

0

8.2

27

7

8.5

80

6

24

.0

26

.0

3.3

60

0

.00

10

03

2

41

.03

4

1.0

3

10

8.9

5

24

40

.2

25

49

.1

0.3

81

0

8.1

56

9

8.5

37

9

26

.0

28

.0

3.7

78

0

.00

10

03

7

36

.73

3

6.7

3

11

7.3

1

24

35

.4

25

52

.7

0.4

08

8

8.0

87

0

8.4

95

9

28

.0

30

.0

4.2

41

0

.00

10

04

3

32

.93

3

2.9

3

12

5.6

6

24

30

.7

25

56

.4

0.4

36

5

8.0

18

1

8.4

54

6

30

.0

32

.0

4.7

53

0

.00

10

04

9

29

.57

2

9.5

7

13

4.0

2

24

25

.9

25

60

.0

0.4

64

0

7.9

50

0

8.4

14

0

32

.0

34

.0

5.3

18

0

.00

10

05

6

26

.60

2

6.6

0

14

2.3

8

24

21

.2

25

63

.6

0.4

91

3

7.8

82

8

8.3

74

0

34

.0

36

.0

5.9

40

0

.00

10

06

3

23

.97

2

3.9

7

15

0.7

4

24

16

.4

25

67

.2

0.5

18

4

7.8

16

4

8.3

34

8

36

.0

38

.0

6.6

24

0

.00

10

07

0

21

.63

2

1.6

3

15

9.0

6

24

11

.7

25

70

.8

0.5

45

3

7.7

50

9

8.2

96

2

38

.0

40

.0

7.3

75

0

.00

10

07

8

19

.54

5

19

.54

6

16

7.4

5

24

06

.9

25

74

.4

0.5

72

1

7.6

86

1

8.2

58

3

40

.0

42

.0

8.1

98

0

.00

10

08

6

17

.69

1

17

.69

2

17

5.8

1

24

02

.1

25

77

.9.

0.5

98

7

7.6

22

2

8.2

20

9

42

.0

44

.0

9.1

00

0

.00

10

09

4

16

.03

5

16

.03

6

18

4.1

7

23

97

.3

25

81

.5

0.6

25

2

7.5

59

0

8.1

84

2

44

.0

46

.0

10

.08

6

0.0

01

01

03

1

4.5

56

1

4.5

57

1

92

.53

2

39

2.5

2

58

5.1

0

.65

14

7

.49

66

8

.14

81

4

6.0

4

8.0

1

1.1

62

0

.00

10

11

2

13

.23

2

13

.23

3

20

0.8

9

23

87

.7

25

88

.6

0.6

77

6

7.4

35

0

8.1

12

5

48

.0

50

.0

12

.33

5

0.0

01

01

21

1

2.0

45

1

2.0

46

2

09

.26

2

38

2.9

2

59

2.2

0

.70

35

7

.37

41

8

.07

76

5

0.0

5

2.0

1

3.6

13

0

.00

10

13

1

10

.97

9

10

.98

0

21

7.6

2

23

78

.1

25

95

.7

0.7

29

3

7.3

13

8

8.0

43

2

52

.0

Page 4: Appendices - Springer LINK

Tab

le A

-l-l

S

atur

ated

Ste

am:

Tem

pera

ture

Tab

le (

51)

(Co

nti

nu

ed

)

54

.0

15

.00

2

0.0

01

01

40

1

0.0

21

1

0.0

22

2

25

.99

2

37

3.2

2

59

9.2

0

.75

50

7

.25

43

8

.00

93

5

4.0

5

6.0

1

6.5

11

0

.00

10

15

0

9.1

58

9

.15

9

23

4.3

5

23

68

.4

26

02

.7

0.7

80

4

7.1

95

5

7.9

75

9

56

.0

58

.0

18

.14

7

0.0

01

01

61

8

.38

0

8.3

81

2

42

.72

2

36

3.5

2

60

6.2

0

.80

58

7

.13

73

7

.94

31

5

8.0

60

.0

19

.92

0

0.0

01

01

71

7

.67

8

7.6

79

2

51

.09

2

35

8.6

2

60

9.7

0

.83

10

7

.07

98

7

.91

08

6

0.0

6

2.0

2

1.8

38

0

.00

10

18

2

7.0

43

7

.04

4

25

9.4

6

23

53

.7

26

13

.2

0.8

56

0

7.0

23

0

7.8

79

0

62

.0

64

.0

23

.91

2

0.0

01

01

93

6

.46

8

6.4

69

2

67

.84

2

34

8.8

2

61

6.6

0

.88

09

6

.96

67

7

.84

77

6

4.0

6

6.0

2

6.1

50

0

.00

10

20

5

5.9

47

5

.94

8

27

6.2

1

23

43

.9

26

10

.1

0.9

05

7

6.9

11

1

7.8

16

8

66

.0

68

.0

28

.56

3

0.0

01

02

17

5

.47

5

5.4

76

2

84

.59

2

33

8.9

2

62

3.6

0

.93

03

6

.85

61

7

.78

64

6

8.0

70

.0

31

.16

0

.00

10

28

8

5.0

45

5

.04

6

29

2.9

7

23

34

.0

26

26

.9

0.9

54

8

6.8

01

7

7.7

56

5

70

.0

?Z.O

3

3.9

6

0.0

01

02

41

4

.65

5

4.6

56

3

01

.36

2

32

9.0

2

63

0.3

0

.97

92

6

.74

78

7

.72

70

7

2.0

7

4.0

3

6.9

6

0.0

01

02

53

4

.29

9

4.3

00

3

09

.74

2

32

4.0

2

63

3.7

1

.00

34

6

.69

45

7

.69

79

7

4.0

7

6.0

4

0.1

0

0.0

01

02

66

3

.97

6

3.9

76

3

18

.13

2

31

8.9

2

63

7.1

1

.02

75

6

.64

18

7

.66

93

7

6.0

7

8.0

4

3.6

5

0.0

01

02

79

3

.67

9

3.6

80

3

26

.52

2

31

3.9

2

64

0.4

1

.05

14

6

.58

96

7

.64

10

7

8.0

80

.0

47

.36

0

.00

10

29

2

3.4

08

3

.40

9

33

4.9

2

23

08

.8

26

43

.8

1.0

75

3

6.5

38

0

7.6

13

2

80

.0

82

.0

51

.33

0

.00

10

30

5

3.1

61

3

.16

2

34

3.3

1

23

03

.8

26

47

.1

1.0

99

0

6.4

86

8

7.5

85

8

82

.0

84

.0

55

.57

0

.00

10

31

9

2.9

34

2

.93

5

35

1.7

1

22

98

.6

26

50

.4

1.1

22

5

6.4

36

2

7.5

58

8

84

.0

86

.0

60

.11

0

.00

10

33

3

2.7

26

2

.72

7

36

0.1

2

22

93

.5

26

53

.6

1.1

46

0

6.3

86

1

7.5

35

1

86

.0

88

.0

64

.95

0

.00

10

34

7

2.5

35

2

.53

6

36

8.5

3

22

88

.4

26

56

.9

1.1

69

3

6.3

36

5

7.5

05

8

88

.0

90

.0

70

.11

0

.00

10

36

1

2.3

60

3

2.3

61

3

37

6.9

4

22

83

.2

26

60

.1

1.1

92

5

6.2

87

3

7.4

79

9

90

.0

92

.0

75

.61

0

.00

10

37

6

2.1

99

2

2.2

00

2

38

5.3

6

22

78

.0

26

63

.4

1.2

15

6

6.2

38

7

7.4

54

3

92

.0

94

.0

81

.46

0

.00

10

39

1

2.0

50

9

2.0

51

9

39

3.7

8

22

72

.9

26

66

.6

1.2

38

6

6.1

90

5

7.4

29

1

94

.0

96

.0

87

.69

0

.00

10

40

6

1.9

14

3

1.9

15

3

40

2.2

0

22

67

.5

26

69

.7

1.2

61

5

6.1

42

7

7.4

04

2

96

.0

98

.0

94

.30

0

.00

10

42

1

1.7

88

3

1. 7

89

3

41

0.6

3

22

62

.2

26

72

.9

1.2

84

2

6.0

95

4

7.3

79

6

98

.0

10

0.0

1

01

.33

0

.00

10

43

7

1.6

72

0

1.6

73

0

41

9.0

6

22

56

.9

26

76

.0

1.3

06

9

6.0

48

5

7.3

55

4

10

0.0

1

05

.0

12

0.8

0

0.0

01

04

77

1

.41

82

1

.41

93

4

40

.17

2

24

3.6

2

68

3.7

1

.36

30

5

.93

31

7

.29

62

1

05

.0

11

0.0

1

43

.27

0

.00

10

51

9

1.2

08

9

1.2

09

9

46

1.3

2

22

30

.0

26

91

.3

1.4

18

5

5.8

20

3

7.2

38

8

11

0.0

1

15

.0

16

9.0

6

0.0

01

05

62

1

.03

52

1

.03

63

4

82

.50

2

21

6.2

2

59

8.7

1

.47

33

5

.70

99

7

.18

32

1

15

.0

12

0.0

1

98

.54

0

.00

10

60

6

0.8

90

5

0.8

91

5

50

3.7

2

22

02

.2

27

06

.0

1.5

27

6

5.6

01

7

7.1

29

3

12

0.0

12

5.0

2

32

.1

0.0

01

06

52

0

.76

92

0

.77

02

5

24

.99

2

18

8.0

2

71

3.0

1

.58

13

5

.49

57

7

.07

69

1

25

.0

13

0.0

2

70

.1

0.0

01

07

00

0

.66

71

0

.66

81

5

46

.31

2

17

3.6

2

71

9.9

1

.63

44

5

.39

17

7

.02

61

1

30

.0

13

4.0

3

13

.1

0.0

01

07

50

0

.58

07

0

.58

18

5

67

.68

2

15

8.9

2

72

6.6

1

.68

69

5

.28

97

6

.97

66

1

34

.0

14

0.0

3

61

.4

0.0

01

08

01

0

.50

74

0

.50

85

5

89

.10

2

14

4.0

2

73

3.1

1

.73

90

5

.18

94

6

.92

84

1

40

.0

14

5.0

4

15

.5

0.0

01

08

53

0

.44

49

0

.44

60

6

10

.59

2

12

8.7

2

73

9.3

1

.79

06

5

.09

10

6

.88

15

1

45

.0

15

0.0

4

76

.0

0.0

01

09

08

0

.39

14

0

.39

24

6

32

.15

2

11

3.2

2

74

5.4

1

.84

16

4

.99

41

6

.83

58

1

50

.0

15

5.0

5

43

.3

0.0

01

09

64

0

.34

53

0

.34

64

6

53

.77

2

09

7.4

2

75

1.2

1

.89

23

4

.89

89

6

.79

11

1

55

.0

16

0.0

6

18

.1

0.0

01

10

22

0

.30

57

0

.30

68

6

75

.47

2

08

1.3

2

75

6.7

1

.94

25

4

.80

50

6

.74

75

1

60

.0

16

5.0

7

00

.8

0.0

01

10

82

0

.27

13

0

.27

24

6

97

.25

2

06

4.8

2

76

2.0

1

.99

23

4

.71

26

6

.70

48

1

65

.0

17

0.0

7

92

.0

0.0

01

11

45

0

.24

14

0

.24

26

7

19

.12

2

04

7.9

2

76

7.1

2

.04

16

4

.62

14

6

.66

30

1

70

.0

* App

roxi

mat

e tr

iple

poi

nt.

Sour

ce:

Rep

rin

ted

wit

h pe

rmis

sion

fro

m A

SM

E.

Page 5: Appendices - Springer LINK

Tab

le A

-l-l

S

atu

rate

d S

team

: T

emp

erat

ure

Tab

le (

51)

(Co

nti

nu

ed

)

Spe

cifi

c V

olum

e, m

3/k

g

En

thal

py

, kJ

/kg

Ent

ropy

, kJ

/kg-

K

Tem

p

Abs

. P

ress

. S

at.

Sat

. S

at.

Sat

. S

at.

Sat

. T

emp

C

kP

a L

iq.

Eva

p.

Vap

or

Liq

uid

Eva

p.

Vap

or

Liq

uid

E

vap.

V

apor

C

T

p

Vf

Vfs

V

g h

f h

fg

hg

Sf

Sfg

S

g T

17

5.0

8

92

.4

0.0

01

12

09

0

.21

54

2

0.2

16

54

7

41

.07

2

03

0.7

2

77

1.8

2

.09

06

4

.53

14

6

.62

21

1

75

.0

18

0.0

1

00

2.7

0

.00

11

27

5

0.1

92

67

0

.19

38

0

76

3.1

2

20

13

.2

27

76

.3

2.1

39

3

4.4

42

6

6.5

81

9

18

0.0

1

85

.0

11

23

.3

0.0

01

13

44

0

.17

27

2

0.1

73

86

7

85

.26

1

99

5.2

2

78

0.4

2

.18

76

4

.35

48

6

.54

24

1

85

.0

19

0.0

1

25

5.1

0

.00

11

41

5

0.1

55

17

0

.15

63

2

80

7.5

2

19

76

.7

27

84

.3

2.2

35

6

4.2

68

0

6.5

03

6

19

0.0

1

95

.0

13

98

.7

0.0

01

14

89

0

.13

96

9

0.1

40

84

8

29

.88

1

95

7.9

2

78

7.8

2

.28

33

4

.18

21

6

.46

54

1

95

.0

20

0.0

1

55

4.9

0

.00

11

56

5

0.1

26

00

0

.12

71

6

85

2.3

7

19

38

.6

27

90

.9

2.3

30

7

4.0

97

1

6.4

27

8

20

0.0

2

05

.0

17

24

.3

0.0

01

16

44

0

.11

38

6

0.1

15

03

8

74

.99

1

91

8.8

2

79

3.8

2

.37

78

4

.01

28

6

.39

06

2

05

.0

21

0.0

1

90

7.7

0

.00

11

72

6

0.1

03

07

0

.10

42

4

89

7.7

3

18

98

.5

27

96

.2

2.4

24

7

3.9

29

3

6.3

53

9

21

0.0

2

15

.0

21

06

.0

0.0

01

18

11

0

.09

34

4

0.0

94

63

9

20

.63

1

87

7.6

2

79

8.3

2

.47

13

3

.84

63

6

.31

76

2

15

.0

22

0.0

2

31

9.8

0

.00

11

90

0

0.0

84

85

0

.08

60

4

94

3.6

7

18

56

.2

27

99

.9

2.5

17

8

3.7

63

9

6.2

81

7

22

0.0

22

5.0

2

55

0.

0.0

01

19

92

0

.07

71

5

0.0

78

35

.9

66

.88

1

83

4.3

2

80

1.2

2

.56

41

3

.68

20

6

.24

61

2

25

.0

23

0.0

2

79

8.

0.0

01

20

87

0

.07

02

4

0.0

71

45

9

90

.27

1

81

1.7

2

80

2.0

2

.61

02

3

.60

06

6

.21

07

2

30

.0

23

5.0

3

06

3.

0.0

01

21

87

0

.06

40

3

0.0

65

25

1

01

3.8

3

17

88

.5

28

02

.3

2.6

56

1

3.5

19

4

6.1

75

6

23

5.0

2

40

.0

33

48

. 0

.00

12

29

1

0.0

58

43

0

.05

96

5

10

37

.60

1

76

4.6

2

80

2.2

2

.70

20

3

.43

86

6

.14

06

2

40

.0

24

5.0

3

65

2.

0.0

01

23

99

0

.05

33

7

0.0

54

61

1

06

1.5

8

17

40

.0

28

01

.6

2.7

47

8

3.3

57

9

6.1

05

7

24

5.0

25

0.0

3

97

8.

0.0

01

25

13

0

.04

87

9

0.0

50

04

1

08

5.7

8

17

14

.7

28

00

.4

2.7

93

5

3.2

77

3

6.0

70

8

25

0.0

2

55

.0

43

25

. 0

.00

12

63

2

0.0

44

63

0

.04

59

0

11

10

.23

1

68

8.5

2

79

8.7

2

.83

92

3

.19

68

6

.03

59

2

55

.0

26

0.0

4

69

4.

0.0

01

27

56

0

.04

08

6

0.0

42

13

1

13

4.9

4

16

61

.5

27

96

.4

2.8

84

8

3.1

16

1

6.0

01

0

26

0.0

2

65

.0

50

88

. 0

.00

12

88

7

0.0

37

42

0

.03

87

1

11

59

.93

1

63

3.5

2

79

3.5

2

.93

06

3

.03

53

5

.96

58

2

65

.0

27

0.0

5

50

6.

0.0

01

30

25

0

.03

42

9

0.0

35

59

1

18

5.2

3

16

04

.6

27

89

.9

2.9

76

3

2.9

54

1

5.9

30

4

27

0.0

27

5.0

5

95

0.

0.0

01

31

70

0

.03

14

2

0.0

32

74

1

21

0.8

6

15

74

.7

27

85

.5

3.0

22

2

2.8

72

5

5.8

94

7

27

5.0

2

80

.0

64

20

. 0

.00

13

32

4

0.0

28

79

0

.03

01

3

12

36

.84

1

54

3.6

2

78

0.4

3

.06

83

2

.79

03

5

.85

86

2

80

.0

28

5.0

6

91

9.

0.0

01

34

87

0

.02

63

8

0.0

27

73

1

26

3.2

1

15

11

.3

27

74

.5

3.1

14

6

2.7

07

4

5.8

22

0

28

5.0

2

90

.0

74

46

. 0

.00

13

65

9

0.0

24

17

0

.02

55

4

12

90

.01

1

47

7.6

2

76

7.6

3

.16

11

2

.62

37

5

.78

48

2

90

.0

29

5.0

8

00

4.

0.0

01

38

44

0

.02

21

3

0.0

23

51

1

31

7.2

7

14

42

.6

27

59

.8

3.2

07

9

2.5

38

9

5.7

46

9

29

5.0

30

0.0

8

59

3.

0.0

01

40

41

0

.02

02

45

0

.02

16

49

1

34

5.0

5

14

06

.0

27

51

.0

3.2

55

2

2.4

52

9

5.7

08

1

30

0.0

3

05

.0

92

14

. 0

.00

14

25

2

0.0

18

50

2

0.0

19

92

7

13

73

.40

1

36

7.7

2

74

1.1

3

.30

29

2

.36

56

5

.66

85

3

05

.0

31

0.0

9

87

0.

0.0

01

44

80

0

.01

68

86

0

.01

83

34

1

40

2.3

9

13

27

.6

27

30

.0

3.3

51

2

2.2

76

6

5.6

27

8

31

0.0

3

15

.0

10

56

1.

0.0

01

47

26

0

.01

53

83

0

.01

68

56

1

43

2.0

9

12

85

.5

27

17

.6

3.4

00

2

2.1

85

6

5.5

85

8

31

5.0

3

20

.0

11

28

9.

0.0

01

49

95

0

.01

39

80

0

.01

54

80

1

46

2.6

0

12

41

.1

27

03

.7

3.4

50

0

2.0

92

3

5.5

42

3

32

0.0

32

5.0

1

20

56

. 0

.00

15

28

9

0.0

12

66

6

0.0

14

19

5

14

94

.03

1

19

4.0

2

68

8.0

3

.50

08

1

.99

61

5

.49

69

3

25

.0

33

0.0

1

28

63

. 0

.00

15

61

5

0.0

11

42

8

0.0

12

98

9

15

26

.52

1

14

3.6

2

67

0.2

3

.55

28

1

.89

62

5

.44

90

3

30

.0

33

5.0

1

37

12

. 0

.00

15

97

8

0.0

10

25

6

0.0

11

85

4

15

60

.25

1

08

9.5

2

64

9.7

3

.69

63

1

.79

16

5

.39

79

3

35

.0

Page 6: Appendices - Springer LINK

Tab

le A

-l-l

S

atur

ated

Ste

am

: T

em

pe

ratu

re T

ab

le (

51)

(Co

nti

nu

ed

)

34

0.0

1

46

05

. 0

.00

16

38

7

0.0

09

14

2

0.0

10

78

0

15

95

.47

1

03

0.7

2

62

6.2

3

.66

16

1

.68

11

5

.34

27

3

40

.0

34

5.0

1

55

45

. 0

.00

16

85

8

0.0

08

07

7

0.0

09

76

3

16

32

.52

9

66

.4

25

98

.9

3.7

19

3

1.5

63

6

5.2

82

8

34

5.0

35

0.0

1

65

35

. 0

.00

17

41

1

0.0

07

05

8

0.0

08

79

9

16

71

.94

8

95

.7

25

67

.7

3.7

80

0

1.4

37

6

5.2

17

7

35

0.0

3

55

.0

17

57

7.

0.0

01

80

85

0

.00

60

51

0

.00

78

59

1

71

6.6

3

81

3.8

2

53

0.4

3

.84

89

1

.29

53

5

.14

42

3

55

.0

36

0.0

1

86

75

. 0

.00

18

95

9

0.0

05

04

4

0.0

06

94

0

17

64

.17

7

21

.3

24

85

.4

3.9

21

0

1.1

39

0

5.0

60

0

36

0.0

3

65

.0

19

83

3.

0.0

02

01

60

0

.00

39

96

0

.00

60

12

1

81

7.9

6

61

0.0

2

42

8.0

4

.00

21

0

.95

58

4

.94

79

3

65

.0

37

0.0

2

10

54

. 0

.00

22

13

6

0.0

02

75

9

0.0

04

97

3

18

90

.21

4

52

.6

23

42

.8

4.1

10

8

0.7

03

6

4.8

14

4

37

0.0

37

1.0

2

13

06

. 0

.00

22

77

8

0.0

02

44

6

0.0

04

72

3

19

10

.50

4

07

.4

23

17

.9

4.1

41

4

0.6

32

4

4.7

73

8

37

1.0

3

72

.0

21

56

2.

0.0

02

36

36

0

.00

20

75

0

.00

44

39

1

93

5.5

7

35

1.4

2

28

7.0

4

.17

94

0

.54

46

4

.72

40

3

72

.0

37

3.0

2

18

20

. 0

.00

24

96

3

0.0

01

58

8

0.0

04

08

4

19

70

.50

2

73

.5

22

44

.0

4.2:

326

0.4

23

3

4.6

55

9

37

3.0

3

74

.0

2208

.1.

0.0

02

84

27

0

.00

06

23

0

.00

34

66

2

04

6.7

2

10

9.5

2

15

6.2

4

.34

93

0

.16

92

4

.51

85

3

74

.0

37

4.1

5

22

12

0.t

0

.00

31

7

0.0

0

.00

31

7

21

07

.37

0

.0

21

07

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4.4

·!2

9

0.0

4

.44

29

3

74

.15

t A

ppro

xim

ate

crit

ical

poi

nt.

Page 7: Appendices - Springer LINK

Tab

le A

-1-2

S

atu

rate

d S

team

: P

ress

ure

Tab

le (5

1)

Abs

. S

peci

fic

Vo

lum

e, m

' /k

g

Ent

halp

y. k

J/kg

E

ntro

py,

kJ/k

g-K

E

nerg

y, k

J / k

g T

emp

. P

ress

S

at.

Sat

. S

at.

Sat

. S

at.

Sat

. S

at.

Sat

. T

emp

. e

kPa

Liq

uid

E

vap.

V

apo

r L

iqui

d E

vap.

V

apo

r L

iqu

id

Eva

p.

Vap

or

Liq

uid

V

apo

r e

T

p V

f V

fg

V -"

h,

h,~

hg

s, S'

.I.!

S.l'.

lI,

u~

T

6.9

83

1

.0

0.0

01

00

01

1

29

.21

1

29

.21

2

9.3

4

24

85

.0

25

14

,4

0.1

06

0

8.8

70

6

8.9

76

7

29

.33

2

38

5.2

6

.98

3

8.3

80

1.

1 0

.00

10

00

1

11

8.0

4

11

8.0

4

35

.20

2

48

1.7

2

51

6.9

0

.12

69

8

.81

49

8

.94

18

3

5.2

0

23

87

.1

8.3

80

9

.66

8

1.2

0

.00

10

00

2

10

8.7

0

10

8.7

0

40

.60

2

47

8.7

2

51

9.3

0

.14

61

8

.76

40

8

.91

01

4

0.6

0

23

88

.9

9.6

68

1

0.8

66

1

.3

0.0

01

00

03

1

00

.76

1

00

.76

4

5.6

2

24

75

.9

25

21

.5

0.1

63

8

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6

Page 8: Appendices - Springer LINK

Tab

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-1-2

S

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Ste

am:

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4

Sour

ce:

Rep

rin

ted

wit

h pe

rmis

sion

fro

m A

SM

E.

Page 9: Appendices - Springer LINK

Tab

le A

-1-2

S

atu

rate

d S

team

: P

ress

ure

Tab

le (

51)

(Co

nti

nu

ed

)

Abs

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ume.

m"/

kg

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24

.65

Page 10: Appendices - Springer LINK

Tab

le A

-1-2

S

atur

ated

Ste

am:

Pre

ssur

e T

able

(51

) (C

on

tin

ue

d)

33

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3

13

00

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01

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0

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0

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53

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56

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1

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51

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50

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30

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36

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40

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10

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4

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49

5

15

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2

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56

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Page 11: Appendices - Springer LINK

720 Appendix A-l

Table A-1-3 Superheated Steam (51)

Abs. Press. kPa Sat. Sat. Temperature-C

(Sat. Temp. C) Liquid Vapor 40. 60. 80.

v 0.0010 129.2 144.47 153.71 162.95 1.0 h 29.34 2514.4 2575.9 2613.3 2650.9

(6.983) s 0.1060 9.9767 9.1842 9.3001 9.4096

v 0.0010 67.01 72.211 76.837 81.459 2.0 h 73.46 2533.6 2575.6 2613.1 2650.7

(17.51) s 0.2607 8.7246 8.8637 8.9797 9.0894

v 0.0010 45.67 48.124 51.211 54.296 3.0 h 101.00 2545.6 2575.4 2612.9 2650.6

(24.10) s 0.3544 8.5785 8.6760 8.7922 8.9019

v 0.0010 34.80 36.081 38.398 40.714 4.0 h 121.41 2554.5 2575.2 2612.7 2650.4

(28.98) s 0.4225 8.4755 8.5426 8.6589 8.7688

v 0.0010 28.19 28.854 30.711 32.565 5.0 h 137.77 2561.6 2574.9 2612.6 2650.3

(32.90) s 0.4763 8.3960 8.4390 8.5555 8.6655

v 0.0010 23.74 24.037 25.586 27.132 6.0 h 151.50 2567.5 2574.7 2612.4 2650.1

(36.18) s 0.5209 8.3312 8.3543 8.4709 8.5810

v 0.0010 18.105 19.179 20.341 8.0 h 173.86 2577.1 2612.0 2649.8

(41.53) s 0.5925 8.2296 8.3372 8.4476

v 0.0010 14.675 15.336 16.266 10.0 h 191.85 2584.8 2611.6 2649.5

(45.83) s 0.6493 8.1511 8.2334 8.3439

v 0.0010 10.023 10.210 10.834 15.0 h 225.97 2599.2 2610.6 2648.8

(54.00) s 0.7549 8.0093 8.0440 8.1551

80. 100. 120.

v 0.0010 7.650 I 8.1172 8.5847 9.0508 20.0 h 251.45 2609.9 2648.0 2686.3 2724.6

(60.09) s 0.8321 7.9094 8.0206 8.1261 8.2262

v 0.0010 5.229 5.4007 5.7144 6.0267 30.0 h 239.30 2625.4 2646.5 2685.1 2723.6

(69.12) s 0.9441 7.7695 7.8300 7.9363 8.0370

v 0.0010 3.993 4.0424 4.2792 4.5146 40.0 h 317.65 2636.9 2644.9 2683.8 2722.6

(75.89) s 1.0261 7.6709 7.6937 7.8009 7.9023

v 0.0010 3.240 3.4181 3.6074 50.0 h 340.56 2646.0 2682.6 2721.6

(81.35) s 1.0912 7.5947 7.6953 7.7972

v = specific volume, m3/kg h = enthalpy, kJ/kg s = entropy, kJ/kg' K Source: Reprinted with permission from ASME.

100.

172.19 2688.6 9.5136

86.080 2688.5 9.1934

57.378 2688.4 9.0060

43.027 2688.3 8.8730

34.417 2688.1 8.7698

28.676 2688.0 8.6854

21.501 2687.8 8.5521

17.195 2687.5 8.4486

11.455 2686.9 8.2601

140.

9.516 2763.1 8.3215

6.3379 2762.3 8.1329

4.7489 2761.4 7.9985

3.7955 2760.6 7.8940

120. 140. 160.

181.42 190.66 199.89 2726.5 2764.6 2802.9 9.6125 9.7070 9.7975

90.700 95.319 99.936 2726.4 2764.5 2802.8 9.2924 9.3870 9.4775

60.460 63.540 66.619 2726.3 2764.5 2802.8 9.1051 9.1997 9.2902

45.339 47.650 49.961 2726.2 2764.4 2802.7 8.9721 9.0668 9.1573

36.267 38.117 39.966 2726.1 2764.3 2802.6 8.8690 8.9636 9.0542

30.219 31.761 33.302 2726.0 2764.2 2802.6 8.7846 8.8793 8.9700

22.659 23.816 24.973 2725.8 2764.1 2802.4 8.6515 8.7463 8.8370

18.123 19.050 19.975 2725.6 2763.9 2802.3 8.5481 8.6430 8.7338

12.075 12.694 13.312 2725.1 2763.5 2802.0 8.3599 8.4551 8.5460

160. 180. 200.

9.980 10.444 10.907 2801.6 2840.3 2879.2 8.4127 8.5000 8.5839

6.6483 6.9582 7.2675 2801.0 2839.8 2878.7 8.2243 8.3119 8.3960

4.9825 5.2154 5.4478 2800.3 2839.2 2878.2 8.0903 8.1782 8.2625

3.9829 4.1697 4.3560 2799.6 2838.6 2877.7 7.9861 8.0742 8.1587

Page 12: Appendices - Springer LINK

Superheated Steam (51) 721

Table A-1-3 Superheated Steam (51) (Continued)

Abs. Press kPa Tern perature-C

(Sat. Temp. C) 180. 200. 300. 400. 500. 600. 700.

v 209.12 218.35 264.51 310.66 356.81 402.97 449.12 1.0 h 2841.4 2880.1 3076.8 3279.7 3489.2 3705.6 3928.9

(6.983) s 9.8843 9.9679 10.3450 10.6711 10.9612 11.2243 11.4663

v 104.55 109.17 132.25 155.33 178.41 201.48 224.56 2.0 h 2841.3 2880.0 3076.8 3279.7 3489.2 3705.6 3928.8

(17.51) s 9.5643 9.6479 10.0251 10.3512 10.6413 10.9044 11.1464

v 69.698 72.777 88.165 103.55 118.94 134.32 149.70 3.0 h 2841.3 2880.0 3076.8 3279.7 3489.2 3705.6 3928.8

(24.10) s 9.3771 9.4607 9.8379 10.1641 10.4541 10.7173 10.9593

v 52.270 54.580 66.122 77.662 89.201 100.74 112.28 4.0 h 2841.2 2879.9 3076.8 3279.7 3489.2 3705.6 3928.8

(28.98) s 9.2443 9.3279 9.7051 10.0313 10.3214 10.5845 10.8265

v 41.814 43.661 52.897 62.129 71.360 80.592 89.822 5.0 h 2841.2 2879.9 3076.7 3279.7 3489.2 3705.6 3928.8

(32.90) s 9.1412 9.2248 9.6021 9.9283 10.2184 10.4815 10.7235

v 34.843 36.383 44.079 51.773 59.467 67.159 74.852 6.0 h 2841.1 2879.8 3076.7 3279.6 3489.2 3705.6 3928.8

(36.18) s 9.0569 9.1406 9.5179 9.8441 10.1342 10.3973 10.6394

v 26.129 27.284 33.058 38.829 44.599 50.369 56.138 8.0 h 2841.0 2879.7 3076.7 3279.6 3489.1 3705.5 3928.8

(41.53) s 8.9240 9.0077 9.3851 9.7113 10.0014 10.2646 10.5066

v 20.900 21.825 26.445 31.062 35.679 40.295 44.910 10.0 h 2840.9 2879.6 3076.6 3279.6 3489.1 3705.5 3928.8

(45.83) s 8.8208 8.9045 9.2820 9.6083 9.8984 10.1616 10.4036

v 13.929 14.546 17.628 20.707 23.785 26.863 29.940 15.0 h 2840.6 2879.4 3076.5 3279.5 3489.1 3705.5 3928.8

(54.00) s 8.6332 8.7170 9.0948 9.4211 9.7112 9.9744 10.2164

240. 280. 300. 400. 500: 600. 700.

v 11.832 12.295 13.219 15.529 17.838 20.146 22.455 20.0 h 2957.4 2996.9 3076.4 3279.4 3489.0 3705.4 3928.7

(60.09) s 8.7426 8.8180 8.9618 9.2882 9.5784 9.8416 10.0836

v 7.8854 8.5024 8.8108 10.351 11.891 13.430 14.969 30.0 h 2957.1 3036.2 3076.1 3279.3 3488.9 3705.4 3928.7

(69.12) s 8.5550 8.7035 8.7744 9.1010 9.3912 9.6544 9.8965

v 5.9118 6.3751 6.6065 7.7625 8.9176 10.072 11.227 40.0 h 2956.7 3036.0 3075.9 3279.1 3488.8 3705.3 3928.6

(75.89) s 8.4217 8.5704 8.6413 8.9680 9.2583 9.5216 9.7636

v 4.7277 5.0986 5.2839 6.2091 7.1335 8.0574 8.9810 50.0 h 2956.4 3035.7 3075.7 3279.0 3488.7 3705.2 3928.6

(81.35) s 8.3182 8.4671 8.5380 8.8649 9.1552 9.4185 9.6606

Page 13: Appendices - Springer LINK

722 Appendix A-1

Table A-1-3 Superheated Steam (51) (Continued)

Abs. Press. kPa

(Sat. Temp. C)

I'

60.0 h (85.95) s

I'

80.0 h (93.51) s

I'

100.0 h (99.63) s

I'

150.0 h (111.4) s

I'

200.0 h (120.2) s

I'

300.0 h (133.5) s

I'

400.0 h (143.6) s

I'

500.0 h (151.8) s

v 600.0 h

(158.8) s

v 800.0 h

(170.4) s

v 1000.0 h (179.9) s

v 1500.0 h (198.3) v

v 2000.0 h (212.4) s

Sat. Sat. Liquid Vapor

0.0010 2.732 359.93 265:J.6 1.1454 7.5327

0.0010 2.0870 391.72 2665.8 1.2:nO 7.4352

0.0010 1.6937 417.51 2675.4 1.3027 7.3598

0.0011 1.1590 467.13 2693.4 1.4336 7.2234

0.0011 0.8854 504.70 2706.3 1.5301 7.1268

0.0011 0.6056 561.4 2724.7

1.6716 6.9909

0.0011 0.4622 604.7 2737.6

1.7764 6.8943

0.0011 0.3747 640.1 2747.5

1.8604 6.8192

0.0011 0.3155 670.4 2755.5

1.9308 6.7575

0.0011 0.2403 720.9 2767.5

2.0457 6.6596

0.0011 0.1943 762.6 2776.3

2.1382 6.5828

0.0012 0.1317 844.7 2789.9

2.3145 6.4406

0.0012 0.09954 908.6 2797.2

2.4469 6.3367

100.

2.8440 2681.3 7.6085

2.1262 2678.8 7.4 703

1.6955 2676.2 7.3618

200.

0.4250 2855.1 7.0592

0.3520 2849.7 6.9662

0.2608 2838.6 6.8148

0.2059 2826.8 6.6922

0.1324 2794.7 6.4508

Temperature-C 120. 140. 160.

3.0025 3.1599 2720.6 2759.8 7.7111 7.8083

2.2464 2.3654 2718.6 2758.1 7.5742 7.6723

1.7927 1.8886 2716.5 2756.4 7.4670 7.5662

1.1876 1.2529 2711.2 2752.2 7.2693 7.3709

240.

0.4647 2940.1 7.2317

0.3857 2936.4 7.1419

0.2869 2928.6 6.9976

0.2276 2920.6 6.8825

0.1483 2899.2 6.6630

0.1084 2875.0 6.4943

0.9349 2747.8 7.2298

0.6167 2738.8 7.0254

280.

0.4841 2981.9 7.3115

0.4021 2978.7 7.2228

0.2995 2972.1 7.0807

0.2379 2965.2 6.9680

0.1556 2947.3 6.7550

0.1144 2928.1 6.5941

300.

0.5226 3064.8 7.4614

0.4344 3062.3 7.3740

0.3241 3057.3 7.2348

0.2580 3052.1 7.1251

0.1697 3038.9 6.9207

0.1255 3025.0 6.7696

3.3165 2798.9 7.9008

2.4836 2797.5 7.7655

1.9838 2796.2 7.6601

1.3173 2792.7 7.4667

0.9840 2789.1 7.3275

0.6506 2781.8 7.1271

0.4837 2774.2 6.9805

340.

0.5606 3147.4 7.6008

0.4663 3145.4 7.5143

0.3483 3141.4 7.3767

0.2776 3137.4 7.2689

0.1832 3127.0 7.0693

0.1360 3116.3 6.9235

180.

3.4726 2838.1 7.9891

2.6011 2836.9 7.8544

2.0783 2835.8 7.7495

1.3811 2832.9 7.5574

1.0325 2830.0 7.4196

0.6837 2824.0 7.2222

0.5093 2817.8 7.0788

380.

0.5984 3230.4 7.7319

0.4979 3228.7 7.6459

0.3723 3225.4 7.5094

0.2969 3222.0 7.4027

0.1964 3213.5 7.2060

0.1461 3204.9 7.0635

200.

3.6281 2877.3 8.0738

2.7183 2876.3 7.9395

2.1723 2875.4 7.8349

1.4444 2872.9 7.6439

1.0804 2870.5 7.5072

0.7164 2865.5 7.3119

0.5343 2860.4 7.1708

400.

0.6172 3272.1 7.7948

0.5136 3270.6 7.7090

0.3842 3267.5 7.5729

0.3065 3264.4 7.4665

0.2029 3256.6 7.2709

0.1511 3248.7 7.1296

Page 14: Appendices - Springer LINK

Superheated Steam (51) 723

Table A-1-3 Superheated Steam (51) (Continued)

Abs. Press. Temperature-C kPa

(Sal. Temp, C) 240. 280. :HJO. 400. 500. 600. 700.

v a.9:383 4.2477 4.4022 5.1736 5;9441 6.7141 (.4839 60.0 h 2956.0 3035.4 3075.4 3278.8 3488.6 3705.1 3928.5

(85.95) s 8.2336 8.3826 8.4536 8.7806 9.0710 9.3343 9.5764

v 2.9515 :U840 3.3000 3.8792 4.4574 5.0351 5.6126 80.0 h 2955.3 3034.9 3075.0 3278.5 3488.4 3705.0 3928.4

(93.51) S 8.0998 8.2491 8.3202 8.6475 8.9380 9.2014 9.4436

v 2.3595 2.5458 2.6387 3.1025 3.5653 4.0277 4.4898 100.0 h 2954.6 3034.4 3074.5 3278.2 3488.1 3704.8 3928.2

(99.63) s 7.9958 8.1454 8.2166 8.5442 8.8348 9.0982 9.3405

v 1.5700 1.6948 1.7570 2.0669 2.3759 2.6845 2.9927 150.0 h 2952.9 3033.0 3073.3 3277.5 3487.6 3704.4 3927.9

(111.4) s 7.8061 7.9565 8.0280 8.3562 8.6472 8.9108 9.1531

v 1.1753 1.2693 1.3162 1.5492 1. 7812 2.0129 2.2442 200.0 h 2951.1 3031. 7 3072.1 3276.7 3487.0 3704.0 3927.6

(120.2) s 7.6707 7.8219 7.8937 8.2226 8.5139 8.7776 9.0201

v 0.7805 0.8438 0.8753 1.0314 1.1865 1.3412 1.4957 300.0 h 2947.5 3028.9 3069.7 3275.2 3486.0 3703.2 3927.0

(133.5) s 7.4783 7.6311 7.7034 8.0338 8.3257 8.5898 8.8325

v 0.5831 0.6311 0.6549 0.7725 0.8892 1.0054 1.1214 400.0 h 2943.9 3026.2 3067.2 3273.6 3484.9 3702.3 3926.4

(143.6) s 7.3402 7.4947 7.5675 7.8994 8.1919 8,4563 8.6992

440. 480. 500. 600. 650. 700. 800.

v 0.6547 0.6921 0.7108 0.8039 0.8504 0.8968 0.9896 500.0 h 3356.1 3441.0 3483.8 3701.5 3812.8 3925.8 4156.4

(151.8) s 7.9160 8.0318 8.0879 8.3526 8.4766 8.5957 8.8213

v 0.5450 0.5762 0.5918 0.6696 0.7084 0.7471 0.8245 600.0 h 3354.8 3439.8 3482.7 3700.7 3812.1 3925.1 4155.9

(158.8) s 7.8305 7.9465 8.0027 8.2678 8.3919 8.5111 8.7368

v 0.4078 0.4314 0.4432 0.5017 0.5309 0.5600 0.6181 800.0 h 3352.1 3437.5 3480.5 3699.1 3810.7 3923.9 4155.0

(170.4) s 7.6950 7.8115 7.8678 8.1336 8.2579 8.3773 8.6033

v 0.3256 0.3445 0.3540 0.4010 0.4244 0.4477 0.4943 1000.0 h 3349.5 3435.1 3478.3 3697.4 3809.3 3922.7 4154.1 (179.9) s 7.5893 7.7062 7.7627 8.0292 8.1537 8.2734 8.4997

v 0.2158 0.2287 0.2350 0.2667 0.2824 0.2980 0.3292 1500.0 h 3342.8 3429.3 3472.8 3693.3 3805.7 3919.6 4151.7 (198.3) s 7.3953 7.5133 7.5703 7.8385 7.9636 8.0838 8.3108

v 0.1610 0.1707 0.1756 0.1995 0.2114 0.2232 0.2467 2000.0 h 3336.0 3423.4 3467.3 3689.2 3802.1 3916.5 4149.4 (212.4) s 7.2555 7.3748 7.4323 7.7022 7.8279 7.9485 8.1763

Page 15: Appendices - Springer LINK

724 Appendix A-1

Table A-1-3 Superheated Steam (51) (Continued)

Abs. Press. kPa

(Sat. Temp. C)

v 3000.0 h (233.8) s

v 4000.0 h (250.3) s

v 5000.0 h (263.9) s

v 6000.0 h (275.5) s

v 8000.0 h (295.0) s

v 10000.0 h

(311.0) s

v 15000.0 h

(342.1) s

v 20000.0 h

(365.7) s

v 30000.0 h

s

v 40000.0 h

s

v 50000.0 h

s

v 60000.0 h

s

v 80000.0 h

s

v 100000.0 h

s

Sat. Sat. Liquid Vapor

0.0012 0.0666 1008.4 2802.3 2.6455 6.1837

0.0013 0.0498 1087.4 2800.3 2.7965 6.0685

0.0013 0.03943 1154.5 2794.2 2.9206 5.9735

0.0013 0.0324 1213.7 2785.0 3.0273 5.8908

0.0014 0.0235 1317.1 2759.9 3.2076 5.7471

0.0015 0.01804 1408.8 2727.7 3.3605 5.6198

0.0017 0.0134 1611.0 2615.0 3.6859 5.3178

0.0020 0.0059 1826.5 2418.4 4.0149 4.9412

Temperature-C 240. 280. 300. 340. 380.

0.06816 0.07712 0.08166 0.08871 0.09584 2822.9 2942.0 2995.1 3093.9 3187.0 6.2241 6.4479 6.5422 6.7088 6.8561

0.05544 0.05883 0.06499 0.07066 2902.0 2962.0 3069.8 3168.4 6.2576 6.3642 6.5461 6.7019

0.04222 0.04530 0.05070 0.05551 2856.9 2925.5 3044.1 3148.8 6.0886 6.2105 6.4106 6.5762

0.03317 0.03614 0.04111 0.04539 2804.9 2885.0 3016.5 3128.3 5.9270 6.0692 6.2913 6.4680

0.02426 0.02896 0.03265 2786.8 2955.3 3084.2 5.7942 6.0790 6.2828

320. 360. 380. 400. 440. 480.

0.01926 0.02331 0.02493 0.02641 0.02911 0.03158 2783.5 2964.8 3035.7 3099.9 3216.2 3323.2 5.7145 6.0110 6.1213 6.2182 6.3861 6.5321

0.01256 0.01428 0.01566 0.01794 0.01989 2770.8 2887.7 2979.1 3126.9 3252.4 5.5677 5.7497 5.8876 6.1010 6.2724

0.008246 0.009947 0.01224 0.01399 2660.2 2820.5 3023.7 3174.4 5.3165 5.5585 5.8523 6.0581

0.001874 0.002831 0.006227 0.007985 1837.7 2161.8 2754.0 2993.9 4.0021 4.4896 5.3499 5.6779

0.001682 0.001909 0.003200 0.004941 1776.4 1934.1 2399.4 2779.8 3.8814 4.1190 4.7893 5.3097

0.001589 0.001729 0.002269 0.003308 1746.8 1877.7 2199.7 2564.9 3.8110 4.0083 4.4723 4.9709

0.001528 0.001632 0.001962 0.002565 1728.4 1847.3 2113.5 2418.8 3.7589 3.9383 4.3221 4.7385

0.001445 0.001518 0.001710 0.001999 1707.0 1814.2 2036.6 2272.8 3.6807 3.8425 4.1633 4.4855

0.001390 0.001446 0.001587 0.001777 1696.3 1797.6 2000.3 2207.7 3.6211 3.7738 4.0664 4.3492

400.

0.09931 3232.5 6.9246

0.07338 3215.7 6.7733

0.05779 3198.3 6.6508

0.04738 3180.1 6.5462

0.03431 3141.6 6.3694

500.

0.03276 3374.6 6.5994

0.02080 3310.6 6.3487

0.01477 3241.1 6.1456

0.008681 3085.0 5.7972

0.005616 2906.8 5.4762

0.003882 2723.0 5.1782

0.002952 2570.6 4.9374

0.002188 2397.4 4.6488

0.001893 2316.1 4.4913

Page 16: Appendices - Springer LINK

Superheated Steam (51) 725

Table A-1-3 Superheated Steam (51) (Continued)

Abs. Press. kPa Temperature-C

(Sat. Temp, C) 440. 480. 500. 600. 650. 700. 800.

v 0.1061 0.1128 0.1161 0.1323 0.1404 0.1483 0.1641 3000.0 h 3322.3 3411.6 3456.2 3681.0 3795.0 3910.3 4144.7 (233.8) s 7.0543 7.1760 7.2345 7.5079 7.6349 7.7564 7.9857

v 0.07866 0.08381 0.08634 0.09876 0.1049 0.1109 0.1229 4000.0 h 3308.3 3399.6 3445.0 3672.8 3787.9 3904.1 4140.0 (250.3) s 6.9069 7.0314 7.0909 7.3680 7.4961 7.6187 7.8495

v 0.06218 0.06642 0.06849 0.07862 0.08356 0.08845 0.09809 5000.0 h 3294.0 3387.4 3433.7 3664.5 3780.7 3897.9 4135.3 (263.9) s 6.7890 6.9164 6.9770 7.2578 7.3872 7.5108 7.7431

v 0.05118 0.05482 0.05659 0.06518 0.06936 0.07348 0.08159 6000.0 h 3279.3 3375.0 3422.2 3656.2 3773.5 3891.7 4130.7 (275.5) s 6.6893 6.8199 6.8818 7.1664 7.2971 7.4217 7.6554

v 0.03740 0.04030 0.04170 0.04839 0.05161 0.05477 0.06096 8000.0 h 3248.7 3349.6 3398.8 3639.5 3759.2 3879.2 4121.3 (295.0) s 6.5240 6.6617 6.7262 7.0191 7.1523 7.2790 7.5158

540. 580. 600. 650. 700. 750. 800.

v 0.03504 0.03724 0.03832 0.04096 0.04355 0.04608 0.04858 10000.0 h 3475.1 3573.7 3622.7 3744.7 3866.8 3989.1 4112.0

(311.0) s 6.7261 6.8446 6.9013 7.0373 7.1660 7.2886 7.4058

v 0.02250 0.02411 0.02488 0.02677 0.02859 0.03036 0.03209 15000.0 h 3421.4 3527.7 3579.8 3708.3 3835.4 3962.1 4088.6

(342.1) s 6.4885 6.6160 6.6764 6.8195 6.9536 7.0806 7.2013

v 0.01621 0.01753 0.01816 0.01967 0.02111 0.02250 0.02385 20000.0 h 3364.7 3479.9 3535.5 3671.1 3803.8 3935.0 4065.3

(365.7) s 6.3015 6.4398 6.5043 6.6554 6.7953 6.9267 7.0511

v 0.009890 0.01095 0.01144 0.01258 0.01365 0.01465 0.01562 30000.0 h 3241.7 3378.9 3443.0 3595.0 3739.7 3880.3 4018.5

s 5.9949 6.1597 6.2340 6.4033 6.5560 6.6970 6.8288

v 0.006735 0.007667 0.008088 0.009053 0.009930 0.01075 0.01152 40000.0 h 3108.0 3272.4 3346.4 3517.0 3674.8 3825.5 3971.7

s 5.7302 5.9276 6.0135 6.2035 6.3701 6.5210 6.6606

v 0.004888 0.005734 0.006111 0.006960 0.007720 0.008420 0.009076 50000.0 h 2968.9 3163.2 3248.3 3438.9 3610.2 3770.9 3925.3

s 5.4886 5.7221 5.8207 6.0331 6.2138 6.3749 6.5222

v 0.003755 0.004496 0.004835 0.005596 0.006269 0.006885 0.007460 60000.0 h 2838.3 3055.8 3151.6 3362.4 3547.0 3717.4 3879.6

s 5.2755 5.5367 5.6477 5.8827 6.0775 6.2483 6.4031

v 00.02641 0.003132 0.003379 0.003974 0.004519 0.005017 0.005481 80000.0 h 2648.2 2874.9 2980.3 3220.3 3428.7 3616.7 3792.8

s 4.9650 5.2374 5.3595 5.6270 5.8470 6.0354 6.2034

v 0.002168 0.002493 0.002668 0.003106 0.003536 0.003952 0.004341 100000.0 h 2538.6 2754.5 2857.5 3105.3 3324.4 3526.1 3714.3

s 4.7719 5.0311 5.1505 5.4267 5.6579 5.8600 6.0397

Page 17: Appendices - Springer LINK

726 Appendix A-1

Table A-l-4 Thermodynamic Property Calculations of Steam

The information presented here is adapted from information supplied by S. G. Penoncello and R. B. Stewart of the Center for Applied Thermodynamic Studies, University of Idaho. The information is presented in the following form:

1. list of pertinent equations that are programmed 2. list of subprograms used to compute the various properties 3. example output that is possible with these programs (to be used to check your

output)

This is for your personal use. You will have to set up your own formats, entrance procedures., and so on, to compute the properties you desire.

The listed programs are for the calculation of p, v, T, u, h, and s for the saturated-liquid state and the saturated-vapor state. For the vapor state, only p, v, T, h, and s are calculated.

The data-initializing subroutine (DATSTM) is used to read the coefficients for the equations. These data are then transferred to the subprograms in COMMON blocks.

1. Equations for thennodynamic property calculations: The property calculations use an equation of state that is explicit in the Helmholtz function. This equation is expressed as*

where l/I = l/Io(T) + RT[ln p + pO(p, 1")]

T = temperature in kelvins

p = density in g/cm3

1" = lOOO/T

1"c = 1000/Tc = 1.544912

R = 4.6151 bar-cm3/g-K

E = 4.8

1" aj = 1"c if j = 1

1" aj = 2.5 if j > 1

Paj = 0.634 if j = 1

Paj = 1.0 if j > 1

With the aid of Equation 0), the thermodynamic properties are defined as

p = p2e:)T = PRT[ 1 + pO + p2e~t]

u = [a(l/I'T)] = RT,..JaO) + d(l/Io1") a1" P f'f\. a1" P d1"

(al/l) [ ~aQ)] dl/lo s = - - = - R In(p) + pQ - - - -aT P a1" p dT

p [(ao) (ao)] d(l/Io1") h = u + - = RT p'T - + 1 + pO + p2 - + --P a1" p ap T d1"

(1)

(2)

(4)

(5)

(6)

(7)

(8)

* Keenan, J. H., Keyes, F. G., Hill, P. G., and Moore, J. G. Steam Tables: Thermodynamic Properties of Water including Vapor, Liquid and Solid Phases, Wiley, New York, 1969.

Page 18: Appendices - Springer LINK

Thermodynamic Property Calculations of Steam 727

The vapor-pressure equation used in calculation of saturation properties is given by

Ps = vapor pressure (bars)

Pc = critical pressure = 220.88 bars

T = saturation temperature (C)

Tc = critical temperature = 374.136 C

'T = 1000/T (T in kelvins)

The saturated-liquid and the saturated-vapor densities are computed from

, 7

!?.. = 1 + L C[j'T K " Pc i~l

In!?.. = c,,1 In - + L Cw'T~ ( ') T 9

Pc Tc i~2

where P' is the saturated-liquid density p" is the saturated-vapor density 'T = (Tc - T)/Tc T = temperature in kelvins Tc = critical temperature = 647.286 K p = density Pc = critical density = 0.31696 g/cm3

(9)

(10)

(11)

2. Subprograms used to compute properties. Coefficients of equations are in DA TSTM. Included here are the subprograms for thermodynamic property calculations. The data­initializing subroutine DATS1M must be called before using these programs. Double­precision variables are used for all subprograms.

Property

Saturated-liquid density

Saturated-vapor density

Pressure Vapor pressure (iJp/iJp )T S, H, U

Q(p, 'T)

(iJQ/iJp)T

Subprograms (Input Parameters Underlined)

Subroutine DLKKHM CT, DL) DL is an approximate value for the

saturated-liquid density Subroutine DVKKHM (T, DV) DV is an approximate value for the

saturated-vapor density Subroutine PKK (1, 1), P) Subroutine VPKK (1, VPRESS) Subroutine DPDDKK (T, 1), DPDD) Subroutine PRPSTM (T, Q, 15, P, S, H, U) for

K = 1: S is returned K = 2: P, S, H, and U are returned K = 3: S, H, and U are returned

(P is an output argument for K = 2 and an input argument for K = 3)

Function QFUN (T, D) Function DQFND (T, D)

Page 19: Appendices - Springer LINK

728 Appendix A-1

Subprograms Property (Input Parameters Underlined)

UlQ/Op2)T

(oQ/OT)p dljlo/dT d(ljIoT)/dT Entropy Internal energy Enthalpy

Function DDQFD (T, D) Function DQFDT (TAU, D) Function DSIODT (T) Function DSTDT (TAU) Function SKK (T, D) Function UKK (T, D) Function HKK (T, D) Function DESTKK (T, P) Estimated vapor density

Source: Penoncello, S. G., and Stewart, R. B., Center for Applied Thermodynamic Studies, University of Idaho (private communication).

c c C c c C c c

c

c c c c <.: <.: C

C

S"9FOCTIN~ UAr~T~ I~PLICI1' RcU'K(A-'I,O-Z) COM~ON /U3/ AI1G,7~ /CCPO/ C(8) /~C2/ RS(21J) /C,/P/ BPI) CO~'ON/CR~R/CR 1)/Q,PP/HF(10) COMON/U P L ~D/F .~C ill

CllEFFlCrr:~T'; A~D CC~STANTS I'S~D IN l'Y;, ,:OUHlON OP STATR ANO ITS ~1''<IV~1IVFS

/kCP/ HS(20)-iEFErtNC~ PROP~~TTE~ hN~ CR[TTCAL ~orUT VALUES

• = ~ ~ 1' 1 t= -4. 'l 0 0 ~= :15 2

R':; 2.· =4.r)lSlD~ T~UC='l'(1)

;(3 IJ! = 1. 'i~ 4q 12 D·~ (?~ 4 =2. SO': ~~ IS ~J.63'JD~1 P..> " -l.DO

HS (7) IS THP, CfdTICAL PHiSSlIJE IN ,",PA ic'> (7) =22.'.J8I1D~

R:; (H) IS TilE CRITICH DENSITY IN GM/C!'I3 [{S (8)=0. 316957DO

RS (9) IS 'LiE CHITICH '!E:1P21:ATUP~ IN KELVINS HS ('J) = 374. 13bi)O~.27)'1500J

~S (10) IS TtlE MOLECliLAR .EIGHT OF IIA':'ER as (10) =1tl. 015400

/CVP/ L(S)-COEtFICIENTS FOR VAPllH PR~SSURE EQnATION

~ lq B 3 b 4

~I~ ~ 7 iJ 8

=-7~ 1. '1242D" =-29.72100 =-11. 'J5286ll~ =-0.80856J<;D0 =O.1094~98DO =O.4.l99Q3DG =0.2'.20658DO =0. "5218084DO

C /CES/ A(10,7)-CCEfFICIENTS OF rHE EQUATiON Of STATE C

A (1,1 = L'I.492Q370 00 11(2,1 =-132.13'1170 00 A J,l = 274.646320 00 II 4,1 =-lfiO.938280 00 II. 5,1 = J42.18431D 00 A n,l =-244.500420 00 II 7,1 = 155.185350 00 A 8,1 = 5.97284870 00 A 9 1 =-41C.3084AD 00 A 16(1)=-~10.058600 00 All,L = -5.19858600 00 A 2,2 = 7.77791820 00 AIJ,L = -J3.301902D 00 A 4,2 = -16.2546220 00 Ai5,2 =-177.310740 00 A 6,2 = 127.48742D 00 A 7,2 = 137.461530 00 A 8,2 = 155.978360 00 A(9 2 = 337.311800 00 AI16(2)=-209.888660 CO A 1, .il = 6.8335354D 00 '\2,3 =-2t:.149751DOO

Page 20: Appendices - Springer LINK

Thermodynamic Property Calculations of Steam 729

A ~,~ 65.3203%0 00 ~. -26.1R197AD 01) II 5'3 0.00 00 A 6'3 0.00 00 A 7:3 0.00 00 A ~'1 0.00 00 A -137.466180 00 A 16 4) ) -733.9684t!0 00 A 1, -0.1561110110 00 A 2,4 -0.725461C80 00 A J,4 -9.27342890 00 A 4,4 4.31258400 00 A 5,4 0.00 00 A 6,4 0.00 00 A 7,4 0.00 CO A 8,4 0.00 00 A ':I 4 0.78749B30 00 A l!l 10.4017-170 00 A -0.39724050 00 A 26.4092820 00 A 3: 5 - 47.74037'40 00 A 4,5 56.32]1300 00 A 5,5 0.00 OCI A 6,5 0.00 00' A 7,5 0.00 001 A 8,5 0.00 00 A 9 5 136.87317IJ 00 A

l~l 045.81880D 00

A -3.96614010 00 A 15.4530610 00 A 3,6 -29.14247/00 00 A 4,6 29.51>87<)6D 00 A 5,6 0.00 00 II 6,6 0.00 00 A 7,6 0.00 00 A 8,6 0.00 00 A 9 6 79.8479"7"00 00 A l!l 399.1751CID 00 A -0.6901l.\l554D 00 A 2.74011"1160 00 A 3:7 -5.10280700 00 A 4,7 3.963(;0850 00 A 5,7 0.00 DO A 6,7 0.00 00 A 7,7 0.00 CO A ~,~ 0.00 00 A 13.041253D 00 A 16, ) 71.531353D 00

C C /CCPO/ C(B)-COEFFICIENTS OF IDEAL PART OF THE HELIIHOLTZ EQUATION C

C

C C C C C C C C

C 1 =1857.06500 C 2 =3229.1200 C 3 =-419.46500 C 4 =36.664900 C 5 =-20.5516DO C 6 =4.85233DO C 7 =4b.00 C 8 =-1011.24900

~:Jll;: ~~ l~t CR 3 =RS 9 RF 7 = RS 1 ) ilF 8 =0. 100+273.1500 RF 9 =0.000611300 FA H =1.0451100/RS (8) BETURN ENO

SUbROUTINE OLKKH"(T,OL)

SATURATEr: LIQUIO Ol:NSITY ESTIIIATOR IJSING AN EQUATION GENBB1TEO FROII KEENAN, KEYES~ HILL, ANO 1I008E'S EQUATION OF STATE POR STEAII

FIT WITH THE 'SATLPIT' PACKAGE

TRE TEIIPEHATURE ARGUIIENT IIUST GOIIE INTO THE SUBROUTINE IN KELVINS

IMPLICIT HEAL -8 (A-H,O-Z) OIIIENSION CL (7) ~ UPON (7) CO~~ON/RCP/R~(2v) EXPON I =-2.000 EXPON 2 =-4.000/.1.000 EXPON 3 =1.00/3.DO EXPON q =2.00/3.~0 EXPON 5 =4.DO EXPON 6 =13.DO/3.00 EXPON 7 =14.00/1.00 CLI1) -0.69762817200-06 CL 2) 0.20d3~7~8810-04

Page 21: Appendices - Springer LINK

730 Appendix A-1

C C C

C C C C C C C C

C C C

C C C

C C C

C

10

10

CLI3l = 0.2115'105033D 01 CL 4 = 0.9413040965D 00 CL 5 = -O.fi8R4953578D 02 CL b = 0.1595673187D 03 (L 7) = -0.9570160317D 02 RHOC=RS (8) TC=RS(9) T A 11= ('1'C- T) /l'C

CALCULATE TRE DENSITY OF THE SATURATED LIQUID

SUI'I=l.DO DO 10 1=1 7 SUI'\=SO~+ct(I)·TAU··fXPON(I) CON1'INOE DL=SUI'I·RHOC RETURN END

SUBROUTINt DVKKHI'I(T.DV)

SATURATED VAPOR DENSITY ESTII'\ATO~ USING AN EQUATION GENERATED PRO~ KEFNAN, KEYES, HILL, AND ~OORP'S EQUATION OF STATE POR STEA"

fIT WITH THE 'SA1VFIT' PACKAGE

THE TEMPERATURE ARGUMENT MUST COI'IE INTO THE SUBROUTINE IN KELVINS

II'IPLICll REAL .~(A-H.O-Z) DHIENSION CV (9) COMI'ION/RCP/HS(20) SOI'1=O.DO CV 2 -0.3466596660D 02 CV 3 0.3323665438D 03 CV 4 -0.1137154193D 04 CV 5 0.3250545A77D 04 CV 6 -0.5898161200D 04 CV 7 0.67372€7149D 04 CV 8 -0.4366771542D 04 CV 9 0.1271639749D 04 CV 1 = O.d4367A1311D 02 'l'C=R (9) TAU= (1'C-TI/TC RHOC=RS(8 SUM=CV(1)-DLOG(T/TC) DO 10 1=2.9 SUI'I=SUI'\+CV~)·TAU··(I/l.ODO) CONTINUE DV=DEXP(S"I'I)~RHOt RETURN END

SUBROUTINE PKK(T,D,P)

CALCULATE PRESSURE IN BARS

I~PLICIT REAL*8(A-H,C-Z) COI'I~ON /HCP/ RS(20) R=RS (2)

P IS TKE CALCULATEC PRESSURE IN BARS

P=D*R.T~(l.DO.D*QFUN(T,D)+D*D·DQFND(T,D» RETURN END

SUBROUTINE VPKK(!,VPBESS)

CALCULATES THE VAPCR PRESSURE IN BARS AT !EI'IPFRATURE, T IN K

IMPLICIT REAL*8IA-H,O-Z) COr.~GN bRCP/ as 20) /CV~/ B(8) PC=RS (7 TAU= (10 O. Da/T)

I IS T~I'IFERATURE IN DE~REES C I=T- 27 3. 15DO IF IX. Ej.05. DO) 1=65.00001 DO TAUC=RS 3) TC=(100 .DO/TAUC)-273.15DO Sl1l'1f'=O.DO DO 10 1=1,6

10 SUIII'=SUIII'+BJ1). (0.65DI)- (O.OlDO*X» *- (1-1» EXPARG=TAD~ TC-X)-SUftP*O.OOOOlDO VP=PC*DEIP( IPARG) VPRESS=VP"10. DO RETURN END

Page 22: Appendices - Springer LINK

Thermodynamic Property Calculations of Steam 731

SOBROUTINE DPDDKK(T,D,DPDD) c C CALCULATES DP/DD A! CONSTANT TAU C

("

L C C C ('

IMPLICIT HEAL*SIA-H,O-Z) CO~~ON IRCPI RS 20) 8=85(2) OPOD=8" -T*(D-O·O-DDQ.D(Tlm +4.000~D·D·OQFND~,D)

t+;~.ODO.D*QFUN(!.D) +1.00u) IiE!URN END

~"Li-UII" [,." "I>""~ I" 1 K PSt, '1) i~frllirr'~~F~L~~~~-~:h!/r r' "'1

1

~~T:'Pr'AlE "nUrINF 'W CALCUUT'. lil~ P[\!,:;!;IJh~ IN '1r>iA-PASlAL.J I ~NT=<CPY I>l K~l/K:;-K, ':~!"iAL;Y ;,~L 1~1'L'~A1 r.NE!iGY 1M K,J/r,;. ~~~IJ}NEJt~?~r:,:R,,:d::~~l'EPH[JRr~ (K), DfNSrTY «(;M/':::f'll)

r nt" K ::: 1; "oS 11 r s I\:':T U ~ ~ 1~ l)

:< = '?; "1'"', "S", "11" ANI> "I:" hi·f l~E!"URNED i\ ::: 3; I'S It, ";P' t. N I.) tt U" .\ R E 11 ET 0 [\ ~ E I>

COM~~.I.cr/~~(20) If ! ~ . L 1. 1 • () i, • K • li l. l) I; ,) Til 10'1

1 F (, • F. ~. 1 0 f! U ,. \ ~=~~KIT.DI . " ..

H=H~KIT,jj IJ= U i' ~ '1, fl II' (~ • c: ;;.1) In,: ;' iJ g N CALL PO;;SJ I',,~,i') t,;() Te ) ,)

200 ,;. oJ l; i;

3~

,nIP (~, IO~0) ~~i~~~ (2(~X,"'''''·'''·· "1<" I~ -.)111' ,:)p .. ~ANI;F: F0H npRPST!III tI .* .. ,.. .... )

C L C

END

"f) NCT I C~ ')1'U N (r, n)

:ALCUL~fES ~=V(T,O)

IM~LICIf dE~l·R(A-H,O-Z) CO~~O~ IC!~I A(10,7) IRCfl 05(2 0 ) .':=RS!1l d="S 2 If.,IT. 1).41)).0:)) 1'=401).0000100 IAu= (1000.DO/7) TAIIC=hS(J) v. P U ~ = ,). tl ~ f=UEXPjE'D) DO ~0 = 1,7 IF IJ.EU.lj (;0 TO 10 IF J. GT • 1 GO TO 15

11 TAUAJ= HS (l DAJ=RS (S) IF ('lAU-TATJAJ.E.;>.0.Dil) GO TO 100 GO to 20

1'> TAUAJ= RS (4) DAJ= RS (6) If !1All-TAllAJ.EIi.O.LO) GO !O 100 2i ~i= = 13:ii6 AU C) *1 (TAU-TAUAJI" (J-2))

DC 2 ') 1= 1, S DDAJ~O-DAJ If (DDAJ.~Q.0.D0) GO TC 105

25 llI=lll+A (I,J)· (D-!JAJ) •• (I-I) 2(, COSTINU~

DO 30 I=9,10 30 Bl=RI+F'A(I,J) "Oh (I-~:I)

QfllN=Uf"'IN+ eJ"llI 50 CONTINUE

Rf.TlJhN 1 (.,) BJ =). DO

GO TO 21 10~ BI=3I

GC 'fO 26 2!,[l

FUNCTIr;~ D(jfND (1, D) C C CALCULATtS DU/DD, 1=CONSTANT C

IMPLICIT ~EAL·8(A-H,0-Z) Cr)I\~ON Io.'ll A (fO, 7) IRC?I ?S (20)

Page 23: Appendices - Springer LINK

732 Appendix A-1

~~~~ HI IF (T. ~().I+OO.DO) 'i=L;~0.00C(11DO TAU= (1000. DO/T) TAUC=\IS (3) DQFND=O. DQ F= DEXPJE" D) DO 50 = 1 .., IF (J. fOe 'l GO TO 10 IF (J.GT.l GO Te 15

1 C TAIIAJ:RS (3

~va~d~lrAUAJ.EQ.I).DO) GO '10 1')') GO TO 20

15 'IAUAJ=RS (iI) ;)AJ=~S (1;) IF !IAU-TAUAJ.I!Q.n.DO) GO TO 100

20 BJ= TAU-HIIC)" «'IAU-TAUAJ)·" (J-~» 21 DBI=O.DO

00 25 1=1,8 DDAJ=D-DAJ IF «(;DAJ.EQ.O.DO) GO TO 105

25 CS1=DB1+A(I,J)"(I-l)"(D-DAJ)U(I-2) 26 CONTINUE

DO JO 1=9,10 30 DBI=DBI+F*A(I,J) *JI-9) >0·' (1-10) +E·~'·A (I,J)·D'· (I-'l)

DQFND=DQFND+DBI· E 50 CONTINUE

HETURN 100 DJ=i).DO

GO TO 21 lOS DBI=DIlI

C C C C

C C C

GO TO 26 END

FUNC'IION DUQFD ('I,D)

CALCULATES THE SECOND DEiIVATI'! OF Q WITH RESPECT TO DENSITY, AT T=CONSrANT

TIIPL1Cl1 aEAL*8 (A-H,O-Z) COIIIION /C~S/ 1.(10,7) /RCP/ RS(20)

~~~~I~l IF d.~1.!.400.DC) T=400.0000100 TAU= (1000. DC/T) rAUC=RS (3) F=DEXP (~·tl) DDQFD=O. DO DO '10 J= 1,7 IF IJ. Mi. II GO TC 10 IF ~.GT.l GO TO 15

10 TAUAJ=RS (3 DAJ= RSIS) IF ITAU-ThUAJ.EQ.O.OO) GO TO 100 GO Tc 20

1 5 6~~~~~ R~ (4)

IF lTAd-~AUAJ. EQ.O. DO) GO TO 100 20 BJ= TAU-TAUe) * «HU-TAUAJ) •• (J-2» 21 DilB =O.DO

ggA,i~D~Dlj8 If (DDAJ.F:Q.().D(1) GO TO las

2S ODBI=D~Bl+A (I,J) • (1-1) * (1-2)'" (D-DAJ).· (1-1) 26 CONTINUE

DO 30 1=9,10 JO DDDI=DDBI+2.DO*E.F>'A~1,J)· !r-9)-O".(1-lJ)

• +F"A (1 J)' (1-9) ~ (l-lvl*O'" 1-11) .+E-E-F'A(I J)~D'*(I-9 DD~FO=UDUfb+DDBI*5J

50 CONTINUE RETUFN

lac BJ=O.DO GO 1'C 21

105 ODIiI=OOlll GO TO 2i. EljD

FUNCTION DQFDT (TAU,D)

CALCULATES DQ/DTAU, D=CONSTANT

IIIPLICIT REAL*6(A-H,O-Z) COftllON /CES/ A(10,7) /~CP/ HS(20) E=RS (1) TAUC=RS (3) I¥ IT.EQ.~OO.DO) T=400.00001DO F=DI!XP IE*O)

Page 24: Appendices - Springer LINK

C C C

C C C

C C C

C C C

Thermodynamic Property Calculations of Steam 733

oQ1'oT=O.oO DO 50 J= 1 t 7 IF iJ.EQ.1l GO TO 10 IF J.GT.l GO TO 15

10 TAU J=RS(3 oAJ=RS (5) GO TO 20

15 TAUAJ=RS (4) OAJ=RS (6)

20 1'0=0.00 RgAJ~0~D1j8 IF 100AJ.EQ.O.OO) GO TO 105 Fo=Fo+A II.J). (o-IJAJ)." (1-1)

25 CONTINU!! DO 35 1=9.10

35 1'0=1'0+ IF*A (I.J)· (fl" (I-'l») IF (TAU-TAUAJ.EQ.O.oO) GO to 100 oQt'DT=oQFDT+FO* IHU-TAUAJ).' (J-2) .

• + (TAU-TAUC) *1'0" J-2). (TAU-TA!JAJ)'" (J-l) 50 CONTINUE

RETURN 100 OQFOT=08FDT

GO TO 5 105 1'o=FD

GO TO 25 END

FUNCTIlJN OSIOoT (I)

CALCULATES D(PSI ZEBO)/DT

I~PLICJT PEAL*S(A-H.O-Z) CO~ftON lCCPO/ C(B) OSI ODT= O. DO DO 10 1=1 6

10 OSIOOT=OSIOOT-!C{I)/l%J.DO)' (1-1)' (10(Ll.DO/T) "(2-1) OS! OOT= OS 10 DT +c (1) /T+C (8) "2. flO/1 BE'rURN END

FUNCTION OSTDT (TAU)

CALCULATES D(P5IZEFO·TAU)/oTAU

I!1PLICIT REAL·fl (A-H,O-7.) COftMON /CCPO/ c(e) D:>TO'I=O. DO DO 10 1= 1 6

10 OSToT=OSTDHC(I). (2-1) "TAU" (1-1) USTDT=DSTDT+C(7).(oLOG(100~.DO)-DLOG(TAU)-1.DO)-C(A)/TAU IlETURN END

FUNCTICN :)KK(T,U)

CALCULATES ENTROPY TN JOULE:)/GRA~-KELVIN

I!1PLICIT hEAL-S!A-H,O-Z) COr,~CN /RCP/ RS 20) R=RS(2) S=C.DO 'rAU=J1000.DO/T) SKK= £1/10. DO)" (O-'l'All"DQI'DT (TAU,D) -DLor; (G) -D*QPUN (T D)

'-DS! D'I(T) . , RETURN ENC

FUNCTION UKK(T,D)

CALCULATES INTERNAL ENERGY IN JUULgS/GHA!1S

I!1PLICI1' ilEAL"S (A-H,O-Z) ~~~~o~ /RCP/ as(~o)

TAU=11 ~o O. oO/T~ ~~~u ~/10.o0)* '"O*TAU"DQFDT(TAU,D) +DSTD'I(TAU) END

Page 25: Appendices - Springer LINK

734 Appendix A-1

c C C

C C C C

FONCTICN HKK(T,D)

CALCULATES ENTHALPY

IMPLICIT REAL*S(A-H,O-Z) COMMCN LRCPL 85(20) TAU= 11000. OO/T) R=RS 2) HKK= R/l0.00)-T*CO.TAU·OyPOTCTAU,D)+1.DC+0.QFUNCT,0) ;g;8:~QFNO(T.0»+OSTOT(TAU)

END

FUNCTIO~ DESTKK C'll N, P) I~PLICIT REAL-8CA-H.0-Z)

VAPOH DENSITY ESTI~ATOR FOR STEAM FRO~ THE KEENAN AND KEYES VOLU~E EXPLICIT EQUATION OF STATE OF 1~36.

TIN=TIN-273.1500+l7j.lbOO TAU=1.000/TIN PHE=P/l.0132500 TAU2='rAU"TAU TAU12=TAU2*TAU2*TAU2-TAU2-TAU2·TAU2 G1=d2.546DO*TAU-l.624600S*TAU2 G2=O.218~8DO-1.26~7005·TAU2 G3=3.6350-04-b.7bBDb4*TAU12-TA012 EHON=flO.870D03*'lAU2 . BO=1.B9DO-26U1.6200*TAO~(10.DO··EXPON) 30U=RO"BO' BO*BO PU=PRE*PRE-PRE*PHE P12=i'''*P4 r p4 B=Bn+UO·BO·Gl*TAU-PRE+BOU·G2-TAU*TAU2*PRB*PRR*PRE-

'E04"eOg> BC"'BO~ 'G3-TAU 12'P 12 V=IU.5~50UDO*Tl~)/PRE+B DESTKK=1.0DO/V ~ETUl(N ENr.

Page 26: Appendices - Springer LINK

TEMP CEG C

0.10 1 10 20 30

40 6,J 80 100 120

140 160 180 2UO 220

240 260 2bO 300 320

330 340 .~50 360 314.136

Thermodynamic Property Calculations of Steam 735

3. The example output possible with the aforementioned subprograms is shown in the following tabular lists:

PkbSUI<!: MPA

.000615

.000657

.\JJU28

.002338

.0:)4246

• CO 73 iB .019940 .04739 .10D4 • 1985"!

• 3613 • 6l1t! 1.0021 1. 55J1 1..317t:

3.3440 4. 0 8t':; 6.4113 tl.5dJ5 11.213

12. a4 5 14.5t!5 Ih.5U 1 d. 65 v a.o~1;

T~ERMOOYNAMIC PROPERTIES Of STEAM

SATURATION TA8LE,- TEMP~I<ATUR[

S~EC'fIC VOLUME INIEk~AL ENERGY M3/KG· IJOO KJ/KG

ENTHAlPV KJ/KG

VF 1.0002 1.0002 1.0004 1.0018 1.0043

1.0078 1.0172 1. OZ'i 1 1.0435 1. ·)603

1.0798 1.102u 1.1274 1.1505 1.1900

1.2291 1.275, 1.J321 1.4036 1.498~

1.:;608 1.63&(, 1.1404 1. a 92!1 3.11">0

... ;VG--·-----IiF·-----uli----HF--20-10869 0.39 2315.5 0.39 192585 4.11 2376.7 4.17 106384 42.01 2~B9.2 42.01 51193 83.95 2402.9 83.95 32896 125.82 2416.6 125.83

19524 7671 3407.5 1673.0 8~,l.9

5~" 77 '0,2.21 3 C. 17 2'.6d 15.4':1

l3..00 10. aJ B.8D 1>.945 3.1150

161.59 251.14 33'1.8" 418.97 ;03.54

588.78 674.91 762.14 850.7C 94 C. 91

1033.3 112d.4 1227. "> 13 32.0 14 .. 4.6

15e5.3 1570.4 1641.9 1125.4 2029.6

2430.1 2456.7 2482.2 2506.5 2529.3

2550.1 25613.4 2583.7 25"5.3 20·)2.4

260 ... J ~59·I.l 2586."! 2563.0 2525.6

2499.0 2464.7 2418.6 2351.9 202'l.0

Ib7.ou ~51.16 334.94 419.·)d 503.75

589.17 615.59 763.27 852.49 ~43.67

10H.4 1134.4 Il36.u 1344.1 14b 1. 5

1525.4 159 ... 3 1670.7 170".7 2099. ]

Hli 2501.5 2503.2 2519.8 2538.1 2550.3

2514.3 26ll~.b 2643.7 2676. 1 2106.3

213 3. 'I 27511.1 2778.2 279J.2 2802.2

2dO j. 9 2191.0) 2779.6 2749.1 2700.2

2660.0 2622.2 2%4.2 24tH.5 209'1. 'J

SF 0.0014 0.0153 0.1510 0.2966 0.4311

0.5726 0.8312 1.0754 1.3069 1.5277

1.1392 1.9428 2.1397 2. HI0 2.5119

2.7016 2.11839 3.0669 3.2534 3.4481

3.5508 3.6595 3.7718 3.91'09 4.4298

SG 9.1539 '1.129\/ 8.9 ... 08 8.6672 8.4534

8.2571 1.9096 7.6123 1.3549 7.1297

0.9300 b. 70;03 6.511511 6.4324 0.7.t!b2

6.1438 6.0J20 5.a572 5.7046 5.5364

5.4419 5.3360 5.2111 5.0533 4.4l9b

Source: Penoncello, S. G., 3.'nd Stewart, R. B., Center for Applied Thermodynamic Studies, University of Idaho (private communication).

Page 27: Appendices - Springer LINK

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Page 28: Appendices - Springer LINK

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Page 29: Appendices - Springer LINK

Tab

le A

-2

Th

erm

od

yna

mic

Pro

pert

ies

of

Fre

on-1

2 (D

ich

loro

difl

uo

rom

eth

an

e)a

Spec

ific

Vol

ume

Ent

halp

y E

ntro

py

m3/k

g k

J/k

g

kJ/

kg

K

Ails

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ess.

Sa

t. Sa

t. Sa

t. Sa

t. Sa

t. Sa

t. T

emp.

M

Pa

Liq

uid

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p.

Vap

or

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uid

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p.

Vap

or

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uid

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p.

Vap

or

C

p fl

f fl

f. fl

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f h

f.

h.

sf

Sf.

S

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0.

0028

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Page 30: Appendices - Springer LINK

0 0.

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0.04

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59

148.

859

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518

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50

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Page 31: Appendices - Springer LINK

Tab

le A

-2-2

S

uper

heat

ed F

reon

-12

Tem

p.

I)

II s

I)

II s

I)

II s

C

m3/k

g kJ

/kg

kJ/

kg

K

m3/k

g kJ

/kg

kJ/k

g K

m

3/k

g kJ

/kg

kJ/

kg

K

O.O

SMPa

O

.lO

MP

a O

.lS

MP

a -2

0.0

0.

3418

57

181.

042

0.79

12

0.16

7701

17

9.86

1 0.

7401

-1

0.0

0.

3562

27

186.

757

0.81

33

0.17

5222

18

5.70

7 0.

7628

0.

1147

16

184.

619

0.73

18

0.0

0.37

0508

19

2.56

7 0.

8350

0.

1826

47

191.

628

0.78

49

0.11

9866

19

0.66

0 0.

7543

10

.0

0.38

4716

19

8.47

1 0.

8562

0.

1899

94

197.

628

0.80

64

0.12

4932

19

6.76

2 0.

7763

20

.0

0.39

8863

20

4.46

9 0.

8770

0.

1972

77

203.

707

0.82

75

0.12

9930

20

2.92

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7977

30

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21

0.55

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0.

204

506

209.

866

0.84

82

0.13

4873

20

9.16

0 0.

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40

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21

6.73

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9175

0.

211

691

216.

104

0.86

84

0.13

9768

21

5.46

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50

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22

2.99

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222.

421

0.88

83

0.14

4 62

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1.83

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8591

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22

9.34

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0.

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55

228.

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0.90

78

0.14

9450

22

8.27

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70

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8978

23

5.77

4 0.

9755

0.

2330

44

235.

285

0.92

69

0.15

4247

23

4.78

9 0.

8980

80

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2917

24

2.28

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0.

240

111

241.

829

0.94

57

0.15

9020

24

1.37

1 0.

9169

90

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0.49

6838

24

8.86

8 1.

0126

0.

2471

59

248.

446

0.96

42

0.16

3774

24

8.02

0 0.

9354

O.2

0MP

a O

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MP

a O

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Pa

0.0

0.08

8608

18

9.66

9 0.

7320

0.

0697

52

188.

644

0.71

39

0.05

7150

18

7.58

3 0.

6984

10

.0

0.09

2550

19

5.87

8 0.

7543

0.

0730

24

194.

969

0.73

66

0.05

9984

19

4.03

4 0.

7216

20

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0.09

6418

20

2.13

5 0.

7760

0.

0762

18

201.

322

0.75

87

0.06

2734

20

0.49

0 0.

7440

30

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8 20

8.44

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0.

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50

207.

715

0.78

01

0.06

5418

20

6.96

9 0.

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40

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3989

21

4.81

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0.

0824

31

214.

153

0.80

10

0.06

8049

21

3.48

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50

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220.

642

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14

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22

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60

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227.

185

0.84

13

0.07

3185

22

6.62

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23

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0.

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233.

785

0.86

08

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00

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52

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Page 32: Appendices - Springer LINK

0.40

MP

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20.0

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198.

762

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19

6.93

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484

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0.

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65

224.

315

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0.03

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231.

161

0.80

77

0.03

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244.

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0.84

67

0.03

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24

4.00

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2.70

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0.

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86

251.

869

0.86

56

0.04

0 31

6 25

1.01

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0.0

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9.62

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258.

845

0.88

40

0.04

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25

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12

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0.

0519

29

265.

862

0.90

21

0.04

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26

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0.0

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27

3.60

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0.

0534

30

272.

923

0.91

98

0.04

4 18

1 27

2.23

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9061

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MP

a O

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Pa

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a 40

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6761

20

7.58

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0228

30

205.

924

0.70

16

0.01

9744

20

4.17

0 0.

6982

50

.0

0.02

8100

21

4.74

5 0.

7373

0.

0240

68

213.

290

0.72

48

0.02

0912

21

1.76

5 0.

7131

60

.0

0.02

9387

22

1.85

4 0.

7590

0.

0252

47

220.

558

0.74

69

0.02

2012

21

9.21

2 0.

7358

70

.0

0.03

0632

22

8.93

1 0.

7799

0.

0263

80

227.

766

0.76

82

0.02

3062

22

6.56

4 0.

7575

80

.0

0.03

1843

23

5.99

7 0.

8002

0.

0274

77

234.

941

0.78

88

0.02

4072

23

3.85

6 0.

7785

90

.0

0.03

3027

24

3.06

6 0.

8199

0.

0285

45

242.

101

0.80

88

0.02

5051

24

1.11

3 0.

7987

10

0.0

0.03

4189

25

0.14

6 0.

8392

0.

0295

88

249.

260

0.82

83

0.02

6005

24

8.35

5 0.

8184

11

0.0

0.03

5332

25

7.24

7 0.

8579

0.

0306

12

256.

428

0.84

72

0.02

6937

25

5.59

3 0.

8376

12

0.0

0.03

6458

26

4.37

4 0.

8763

0.

0316

19

263.

613

0.86

57

0.02

7851

26

2.83

9 0.

8562

13

0.0

0.03

7572

27

1.53

1 0.

8943

0.

0326

12

270.

820

0.88

38

0.02

8751

27

0.10

0 0.

8745

14

0.0

0.Q

3867

3 27

8.72

0 0.

9119

0.

0335

92

278.

055

0:90

16

0.02

9639

27

7.38

1 0.

8923

15

0.0

0.03

9764

28

5.94

6 0.

9292

0.

0345

63

285.

320

0.91

89

0.03

0515

28

4.68

7 0.

9098

Page 33: Appendices - Springer LINK

Tab

le A

-2-2

S

uper

heat

ed F

reo

n-1

2 (

Co

ntin

ue

d)

Tem

p.

., It

s .,

It s

., It

s C

m

3/k

g k

J/k

g

kJ/

kg

K

m3/k

g k

J/k

g

kJ/

kg

K

m3/k

g k

J/k

g

kJ/

kg

K

l.o

oM

Pa

1.2

0M

Pa

1.4

0M

Pa

50.0

0.

0183

66

210.

162

0.70

21

0.01

4483

20

6.66

1 0.

6812

60

.0

0.01

9410

21

7.81

0 0.

7254

0.

0154

63

214.

805

0.70

60

0.01

2579

21

1.45

7 0.

6876

70

.0

0.02

0397

22

5.31

9 0.

7476

0.

0163

68

222.

687

0.72

93

0.01

3 44

8 21

9.82

2 0.

7123

80

.0

0.02

1341

23

2.73

9 0.

7689

0.

0172

21

230.

398

0.75

14

0.01

4-24

7 22

7.89

1 0.

7355

90

.0

0.02

2251

24

0.10

1 0.

7895

0.

0180

32

237.

995

0.77

27

0.01

4997

23

5.76

6 0.

7575

10

0.0

0.02

3133

24

7.43

0 0.

8094

0.

0188

12

245.

518

0.79

31

0.01

5710

24

3.51

2 0.

7785

11

0.0

0.02

3993

25

4.74

3 0.

8287

0.

0195

67

252.

993

0.81

29

0.01

6393

25

1.17

0 0.

7988

12

0.0

0.02

4835

26

2.05

3 0.

8475

0.

0203

01

260.

441

0.83

20

0.01

7053

25

8.77

0 0.

8183

13

0.0

0.02

5661

26

9.36

9 0.

8659

0.

0210

18

267.

875

0.85

07

0.01

7695

26

6.33

4 0.

8373

14

0.0

0.02

6474

27

6.69

9 0.

8839

0.

0217

21

275.

307

0.86

89

0.01

8321

27

3.87

7 0.

8558

15

0.0

0.02

7275

28

4.04

7 0.

9015

0.

0224

12

282.

745

0.88

67

O.o

t893

4 28

1.41

1 0.

8738

16

0.0

0.02

8068

29

1.41

9 0.

9187

0.

0230

93

290.

195

0.90

41

0.01

9535

28

8.94

6 0.

8914

1.60

MP

a 1.

80 M

Pa

2.00

MP

a 70

.0

0.01

1208

21

6.65

0 0.

6959

0.

009

406

213.

049

0.67

94

80.0

0.

0119

84

225.

177

0.72

04

0.01

0 18

7 22

2.19

8 0.

7057

0.

0087

04

218.

859

0.69

09

90.0

0.

0126

98

233.

390

0.74

33

0.01

0884

23

0.83

5 0.

7298

0.

0094

06

228.

056

0.71

66

100.

0 0.

0133

66

241.

397

0.76

51

0.01

1526

23

9.15

5 0.

7524

0.

0100

35

236.

760

0.74

02

110.

0 0.

0140

00

249.

264

0.78

59

0.01

2126

24

7.26

4 0.

7739

0.

010

615

245.

154

0.76

24

120.

0 0.

0146

08

257.

035

0.80

59

0.01

2697

25

5.22

8 0.

7944

0.

0111

59

253.

341

0.78

35

130.

0 0.

0151

95

264.

742

0.82

53

0.01

3 24

4 26

3.09

4 0.

8141

0.

0116

76

261.

384

0.80

37

140.

0 O

.ot5

765

272.

406

0.84

40

0.01

3 77

2 27

0.89

1 0.

8332

0.

0121

72

269.

327

0.82

32

150.

0 0.

0163

20

280.

044

0.86

23

0.01

4284

27

8.64

2 0.

8518

0.

012

651

277.

201

0.84

20

160.

0 0.

0168

64

287.

669

0.88

01

0.01

4784

28

6.36

4 0.

8698

0.

0131

16

285.

027

0.86

03

170.

9 0.

0173

98

295.

290

0.89

75

0.01

5272

29

4.06

9 0.

8874

0.

013

570

292.

822

0.87

81

180.

0 0.

0179

23

302.

914

0.91

45

0.01

5752

30

1.76

7 0.

9046

0.

0140

13

300.

598

0.89

55

Page 34: Appendices - Springer LINK

2.50

MP

a 3.

00 M

Pa

3.50

MP

a

90.0

0.

0065

95

219.

562

0.68

23

100.

0 0.

0072

64

229.

852

0.71

03

0.00

5231

22

0.52

9 0.

6770

11

0.0

0.00

7837

23

9.27

1 0.

7352

0.

0058

86

232.

068

0.70

75

0.00

4 32

4 22

2.12

1 0.

6750

12

0.0

0.00

8351

24

8.19

2 0.

7582

0.

0064

19

242.

208

0.73

36

0.00

4959

23

4.87

5 0.

7078

13

0.0

0.00

8827

25

6.79

4 0.

7798

0.

0068

87

251.

632

0.75

73

0.00

5456

24

5.66

1 0.

7349

14

0.0

0.00

9 27

3 26

5.18

0 0.

8003

0.

0073

13

260.

620

0.77

93

0.00

5884

25

5.52

4 0.

7591

50.0

0.

0096

97

273.

414

0.82

00

0.00

7709

26

9.31

9 0.

8001

0.

0062

70

264.

846

0.78

14

160.

0 0.

010

104

281.

540

0.83

90

0.00

8083

27

7.81

7 0.

8200

0.

006

626

273.

817

0.80

23

170.

0 0.

0104

97

289.

589

0.85

74

0.00

8439

28

6.17

1 0.

8391

0.

0069

61

282.

545

0.82

22

180.

0 0.

010

879

297.

583

0.87

52

0.00

8782

29

4.42

2 0.

8575

0.

0072

79

291.

100

0.84

13

190.

0 0.

0112

50

305.

540

0.89

26

0.00

9114

30

2.59

7 0.

8753

0.

0075

84

299.

528

0.85

97

200.

0 0.

01 1

614

31

3.47

2 0.

9095

0.

0094

36

310.

718

0.89

27

0.00

7878

30

7.86

4 0.

8775

4.00

MP

a 12

0.0

0.00

3736

22

4.86

3 0.

6771

13

0.0

0.00

4 32

5 23

8.44

3 0.

7111

14

0.0

0.00

4 78

1 24

9.70

3 0.

7386

15

0.0

0.00

5172

25

9.90

4 0.

7630

16

0.0

0.00

5522

26

9.49

2 0.

7854

17

0.0

0.00

5845

27

8.68

4 0.

8063

18

0.0

0.00

6147

28

7.60

2 0.

8262

19

0.0

0.00

6434

29

6.32

6 0.

8453

20

0.0

0.00

6708

30

4.90

6 0.

8636

21

0.0

0.00

6972

31

3.38

0 0.

8813

22

0.0

0.00

7228

32

1.77

4 0.

8985

23

0.0

0.00

7477

33

0.10

8 0.

9152

Page 35: Appendices - Springer LINK

744 Appendix A-3

Appendix A-3 Air Tables

In the first section of this appendix, air is treated as an ideal gas. to account for the variation of Cp and Cu with temperature, two temperature dependent functions are presented:

cf>(T) = fT cp(T) dT JT • T

IjJ(T) = fT cu(T) dT JT • T

where To is an arbitrarily selected reference temperature. These functions are convenient to use when making entropy-difference calculations. This convenience can be demonstrated using the following two equations:

dT dp ds = c - - R-

p T P

dT dv ds = c - + R-

u T v

Integrating these two equations from the reference state (To, vo, Po, So, and so on) to (T, v, P, s, and so on) yields

s - So = iT cp dT - R In(~) • T Po

s - So = iT cu dT + R In(~) • T Vo

Using the cf> and IjJ definitions yields

S - So = cf>(T) - R In(:J

s - So = IjJ(T) + R In(:J Therefore,

or

Page 36: Appendices - Springer LINK

Low-Density Air (51) 745

Also presented in this table are p* and v*, which are defined as

In p* tfJ(T)

R

In v* = _ t/I(T) R

Thus for an isentropic process (~s = 0),

tfJ(T2) - tfJ(T1) = R In(::) = R In(:~) t/I(T2) - t/I(T1) = -Rlne:) = -Rln(~D

The forms of Cp and Co (=cp - R) used in these calculations were deduced from data presented by J. H. Keenan and J. Kaye in their book Gas Tables.t These data were fit by an orthogonal polynomial procedure using evenly spaced data. This six-term polynomial fits the given data to within 1 % over the whole temperature range. Thus for educational purposes, the following tables will be sufficient. For research work, refer to the original data in the book Gas Tables.

t Keenan, J. H., and Kaye, J. Gas Tables: Thermodynamic Properties of Air Products of Combustion and Component Gases-Compressible Flow Functions, Wiley, 1948.

Page 37: Appendices - Springer LINK

746 Appendix A-3

Table A-3-1 Low-Density Air (51)

Specific Specific Internal Specific Heat Enthalpy Heat Energy Heat Pressure Volume

Temp kJ/kg· K kJ/kg kJ/kg· K kJ/kg Ratio Ratio Ratio <P K cp h Cu u k p* v* kJ/kg· K

30 1.0019 30.10 0.7150 21.50 1.4013 0.0018 11399.2500 0.16139 35 1.0012 35.11 0.7143 25.07 1.4017 0.0030 7764.9370 0.31582 40 1.0005 40.11 0.7136 28.63 1.4021 0.0048 5569.7960 0.44951 45 0.9999 45.10 0.7130 32.20 1.4024 0.0072 4155.9790 0.56735 50 0.9993 50.10 0.7124 35.76 1.4028 0.0104 3199.0170 0.67270

55 0.9988 55.09 0.7118 39.32 1.4031 0.0145 2525.1370 0.76794 60 0.9982 60.08 0.7113 42.87 1.4034 0.0197 2035.0260 0.85485 65 0.9977 65.07 0.7108 46.42 1.4037 0.0260 1668.8710 0.93475 70 0.9973 70.05 0.7103 49.97 1.4039 0.0336 1389.0480 1.00869 75 0.9968 75.03 0.7099 53.52 1.4042 0.0427 1171.0100 1.07750

80 0.9964 80.01 0.7095 57.07 1.4044 0.0534 998.2355 1.14184 85 0.9960 84.99 0.7091 60.61 1.4046 0.0660 859.3016 1.20225 90 0.9957 89.97 0.7088 64.15 1.4048 0.0804 746.1239 1.25919 95 0.9954 94.94 0.7085 67.69 1.4050 0.0970 652.8608 1.31303

100 0.9951 99.91 0.7082 71.23 1.4052 0.1159 575.2141 1.36409

105 0.9948 104.89 0.7079 74.77 1.4053 0.1373 509.9674 1.41264 110 0.9946 109.86 0.7077 78.31 1.4055 0.1613 454.6800 1.45893 115 0.9944 114.83 0.7075 81.84 1.4056 0.1882 407.4740 1.50315 120 0.9942 119.80 0.7073 85.38 1.4057 0.2181 366.8876 1.54548 125 0.9940 124.76 0.7071 88.91 1.4058 0.2512 331.7701 1.58607

130 0.9939 129.73 0.7070 92.45 1.4058 0.2878 301.2059 1.62506 135 0.9938 134.70 0.7069 95.98 1.4059 0.3280 274.4613 1.66258 140 0.9937 139.66 0.7068 99.51 1.4060 0.3720 250.9413 1.69873 145 0.9937 144.63 0.7067 103.04 1.4060 0.4201 230.1614 1.73361 150 0.9936 149.60 0.7067 106.58 1.4060 0.4724 211.7229 1.76731

155 0.9936 154.56 0.7067 110.11 1.4060 0.5292 195.2959 1.79990 160 0.9937 159.53 0.7067 113.64 1.4060 0.5907 180.6058 1.83145 165 0.9937 164.50 0.7068 117.17 1.4060 0.6571 167.4227 1.86204 170 0.9938 169.46 0.7068 120.71 1.4059 0.7287 155.5524 1.89171 175 0.9939 174.43 0.7069 124.24 1.4059 0.8057 144.8312 1.92052

180 0.9940 179.40 0.7070 127.77 1.4058 0.8882 135.1191 1.94853 185 0.9941 184.37 0.7072 131.31 1.4057 0.9767 126.2968 1.97577 190 0.9942 189.33 0.7073 134.84 1.4056 1.0712 118.2617 2.00229 195 0.9944 194.30 0.7075 138.38 1.4055 1.1721 110.9255 2.02813 200 0.9946 199.28 0.7077 141.92 1.4054 1.2797 104.2115 2.05331

205 0.9948 204.25 0.7079 145.45 1.4053 1.3940 98.0531 2.07788 210 0.9951 209.22 0.7082 148.99 1.4052 1.5155 92.3924 2.10187 215 0.9953 214.20 0.7084 152.53 1.4050 1.6444 87.1787 2.12529 220 0.9956 219.17 0.7087 156.07 1.4049 1.7809 82.3673 2.14818 225 0.9959 224.15 0.7090 159.62 1.4047 1.9254 77.9191 2.17056

Page 38: Appendices - Springer LINK

Low-Density Air (51) 747

Table A-3-1 Low-Density Air (51) (Continued)

Specific Specific Internal Specific Heat Enthalpy Heat Energy Heat Pressure Volume

Temp kJ/kg' K kJ/kg kJ/kg' K kJ/kg Ratio Ratio Ratio 4> K c., h Cu u k p* v* kJ/kg' K

230 0.9962 229.13 0.7093 163.16 1.4045 2.0780 73.7993 2.19246 235 0.9966 234.11 0.7096 166.71 1.4043 2.2392 69.9774 2.21390 240 0.9969 239.09 0.7100 170.26 1.4041 2.4091 66.4261 2.23489 245 0.9973 244.08 0.7104 173.81 1.4039 2.5880 63.1211 2.25545 250 0.9977 249.06 0.7108 177.36 1.4037 2.7763 60.0407 2.27561

255 0.9981 254.05 0.7112 180.92 1.4035 2.9743 57.1658 2.29538 260 0.9985 259.04 0.7116 184.47 1.4032 3.1822 54.4788 2.31477 265 0.9990 264.03 0.7120 188.03 1.4030 3.4003 51.9643 2.33380 270 0.9994 269.03 0.7125 191.59 1.4027 3.6290 49.6082 2.35248 275 0.9999 274.03 0.7130 195.15 1.4024 3.8686 47.3978 2.37082

280 1.0004 279.03 0.7135 198.72 1.4022 4.1194 45.3218 2.38885 285 1.0009 284.03 0.7140 202.29 1.4019 4.3816 43.3697 2.40657 290 1.0014 289.03 0.7145 205.86 1.4016 4.6558 41.5322 2.42398 295 1.0020 294.04 0.7150 209.43 1.4013 4.9421 39.8007 2.44111 300 1.0025 299.05 0.7156 213.01 1.4010 5.2409 38.1675 2.45796

305 1.0031 304.06 0.7162 216.59 1.4006 5.5526 36.6255 2.47454 310 1.0037 309.08 0.7167 220.17 1.4003 5.8775 35.1682 2.49086 315 1.0043 314.10 0.7173 223.76 1.4000 6.2159 33.7897 2.50693 320 1.0049 319.12 0.7180 227.35 1.3996 6.5683 32.4846 2.52275 325 1.0055 324.15 0.7186 230.94 1.3993 6.9349 31.2480 2.53834

330 1.0062 329.18 0.7192 234.53 1.3989 7.3162 30.0752 2.55370 335 1.0068 334.21 0.7199 238.13 1.3986 7.7125 28.9622 2.56884 340 1.0075 339.24 0.7205 241.73 1.3982 8.1241 27.9049 2.58377 345 1.0081 344.28 0.7212 245.33 1.3978 8.5516 26.9000 2.59848 350 1.0088 349.32 0.7219 248.94 1.3975 8.9952 25.9440 2.61300

355 1.0095 354.37 0.7226 252.55 1.3971 9.4554 25.0339 2.62732 360 1.0103 359.42 0.7233 256.17 1.3967 9.9325 24.1671 2.64144 365 1.0110 364.47 0.7241 259.79 1.3963 10.4269 23.3408 2.65539 370 1.0117 369.53 0.7248 263.4] 1.3959 10.9391 22.5526 2.66915 375 1.0125 374.59 0.7255 267.04 1.3955 11.4696 21.8003 2.68274

380 1.0132 379.65 0.7263 270.67 1.3950 12.0186 21.0819 2.69616 385 1.0140 384.72 0.7271 274.30 1.3946 12.5866 20.3954 2.70941 390 1.0148 389.79 0.7279 277.94 1.3942 13.1741 ~9.7389 2.72251 395 1.0156 394.87 0.7287 281.58 1.3938 13.7814 19.1109 2.73544 400 1.0164 399.95 0.7295 285.23 1.3933 14.4091 18.5097 2.74822

405 1.0172 405.03 0.7303 288.88 1.3929 15.0576 17.9340 2.76086 410 1.0180 410.12 0.7311 292.53 1.3925 15.7274 17.3823 2.77335 415 1.0189 415.21 0.7319 296.19 1.3920 16.4188 16.8533 2.78570 420 1.0197 420.31 0.7328 299.85 1.3916 17.1324 16.3460 2.79791 425 1.0205 425.41 0.7336 303.52 1.3911 17.8686 15.8590 2.80998

Page 39: Appendices - Springer LINK

748 Appendix A-3

Table A-3-1 Low-Density Air (51) (Continued)

Specific Specific Internal Specific Heat Enthalpy Heat Energy Heat Pressure Volume

Temp kJ/kg' K kJ/kg kJ/kg' K kJ/kg Ratio Ratio Ratio cf> K cp h Cu u k p* v* kJ/kg' K

430 1.0214 430.51 0.7345 307.19 1.3907 18.6280 15.3915 2.82193 435 1.0223 435.62 0.7353 310.86 1.3902 19.4109 14.9424 2.83374 440 1.0231 440.74 0.7362 314.54 1.3897 20.2180 14.5109 2.84544 445 1.0240 445.85 0.7371 318.23 1.3893 21.0496 14.0960 2.85700 450 1.0249 450.98 0.7380 321.91 1.3888 21.9063 13.6969 2.86845

455 1.0258 456.lO 0.7389 325.61 1.3883 22.7887 13.3128 2.87979 460 1.0267 461.23 0.7398 329.30 1.3878 23.6972 12.9432 2.89101 465 1.0276 466.37 0.7407 333.01 1.3874 24.6323 12.5871 2.90211 470 1.0286 471.51 0.7416 336.71 1.3869 25.5946 12.2442 2.91311 475 1.0295 476.66 0.7426 340.42 1.3864 26.5846 11.9136 2.92400

480 1.0304 481.81 0.7435 344.14 1.3859 27.6028 11.5949 2.93479 485 1.0314 486.96 0.7444 347.86 1.3854 28.6499 11.2875 2.94548 490 1.0323 492.12 0.7454 351.59 1.3849 29.7264 10.9909 2.95606 495 1.0333 497.28 0.7464 355.32 1.3844 30.8328 10.7046 2.96655 500 1.0342 502.45 0.7473 359.05 1.3839 31.9697 10.4282 2.97694

505 1.0352 507.63 0.7483 362.79 1.3834 33.1377 10.1613 2.98724 510 1.0362 512.81 0.7493 366.54 1.3830 34.3373 9.9034 2.99745 515 1.0372 517.99 0.7502 370.29 1.3825 35.5693 9.6541 3.00757 520 1.0381 523.18 0.7512 374.04 1.3820 36.8341 9.4131 3.01759 525 1.0391 528.37 0.7522 377.80 1.3814 38.1324 9.1800 3.02754

530 1.0401 533.57 0.7532 381.56 1.3809 39.4648 8.9546 3.03739 535 1.0411 538.77 0.7542 385.33 1.3804 40.8319 8.7364 3.04717 540 1.0421 543.98 0.7552 389.11 1.3799 42.2343 8.5253 3.05686 545 1.0431 549.20 0.7562 392.89 1.3794 43.6727 8.3208 3.06647 550 1.0441 554.41 0.7572 396.67 1.3789 45.1477 8.1228 3.07600 .

555 1.0452 559.64 0.7582 400.46 1.3784 46.6601 7.9310 3.08546 560 1.0462 564.87 0.7593 404.26 1.3779 48.2104 7.7451 3.09484 565 1.0472 570.10 0.7603 408.06 1.3774 49.7993 7.5649 3.10415 570 1.0482 575.34 0.7613 411.86 1.3769 51.4275 7.3902 3.11338 575 1.0493 580.58 0.7623 415.67 1.3764 53.0956 7.2208 3.12254

600 1.0545 607.38 0.7675 435.30 1.3738 62.0154 6.4511 3.16711 625 1.0597 633.86 0.7728 454.61 1.3713 72.0802 5.7815 3.21027 650 1.0651 660.48 0.7781 474.05 1.3687 83.3462 5.2000 3.25195 675 1.0704 687.22 0.7835 493.63 1.3662 95.9135 4.6925 3.29226 700 1.0758 714.11 0.7889 513.35 1.3637 109.8880 ·4.2474 3.33130

725 1.0812 741.13 0.7943 533.19 1.3612 125.3818 3.8555 3.36915 750 1.0866 768.28 0.7996 553.18 1.3588 142.5124 3.5090 3.40591 775 1.0919 795.57 0.8050 573.29 1.3564 161.4037 3.2016 3.44164 800 1.0973 822.99 0.8103 593.54 1.3541 182.1859 2.9279 3.47640 825 1.1025 850.54 0.8156 613.92 1.3518 204.9956 2.6834 3.51025

Page 40: Appendices - Springer LINK

Low-Density Air (5i) 749

Table A-3-1 Low-Density Air (51) (Continued)

Specific Specific Internal Specific Heat Enthalpy Heat Energy l-leat Pressure Volume

Temp kJ/kg· K kJ/kg kJ/kg· K kJ/kg Ratio Ratio Ratio cf> K cp h Cu u k p* v* kJ/kg· K

850 1.1078 878.22 0.8209 634.44 1.3495 229.9759 2.4644 3.54325 875 1.1130 906.03 0.8260 655.08 1.3474 257.2771 2.2677 3.57545 900 1.1181 933.97 0.8312 675.85 1.3452 287.0562 2.0905 3.60688 925 1.1231 962.04 0.8362 696.75 1.3431 319.4775 1.9305 3.63759 950 1.1281 990.23 0.8412 717.77 1.3411 354.7121 1.7858 3.66762

975 1.1330 1018.54 0.8460 738.91 1.3391 392.9391 1.6545 3.69699 1000 1.1378 1046.97 0.8508 760.17 1.3372 434.3443 1.5351 3.72575 1025 1.1424 1075.52 0.8555 781.55 1.3354 479.1220 1.4264 3.75391 1050 1.1470 1104.19 0.8601 803.04 1.3336 527.4736 1.3273 3.78150 1075 1.1515 1132.96 0.8646 824.65 1.3319 579.6073 1.2367 3.80855

1100 1.1559 1161.85 0.8690 846.36 1.3302 635.7429 1.1537 3.83508 1125 1.1602 1190.84 0.8733 868.19 1.3286 696.1030 1.0776 3.86112 1150 1.1644 1219.94 0.8775 890.12 1.3270 760.9244 1.0077 3.88667 1175 1.1685 1249.14 0.8815 912.14 1.3255 830.4458 0.9434 3.91176 1200 1.1724 1278.44 0.8855 934.27 1.3240 904.9194 0.8842 3.93641

1225 1.1763 1307.83 0.8894 956.50 1.3226 984.6049 0.8296 3.96063 1250 1.1800 1337.32 0.8931 978.81 1.3213 1069.7660 0.7791 3.98444 1275 1.1837 1366.90 0.8967 1001.22 1.3200 1160.6820 0.7324 4.00785 1300 1.1872 1396.56 0.9002 1023.72 1.3187 1257.6350 0.6892 4.03087 1325 1.1906 1426.32 0.9037 1046.30 1.3175 1360.9180 0.6492 4.05353

1350 1.1939 1456.15 0.9070 1068.97 1.3164 1470.8360 0.6120 4.07582 1375 1.1971 1486.07 0.9102 1091.71 1.3152 1587.6960 0.5774 4.09776 1400 1.2002 1516.06 0.9133 1114.53 1.3142 1711.8180 0.5453 4.11936 1425 1.2032 1546.13 0.9163 1137.43 1.3131 1843.5370 0.5154 4.14064 1450 1.2061 1576.26 0.9192 1160.40 1.3122 1983.1850 0.4875 4.16160

1475 1.2089 1606.47 0.9220 1183.44 1.3112 2131.1110 0.4615 4.18224 1500 1.2116 1636.75 0.9247 1206.55 1.3103 2287.6740 0.4372 4.20259 1525 1.2142 1667.09 0.9273 1229.72 1.3094 2453.2380 0.4145 4.22264 1550 1.2167 1697.50 0.9298 1252.95 1.3086 2628.1760 0.3932 4.24241

1575 1.2191 1727.96 0.9322 1276.25 1.3078 2812.8800 0.3733 4.26190

1600 1.2215 1758.49 0.9346 1299.60 1.3070 3007.7320 0.3547 4.28113 1625 1.2238 1789.07 0.9368 1323.01 1.3063 3213.1540 0.3372 4.30009

1650 1.2260 1819.70 0.9390 1346.48 1.3056 3429.5480 0.3208 4.31879

1675 1.2281 1850.39 0.9412 1370.00 1.3049 3657.3480 0.3054 4.33725 1700 1.2301 1881.13 0.9432 1393.57 1.3042 3896.9740 0.2909 4.35546

1725 1.2321 1911.92 0.9452 1417.19 1.3036 4148.8930 0.2772 4.37344 1750 1.2340 1942.76 0.9471 1440.85 1.3030 4413.5360 0.2644 4.39119 1775 1.2359 1973.64 0.9489 1464.57 1.3024 4691.3870 0.2523 4.40871 1800 1.2377 2004.57 0.9507 1488.33 1.3018 4982.9140 0.2409 4.42601 1825 1.2394 203).54 0.9525 1512.13 1.3012 5288.5970 0.2301 4.44310

Page 41: Appendices - Springer LINK

750 Appendix A-3

Table A-3-1 Low-Density Air (51) (Continued)

Specific Specific Internal Specific Heat Enthalpy Heat Energy Heat Pressure Volume

Temp kJ/kg' K kJ/kg kJ/kg' K kJ/kg Ratio Ratio Ratio cf>

K Cp h Cv u k p* v* kJ/kg' K

1850 1.2411 2066.56 0.9542 1535.97 1.3007 5608.9530 0.2199 4.45998 1875 1.2427 2097.61 0.9558 1559.86 1.3002 5944.4850 0.2103 4.47666 1900 1.2443 2128.71 0.9574 1583.78 1.2997 6295.6930 0.2012 4.49313 1925 1.2458 2159.84 0.9589 1607.74 1.2992 6663.1380 0.1926 4.50941 1950 1.2473 2191.01 0.9604 1631.74 1.2988 7047.3410 0.1845 4.52550

1975 1.2488 2222.22 0.9619 1655.78 1.2983 7448.8710 0.1768 4.54140 2000 1.2502 2253.46 0.9633 1679.85 1.2979 7868.3150 0.1695 4.55712 2025 1.2516 2284.74 0.9647 1703.96 1.2974 8306.2150 0.1626 4.57267 2050 1.2530 2316.05 0.9661 1728.10 1.2970 8763.1770 0.1560 4.58804 2075 1.2543 2347.39 0.9674 1752.28 1.2966 9239.7930 0.1497 4.60324

2100 1.2557 2378.77 0.9687 1776.48 1.2962 9736.7040 0.1438 4.61827 2125 1.2569 2410.18 0.9700 1800.72 1.2958 10254.5400 0.1382 4.63315 2150 1.2582 2441.62 0.9713 1825.00 1.2954 10793.9200 0.1328 4.64786 2175 1.2594 2473.10 0.9725 1849.30 1.2950 11355.5100 0.1277 4.66241 2200 1.2607 2504.60 0.9738 1873.63 1.2947 11939.9900 0.1229 4.67682

Page 42: Appendices - Springer LINK

Saturated Air: Temperature Table (SI) 751

Table A-3-2 Saturated Air: Temperature Table (SI)

Pressure Volume Density Enthalpy Entropy Temp Liquid Vapor Vapor Liquid Liquid Vapor Liquid Vapor

K MPa MPa m3 /kg m3/kg kJ/kg kJ/kg kJ/kg' K kJ/kg' K

60 0.00655 0.00250 6.876 947.39 -144.89 59.72 2.726 6.315 61 0.00791 0.00319 5.480 943.51 -145.46 60.70 2.717 6.261 62 0.00950 0.00402 4.408 939.58 -145.70 61.66 2.713 6.210 63 0.01134 0.00504 3.578 935.59 -145.64 62.62 2.714 6.162 64 0.01346 0.00625 2.928 931.56 -145.33 63.58 2.719 6.115

65 0.01589 0.00768 2.415 927.48 -144.82 64.53 2.727 6.070 66 0.01867 0.00938 2.006 923.36 -144.12 65.47 2.737 6.028 67 0.02183 0.01137 1.679 919.20 -143.26 66.40 2.750 5.987 68 0.02542 0.01368 1.414 915.01 -142.28 67.32 2.765 5.948 69 0.02946 0.01636 1.198 910.77 -141.17 68.24 2.781 5.911

70 0.03399 0.01945 1.021 906.51 -139.96 69.14 2.798 5.875 71 0.03908 0.02297 0.8754 902.21 -138.66 70.03 2.816 5.840 72 0.04475 0.02699 0.7543 897.88 -137.29 70.91 2.835 5.807 73 0.05105 0.03154 0.6532 893.51 -135.85 71.78 2.855 5.775 74 0.05804 0.03667 0.5683 889.11 -134.34 72.64 2.876 5.744

75 0.06576 0.04243 0.4966 884.68 -132.78 73.48 2.896 5.714 76 0.07426 0.04888 0.4358 880.22 -131.18 74.31 2.918 5.685 77 0.08361 0.05606 0.3840 875.73 -129.53 75.12 2.939 5.658 78 0.09384 0.06404 0.3396 871.20 -127.84 75.92 2.961 5.631 79 0.10503 0.07286 0.3014 866.64 -126.12 76.70 2.982 5.605

80 0.11722 0.08259 0.2685 862.05 -124.37 77.46 3.004 5.580 81 0.13048 0.09328 0.2399 857.41 -122.58 78.21 3.026 5.555 82 0.14486 0.10500 0.2150 852.75 -120.78 78.94 3.048 5.531 83 0.16043 0.11780 0.1932 848.04 -118.94 79.65 3.070 5.508 84 0.17725 0.13176 0.1742 843.30 -117.08 80.34 3.092 5.486

85 0.19538 0.14693 0.1574 838.51 -115.20 81.01 3.114 5.464 86 0.21488 0.16339 0.1426 833.68 -113.30 81.66 3.136 5.443 87 0.23582 0.18119 0.1295 828.81 -111.38 82.29 3.158 5.422 88 0.25826 0.20041 0.1179 823.90 -109.45 82.90 3.180 5.402 89 0.28227 0.22112 0.1075 818.93 -107.49 83.49 3.202 5.383

90 0.30790 0.24338 0.09828 813.92 -105.52 84.05 3.223 5.363 91 0.33524 0.26727 0.09001 808.85 -103.53 84.59 3.245 5.344 92 0.36435 0.29286 0.08258 803.73 -101.52 85.10 3.267 5.326 93 0.39529 0.32022 0.07590 798.56 -99.49 85.59 3.288 5.308 94 0.42812 0.34942 0.06988 793.32 -97.45 86.05 3.309 5.290

Source: ASH RAE 1981 Fundamentals Handbook, with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, Ga.

Page 43: Appendices - Springer LINK

752 Appendix A-3

Table A-3-2 Saturated Air: Temperature Table (51) (Continued)

Pressure Volume Density Enthalpy Entropy Temp Liquid Vapor Vapor Liquid Liquid Vapor Liquid Vapor

K MPa MPa m3/kg m3/kg kJ/kg kJ/kg kJ/kg· K kJ/kg· K

95 0.46292 0.38054 0.06444 788.02 -95.39 86.49 3.331 5.272 96 0.49975 0.41365 0.05951 782.66 -93.32 86.90 3.352 5.255 97 0.53867 0.44883 0.05503 777.22 -91.23 87.28 3.373 5.238 98 0.57976 0.48615 0.05097 771.72 -89.12 87.62 3.394 5.222 99 0.62308 0.52570 0.04726 766.13 -86.99 87.94 3.415 5.205

100 0.66869 0.56753 0.04388 760.47 -84.84 88.23 3.436 5.189 101 0.71666 0.61174 0.04078 754.72 -82.68 88.48 3.457 5.173 102 0.76706 0.65840 0.03795 748.88 -80.49 88.70 3.478 5.157 103 0.81994 0.70758 0.03535 742.94 -78.28 88.89 3.499 5.141 104 0.87538 0.75937 0.03295 736.90 -76.06 89.03 3.520 5.126

105 0.93343 0.81385 0.03075 730.75 -73.80 89.14 3.540 5.110 106 0.99416 0.87108 0.02872 724.49 -71.53 89.21 3.561 5.094 107 1.0576 0.93116 0.02685 718.10 -69.23 89.24 3.582 5.079 108 1.1239 0.99417 0.02511 711.58 -66.90 89.22 3.603 5.064 109 1.1931 1.06017 0.02350 704.91 -64.54 89.16 3.624 5.048

110 1.2651 1.12926 0.02201 698.09 -62.16 89.05 3.644 5.033 111 1.3402 1.20151 0.02062 691.10 -59.74 88.89 3.665 5.018 112 1.4183 1.27701 0.01933 683.94 -57.28 88.67 3.686 5.002 113 1.4995 1.35583 0.01813 676.57 -54.78 88.40 3.708 4.987 114 1.5838 1.43807 0.01701 668.99 -52.25 88.07 3.729 4.971

115 1.6714 1.52380 0.01596 661.18 -49.67 87.67 3.750 4.955 116 1.7623 1.61312 0.01497 653.10 -47.03 87.20 3.772 4.939 117 1.8565 1.70612 0.01405 644.74 -44.35 86.65 3.794 4.923 118 1.9540 1.80288 0.01318 636.05 -41.60 86.02 3.816 4.906 119 2.0551 1.90350 0.01237 627.00 -38.78 85.31 3.838 4.889

120 2.1596 2.00808 0.01159 617.53 -35.89 84.49 3.861 4.872 121 2.2677 2.11673 0.01087 607.59 -32.91 83.56 3.884 4.854 122 2.3794 2.22958 0.01017 597.09 -29.82 82.50 3.908 4.836 123 2.4948 2.34673 0.009518 585.94 -26.62 81.30 3.933 4.817 124 2.6139 2.46835 0.008890 574.01 -23.27 79.93 3.958 4.796

126 2.8635 2.72567 0.007708 547.03 -16.01 76.57 4.013 4.752 128 3.1288 3.00345 0.006590 513.58 -7.58 71.98 4.075 4.701 130 3.4103 3.30541 0.005469 466.98 3.24 65.13 4.154 4.634 132 3.7089 3.64552 0.004068 384.50 20.94 50.73 4.284 4.511 *132.42 3.774 3.733 0.00348 364. 25.5 41.3 4.32 4.44 t132.52 3.766 0.00309 33.6 4.38

* Maximum pressure. t Maximum temperature.

Page 44: Appendices - Springer LINK

Saturated Air: Pressure Table (51) 753

Table A-3-3 Saturated Air: Pressure Table (51)

Temp, K Volume, m3/kg Enthalpy, kJ/kg Entropy, kJ/kg' K Pressure atm Liquid Vapor Liquid Vapor Liquid Vapor Liquid Vapor

1 78.8 81.8 0.01144 0.22295 0 205.18 0 2.5552 2 85.55 88.31 0.00119 0.11703 12.051 210.50 0.14468 2.4275 3 90.94 92.63 0.00122 0.08008 20.200 213.26 0.23515 2.3491 5 96.38 98.71 0.00128 0.04930 31.975 215.85 0.35877 2.2478

7 101.04 103.16 0.00132 0.03554 41.298 216.85 0.45062 2.1699 10 106.47 108.35 0.00138 0.02481 53.490 216.99 0.56423 2.0863 15 113.35 114.91 0.00149 0.01605 71.236 215.23 0.71927 1.9810 20 118.77 120.07 0.00161 0.01141 87.258 214.43 0.85186 1.8909

25 123.30 124.41 0.00174 0.00852 102.42 205.80 0.96961 1.8042 30 127.26 128.12 0.00192 0.00644 117.82 198.20 1.0843 1.7141 35 130.91 131.42 0.00224 0.00463 135.70 186.43 1.2224 1.6091 37.17 132.52 0.00313 164.19 1.4282

Source: Adapted from ASH RAE 1981 Fundamentals Handbook, with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, Ga.

Page 45: Appendices - Springer LINK

754 Appendix A-3

Table A-3-4 Superheated Air (51)

p (atm) Temperature, K

90 100 110 120 130 140 150 160 1 v 0.24758 0.27731 0.30669 0.33584 0.36481 0.39365 0.42241 0.45110

h 213.74 224.21 234.63 244.99 255.35 265.71 276.00 289.71 s 2.6554 2.7655 2.8650 2.9558 3.0390 3.1157 3.1865 3.2528

3 v 0.08823 0.09883 0.10908 0.11920 0.12914 0.13902 0.14883 h 221.27 232.04 242.78 253.45 263.98 274.45 284.88

2.4323 2.5349 2.6285 2.7137 2.7918 2.8640 2.9312

10 v 0.02551 0.02942 0.03305 0.03650 0.03978 0.04299 h 219.37 232.73 245.10 256.87 268.34 279.55

2.1080 2.2244 2.3235 2.4109 2.4900 2.5625

50 v 0.00148 0.00178 0.00267 0.00498 0.00649 h 72.790 108.53 162.22 213.71 240.06 s 0.70442 0.98999 1.3878 1.7441 1.9140

100 v 0.00141 0.00154 0.00174 0.00203 0.00249 h 69.924 97.790 127.55 158.81 189.36

0.62120 0.84427 1.0649 1.2804 1.4776

v [=] m3/kg h [=] kJ/kg s [=] kJ/kg· K Source: Adapted from ASHRAE 1981 Fundamentals Handbook, with permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, Ga.

Page 46: Appendices - Springer LINK

Superheated Air (51) 755

Temperature, K

170 180 190 200 220 240 260 280 300 0.47973 0.50828 0.53684 0.56537 0.62234 0.67928 0.73615 0.79299 0.84979

296.48 306.69 316.89 327.04 347.27 367.44 387.57 407.67 427 .76 3.3149 3.3733 3.4282 3.4807 3.5773 3.6637 3.7465 3.8191 3.8881

0.15856 0.16827 0.17794 0.18757 0.20677 0.22590 0.24503 0.26409 0.28311 295.23 305 .56 315.85 326.10 346.51 366.78 387.02 407.18 427.35

2.9941 3.0532 3.1088 3.1613 3.2583 3.3467 3.4278 3.5024 3.5218

0.04617 0.04924 0.05231 0.05535 0.06133 0.06723 0.07314 0.07897 0.08477 290.57 301.42 312.15 322.79 343.75 364.47 385.05 405.52 425.93

2.6291 2.6910 2.7490 2.8035 2.9033 2.9934 3.0760 3.1519 3.2224

0.00752 0.00843 0.00927 0.01006 0.01154 0.01294 0.01427 0.01558 0.01685 258.81 274.76 289.05 302.35 327.24 350.83 373.65 395.92 417.82

2.0276 2.1188 2.1961 2.2642 2.3829 2.4835 2.5770 2.6595 2.7352

0.00305 0.00361 0.00412 0.00460 0.00548 0.00628 0.00704 0.00776 0.00845 216.09 238.78 258.39 275.79 306.46 334.01 359.77 384.32 408.08

1.6395 1.7690 1.8750 1.9641 2.1105 2.2303 2.3332 2.4240 2.5059

so Temperature- ~~tb ";'i f£,)#> ~b\.oo lIdJ"vI'~ ,... entropy diagram

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Page 47: Appendices - Springer LINK

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-14

6.6

91

2\

3.29

1 66

.600

2.

4845

3.

2849

5.

7694

70

0.

0385

8 0.

001

189

0.52

5785

0.

5269

74

-13

6.56

9 20

7.72

7 71

.158

2.

6345

2.

9703

5.

6048

75

0.

0761

2 0.

0012

21

0.28

0970

0.

2821

91

-12

6.2

87

20

1.66

2 75

.375

2.

7755

2.

6915

5.

4670

77

.35

0.10

1325

0.

0012

37

0.21

5504

0.

2167

41

-12

1.43

3 19

8.64

5 77

.212

2.

8390

2.

5706

5.

4096

80

0.

1370

0.

0012

56

0.16

2794

0.

164

050

-11

5.9

26

19

5.08

9 79

.163

2.

9083

2.

4409

5.

3492

85

0.

2291

0.

001

296

0.10

0434

0.

1017

30

-10

5.46

1 18

7.89

2 82

.431

3.

0339

2.

2122

5.

2461

90

0.

3608

0.

0013

40

0.06

4 95

0 0.

0662

90

-94

.81

7

179.

894

85.0

77

3.15

35

2.00

01

5.15

36

95

0.54

11

0.00

1392

0.

0435

04

0.04

4 89

6 -8

3.8

95

17

0.87

7 86

.982

3.

2688

1.

7995

5.

0683

10

0 0.

7790

0.

0014

52

0.02

9861

0.

0313

13

-72

.57

1

160.

562

87.9

91

3.38

16

1.60

60

4.98

76

105

1.08

43

0.00

1 52

4 0.

0207

45

0.02

2269

-6

0.6

91

14

8.57

3 87

.882

3.

4930

1.

4150

4.

9080

11

0 1.

4673

0.

0016

13

0.01

4402

0.

0160

15

-41

(02

7

134.

319

86.2

92

3.60

54

1.22

09

4.82

63

115

1.93

95

0.00

1797

0.

009

696

0.01

1493

-

34.1

57

116.

701

82.5

44

3.72

14

1.01

45

4.73

59

120

2.51

35

0.00

1904

0.

0061

30

0.00

8034

-1

8.0

17

93

.092

75

.075

3.

8450

0.

7803

4.

6253

12

5 3.

2079

0.

0023

23

0.00

2568

0.

0048

91

+6.

202

50.1

14

56.3

16

4.03

56

0.39

89

4.43

45

126.

1 3.

4000

0.

0031

84

0.00

0000

O

.()(iJ

184

+

30.

791

0.00

0 30

.791

4.

2269

0.

0000

4.

2269

Page 48: Appendices - Springer LINK

Tab

le A

-4-2

S

up

erh

ea

ted

Nit

rog

en

., It

s .,

It J

., It

s

Tem

p.

m3/k

g k

J/k

g

kJ/

kg

K

m·l

/kg

k.J/

kg

kJ/

kg

K

m3/k

g k

J/k

g

kJ/

kg

K

K

0.1

MP

a 0.

2 M

Pa

0.5

MP

a

100

0.29

0978

10

1.96

5 5.

6944

0.

1424

75

100.

209

5.47

67

0.05

5520

94

.345

5.

1706

12

5 0.

3672

17

128.

505

5.93

13

0.18

1711

12

7.37

1 5.

7194

0.

0734

22

123.

824

5.43

43

150

0.44

2619

15

4.77

9 6.

1228

0.

2200

14

153.

962

5.91

32

0.09

0150

15

1.47

0 5.

6361

17

5 0.

5175

76

180.

935

6.28

41

0.25

7 X

90

180.

314

6.07

60

0.10

6 39

4 17

8.43

4 5.

8025

20

0 0.

592

288

207.

029

6.42

34

0.29

5531

20

6.53

7 6.

2160

0.

122

394

205.

063

5.94

47

225

0.66

6552

23

3.08

5 6.

5460

0.

3328

41

232.

690

6.33

88

0.13

8173

23

1.45

9 6.

0690

25

0 0.

7413

75

259.

122

6.65

61

0.37

0418

25

8.79

6 6.

4491

0.

1540

06

257.

828

6.18

01

275

0.81

5563

28

5.14

4 6.

7550

0.

4076

19

284.

876

6.54

85

0.16

9642

28

4.07

6 6.

2800

30

0 0.

8902

05

311.

158

6.84

57

0.44

5047

31

0.93

7 6.

6393

0.

1853

46

310.

273

6.37

15

1.0

MP

a 2.

0 M

Pa

4.0

MP

a

125

0.03

3065

11

7.42

2 5.

1872

0.

0140

21

101.

489

4.88

78

150

0.04

1884

14

7.17

6 5.

4042

0.

0195

46

137.

916

5.15

47

0.00

8234

11

5.71

6 4.

8384

17

5 0.

0501

25

175.

255

5.57

79

0.02

4155

16

8.70

9 5.

3449

0.

011

186

154.

851

5.08

04

200

0.05

8096

20

2.59

6 5.

7237

0.

0284

36

197.

609

5.49

92

0.01

3648

18

7.52

1 5.

2553

22

5 0.

0658

75

229.

526

5.85

02

0.03

2697

22

5.57

8 5.

6309

0.

0158

94

217.

757

5.39

76

250

0.07

3634

25

6.22

0 5.

9632

0.

0365

57

253.

032

5.74

69

0.01

8060

24

6.79

3 5.

5202

27

5 0.

0812

60

282.

720

6.06

39

0.04

0485

28

0.13

2 5.

8501

0.

0201

33

275.

056

5.62

77

300

0.08

8899

30

9.17

3 6.

1563

0.

044

398

307.

014

5.94

36

0.02

2178

30

2.84

8 5.

7248

Page 49: Appendices - Springer LINK

Tab

le A

-4-2

S

uper

heat

ed N

itro

ge

n (

Co

ntin

ue

d)

6.0

MP

a 8.

0 M

Pa

10.0

MP

a

150

0.00

4 41

3 87

.090

4.

5667

0.

0029

17

61.9

03

4.35

18

0.00

2388

48

.687

4.

2287

17

5 0.

006

913

140.

183

4.89

66

0.00

4 86

3 12

5.53

6 4.

7470

0.

0037

50

112.

489

4.62

39

200

0.00

8772

17

7.44

7 5.

0961

0.

006

390

167.

680

4.97

26

0.00

5016

15

8.57

8 4.

8709

22

5 0.

0103

96

210.

139

5.24

10

0.00

7691

20

2.86

7 5.

1384

0.

0061

04

196.

079

5.04

74

250

om I

934

240.

1010

6 5.

3796

0.

0089

03

235.

141

5.27

50

0.00

7112

22

9.86

1 5.

1900

27

5 0.

013

383

270.

222

5.49

17

0.01

0034

26

5.67

6 5.

3910

0.

0080

46

261.

450

5.31

03

300

0.01

4800

29

8.90

7 5.

5916

0.

011

133

295.

219

5.49

42

0.00

8950

29

1.80

0 5.

4163

15.0

MP

a 20

.0 M

PIl

150

0.00

1956

36

.922

4.

0798

0.

0017

81

33.6

37

3.99

56

175

0.00

2603

92

.284

4.

4213

0.

0021

86

83.4

53

4.30

29

200

0.00

3369

14

0.88

6 4.

6813

0.

0026

85

130.

291

4.55

35

225

0.00

4 10

6 18

2.03

4 4.

8752

0.

0032

08

172.

307

4.75

11

250

0.00

4 80

8 21

8.71

0 5.

0303

0.

0037

28

210.

456

4.91

27

275

0.00

5461

25

2.46

5 5.

1845

0.

004

223

245.

640

5.04

67

300

0.00

6091

28

4.52

3 5.

2707

0.

004

704

278.

942

5.16

29

Page 50: Appendices - Springer LINK

Appendix A-5 759

Appendix A-5 Critical Constants

AS-l Critical Constants table

Molecular Temp. Pressure Volume Substance Formula Weight K MPa m3/kg-mol

Ammonia NH3 17.03 405.5 11.28 .0724 Argon Ar 39.948 151 4.86 .0749 Bromine Br2 159.808 584 10.34 .1355 Carbon Dioxide CO2 44.01 304.2 7.39 .0943 Carbon Monoxide CO 28.011 133 3.50 .0930 Chlorine CI2 70.906 417 7.71 .1242 Deuterium (normal) O2 4.00 38.4 1.66 Helium He 4.003 5.3 0.23 .0578 Helium3 He 3.00 3.3 0.12 Hydrogen (normal) H2 2.016 33.3 1.30 .0649 Krypton Kr 83.80 209.4 5.50 .0924 Neon Ne 20.183 44.5 2.73 .0417 Nitrogen N2 28.013 126.2 3.39 .0899 Nitrous Oxide N20 44.013 309.7 7.27 .0961 Oxygen O2 31.999 154.8 5.08 .0780 Sulfur Dioxide S02 64.063 430.7 7.88 .1217 Water H2O 18.015 647.3 22.09 .0568 Xenon Xe 131.30 289.8 5.88 .1186 Benzene C6 H6 78.115 562 4.92 .2603 n-Butane C4H lO 58.124 425.2 3.80 .2547 Carbon Tetrachloride CCI4 153.82 556.4 4.56 .2759 Chloroform CHCI3 119.38 536.6 5.47 .2403 Dichlorodifluoromethane CCI2F 2 120.91 384.7 4.01 .2179 Dichlorofluoromethane CHCI2F 102.92 451.7 5.17 .1973 Ethane C2H6 30.070 305.5 4.88 .1480 Ethyl Alcohol C2HsOH 46.07 516 6.38 .1673 Ethylene C2H4 28.054 282.4 5.12 .1242 n-Hexane C6 HI4 86.178 507.9 3.03 .3677 Methane CH4 16.043 191.1 4.64 .0993 Methyl Alcohol CH30H 32.042 513.2 7.95 .1180 Methyl Chloride CH3CI 50.488 416.3 6.68 .1430 Propane C3HS 44.097 370 4.26 .1998 Propene C3H6 42.081 365 4.62 .1810 Propyne C3H4 40.065 401 5.35 Trichlorofluoromethane CCI3F 137.37 471.2 4.38 .2478

Page 51: Appendices - Springer LINK

760 Appendix A--6

Appendix A-6

Gas*

Air CO CO2

N2

O2

Approximate Values of CPI CV1 and R

Cp Cv

kJ kJ kg·K kg·K

1 0.716 1.04 0.749 0.85 0.665 1.04 0.737 0.917 0.661

* Assumed to be an ideal gas at low pressure

R

kJ kg·K

0.287 0.297 0.189 0.296 0.260

Source: Adapted from the 1977 Fundamentals Volume, ASHRAE Handbook and Product Directory, with permission of the American Society of Heating, Refrigerating and Air-Conditioning.Engineers, Atlanta, Ga.

Page 52: Appendices - Springer LINK

Appendix

Appendix B 761

B More History

Democritus (460 Bc?-370 BC?, Greek) was a great philosopher of the physical world. In addition to his interests in theology, ethics, and religion, he was a founder of the atomic theory. To his way of thinking, atoms were external, invisible, and the basic building blocks of the universe (that is, atoms were indivisible). He believed that atoms were of different sizes, shapes, weights, and configurations and always in chaotic motion.

Epicurus (341-270 BC, Greek) continued the teaching and philosophy of Demo­critus, although his primary claim to fame was in ethical thought.

Galileo Galilei (1564-1642, Italian) invented a thermometer in 1592, but it did not have a well-founded scale.

Otto von Guericke (1602-1686, German) brilliantly demonstrated, before the em­peror at Regensburg in 1654, that he could produce a vacuum with his experiment of the Magdeburg hemispheres.

Evangelista Torricelli (1608-1647, Italian), a student of Galileo, was primarily a mathematician. But his pioneering work, which correctly distinguished between weight and pressure and demonstrated that air has weight, was fundamental in the beginnings of thermodynamics.

Edme Mariotte (1620-1684, French) was a scientist who independently discovered Boyle's law.

Blaise Pascal (1623-1662, French), a theologian and mathematician (probability theory), also conducted experiments with fluids, primarily to study pressure.

Robert Boyle (1627-1691, English) was the most famous scientist of his day (like Newton, 20 years later). He developed a vacuum pump and deduced his ideal-gas law (pIT = constant) in 1662. Besides his scientific endeavors, he led the life of a courtier and public figure. He was also a devout Christian and biblical scholar who endeavored to show that religion and science were not only reconcilable but integrally related.

Robert Hooke (1635-1703, English) was an experimentalist. While working for Robert Boyle, he constructed an air pump and studied combustion.

Sir Isaac Newton (1642-1727, English), often credited with being the greatest scientist of all time, invented a thermometer in 1720 long before the discovery of the first law of thermodynamics. He proposed a scale with zero for the ice point and 12 for the normal human body temperature. He credited his scientific success to hard work and patient thought.

Gottfried Wilhelm Leibnitz (1646-1716, German), a brillant and influential man of his day, made contributions in many areas of science and mathematics. He directly contributed to the development of the first law of thermodynamics, proposed the invention of a barometer with mercury, and studied the steam engine.

G. Amontons (1663-1705, French) made major contributions to thermometry in two papers in 1702 and 1703.

Page 53: Appendices - Springer LINK

762 Appendix B

Gabriel Daniel Fahrenheit (1686-1736, German) was the first to use mercury-in­glass thermometers indicating the temperature in degrees. Fahrenheit's scale was a modification of one proposed by Sir Isaac Newton. Fahrenheit lowered the zero of Newton's scale to the temperature of a salt-ice mixture and made the degree smaller so that body temperature was 96. Measurements showed the ice and steam points to be at 32 and 212, respectively, based on the reference points at 0 and 96. Subsequently, 32 and 212 were adopted as reference points. Refinements in thermometers since that time have revealed that the minimum temperature of the salt-ice mixture and the normal body temperature are not exactly 0 and 96 on the present Fahrenheit scale.

Daniel Bernoulli (1700-1782, Swedish) came from several generations of distinguished scientists and mathematicians. He showed that the impact of molecules on the walls of a container could be used to describe pressure. In addition, he was the first to state Bernoulli's principle.

Anders Celsius (1704-1744, Swedish) was an astronomer from a distinguished scientific family. In 1742 he devised the thermometric scale used today that bears his name (formerly the Centigrade scale).

Joseph Black (1728-1799, Scottish) is best known for his enunciation of the concept of latent heat of transformation and his rediscovery of what turned out to be carbon dioxide.

James Watt (1736-1819, Scottish) was trained to be an instrument maker. While serving in this capacity at the University of Glasgow, he was called on to repair a model of a Newcomen steam engine. He improved the engine and in fact held patents on most of the basic features of the modern reciprocating steam engine. He also carried on extended research on the properties of steam, about which practically nothing was known at the time. After many attempts at building a commercially viable steam engine and many scrapes with financial disaster, Watt eventually manufactured a successful engine. Engines built by Boulton and Watt, Birmingham, played an important part in the industrial growth of Great Britain during the nineteenth century.

Antoine Laurent Lavoisier (1745-1794, French) was a great chemist who died in the purge of scientists in France in 1793. Among his many scientific achievements were the giving of modern names to the gases hydrogen (from "inflammable air") and nitrogen ("phlogisticated air") and the establishment of the modern nomenclature of chemistry.

Jacques Alexandre Cesar Charles (1746-1823, French) was an experimentalist and codiscoverer of the ideal-gas law relating volume and temperature (v/T = constant). Actually, it was not Charles who published a description of this gas behavior but Gay-Lussac.

Benjamin Thompson (1753-1814, American) was born in Woburn, Massachusetts, but was made a count of the Holy Roman Empire for the cannon-boring experiments he made while in Bavaria. In these experiments he discovered the equivalence of work and heat (1797) while boring solid metal submerged in water. He convinced himself, but not the world, that the caloric theory of heat (a theory that supposed heat to be a substance without mass) did not explain all known phenomena of heat and that work and heat were in some manner related.

John Dalton (1766-1844, English) was a self-taught scientist. Though color-blind (red), Dalton made most of his contributions in atomic theory and meteorology. His law of partial pressures was a major discovery.

Thomas J. Seebeck (1770-1831, Estonian) discovered the thermocouple in 1821. Although he was educated as a doctor of medicine at G6ttingen University in Germany, he chose to lecture and experiment in the physical sciences.

Joseph Louis Gay-Lussac (1778-1850, French) was a chemist who presented the ideas of Charles regarding thermal expansion of an ideal gas. Also to his credit, Gay-

Page 54: Appendices - Springer LINK

Appendix B 763

Lussac announced a "law" that gases combine chemically in simple proportions by volume. This idea was further extended by Dalton and Avogadro.

Jean-Charles-Athanase Peltier (1785-1845, French) discovered that the junction of two dissimilar metals will absorb or reject heat dependent on the direction of electrical current. Today this effect is the basis of a thermometer called the thermocouple.

The Reverend Robert Stirling (1790-1878, Scottish) was the first person to propose the use of regeneration in heat-engine cycles. He spent 29 years with his brother James designing, improving, and selling his "air engine." The Stirling brothers did not understand the thermodynamic reasons for regeneration (thermodynamics itself had not yet evolved). It was James who had the idea of closing and pressurizing the system, using gas at all times with pressure greater than atmospheric.

Nicholas Leonard Sadi Carnot (1796-1832, French), who lived during the turbulent Napoleonic period, was an officer in the French army engineers. In the only paper he published during his lifetime, "Reflections on the Motive Power of Heat," he devised and analyzed the Carnot cycle. In this paper, written when he was only 23 or 24, he originated the use of cycles in thermodynamic analysis and laid the foundations for the second law by describing and analyzing the Carnot cycle and stating the Carnot principle. Even though i).e employed the caloric theory in his reasoning, his conclusions are correct because the second law is a principle that is independent of the first law. Carnot's cycle is independent of the theory of heat as well as the working substance.

John Ericsson (1803-1889, Swedish) built a steam locomotive, the Novelty. Among his other inventions were the revolving naval gun turret, the marine screw propeller, and the steam fire engine. He is well known as the designer and builder of the ironclad Monitor used by the United States in answer to the Confederate Merrimac during the Civil War. Under Ericsson's supervision, the Monitor was built in only 126 days. During the last few years of his life, he was a recluse in New York City and a disbeliever in the telephone.

Julius Robert von l\fayer (1814-1878, German) independently deduced the first law of thermodynamics and properly applied this conservation law. Personal grief and lack of appreciation of his work prompted Mayer to attempt suicide. Although he was treated in a mental institute and released, his mind never completely recovered.

Alphonse-Eugene Beau de Rochas (1815-1893, French) was an engineer who originated the principle of the four-stroke internal combustion engine. He patented this idea in 1862 but did not develop the engine.

James Prescott Joule (1818-1889, English) inherited a large brewery in Manchester, England. His financial independence made it possible for him to devote his life to scientific research, chiefly in the fields of electricity and thermodynamics. His research was significant in the budding science of thermodynamics, in which he established two fundamental principles: one was the equivalence of heat and work; the other was the dependence of the internal energy change of an ideal gas on temperature change. As a result of this work, the modern kinetic theory of heat superseded the caloric theory of heat. Joule once remarked, "I believe I have done two or three little things, but nothing to make a fuss about."

William John MacQuom Rankine (1820-1872, Scottish), while a professor of civil engineering at the University of Glasgow, made several outstanding contributions to the development of thermodynamics-he was the first to write formally on the subject-and its engineering applications. He was a versatile genius and a prolific contributor to the engineering and scientific literature of his day.

Hermann Ludwig Ferdinand Helmholtz (1821-1894, German) is best known for his statement of the law of the conservation of energy (the first law of thermodynamics).

Rudolph Julius Emmanuel Clausius (1822-1888, German), a mathematical physicist, was a genius in mathematical investigations of natural phenomena. After a study of the work of Sadi Carnot, he presented in 1850 a clear general statement of the second law. He

Page 55: Appendices - Springer LINK

764 Appendix B

applied the second law and showed the value of the property he called entropy in an exhaustive treatise on steam engines. In addition, his work in the kinetic theory of gases prompted J. C. Maxwell to credit him with being its founder.

William Thomson (1824-1907, English), knighted Lord Kelvin, was professor of natural philosophy at the University of Glasgow for 53 years. He is said by some to be the greatest English physicist. Before his graduation from Cambridge, he had already estab­lished a reputation in scientific circles by his original thinking. He contributed most to the science of thermodynamics-having established a thermometric scale of absolute tempera­tures that is independent of the properties of any gas, having helped establish the first law of thermodynamics on a firm foundation, and having stated significantly the second law. In 1851, he presented a paper in which the first and second laws were wmbined for the first time.

Julius Thomsen (1826-1909, Danish) appears to be the first to have applied the first-law concept (conservation of energy) to the field of chemistry (1853).

Pierre Eugene Marcelin Berthelot (1827-1907, French) was a founder of ther­mochemistry and coined the terms exothermic and endothermic to describe whether heat leaves or is absorbed by a reaction.

George B. Brayton (1830-1892, American) invented a breech-loading gun, a rivet­ing machine, and a sectional steam generator in additiori to the internal combustion engine for which he is best remembered. The Brayton engine, developed around 1870, was a reciprocating oil-burning engine with fuel injection directly into the cylinder and a compressor that was separate from the power cylinder. Although his cycle was first used with reciprocating engines, it is now used only for gas turbines.

James Clerk MaxweU (1831-1879, Scottish), at the age of 15, presented a paper to the Royal Society of Edinburgh on the calculation of the refractive index of a material. By the time he was 29, he was a professor of natural philosophy at Kings College, London. He wrote on many scientific matters, but his greatest contributions were in electromagnetic theory. In thermodynamics, he contributed the Maxwell relations.

Nikolaus A. Otto (1832-1891, German), with his partner Eugen Langen, built a gas engine in 1867 in Dertz, Germany, and began marketing it. In 1876, Otto produced a successful four-stroke cycle engine that was far superior to any internal combustion engine previously built. The principle of the four-stroke cycle, however, had been worked out in 1862 by a Frenchman, Alphonse Beau de Rochas.

Gottlieb Wilhelm Daimler (1834-1900, German) patented, in 1885, the first high­speed internal combustion, vertical single-cylinder engine. In 1889, a twin-cylinder V-type engine was patented and used in French cars.

Johannes Diderik van der Waals (1837-1923, Dutch) worked in the area of thermodynamics that deals with the behavior of liquids and gases. Using the work of Clausius, van der Waals postulated the equation of state that bears his name. In 1910, he won a Nobel prize for this work.

Josiah Willard Gibbs (1839-1903, American) received from Yale University in 1863 the first Ph.D. in engineering awarded in America. He undoubtedly contributed more to the science of thermodynamics than any other American, not the least of which is the Gibbs phase rule, but the name of this man, one of the outstanding scientists of all time, is virtually unknown to the general public.

Sir James Dewar (1842-1923, Scottish), educated at Edinburgh University, was elected a professor at Cambridge and later at the Royal Institute in London. His major contributions were his studies of low-temperature phenomena and his invention of the vacuum flask (Dewar flask).

Ludwig Boltzmann (1844-1906, Austrian) had several great achievements­especially the development of statistical mechanics and the statistical explanation of the

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Appendix B 765

second law of thermodynamics. During his lifetime he made extensive calculations in the kinetic theory of gases and derived Stefan's law of blackbody radiation using ther­modynamics. His statistical approach to the entropy concept was monumental. In fact, the mathematical relation linking entropy and probability is carved on a monument at Boltzmann's grave.

Jacobus Hendricus van't Hoff (1852-1911, Dutch) was the first Nobel laureate in chemistry (1901). From his first publication in 1874 until his death, he was an active researcher in areas of chemistry that overlapped with thermodynamics.

Heike Kamerlingh Onnes (1853-1926, Dutch) won the 1913 Nobel prize for his successful experiment to produce liquid helium in 1908. His efforts to solidify helium failed, but his student, Willem Henduk Keesom, did succeed in 1926.

Sir Dugald Clerk (1854-1932, Scottish) invented the two-stroke Clerk cycle internal combustion engine used on light motorcycles. He built the engine i:1 1876 and patented the two-stroke engine in 1881.

KudoU Diesel (1858-1913, German) obtained in 1893 a patent on the type of engine that now bears his name. One of his engines blew up at the first injection of fuel and Diesel narrowly escaped being killed. Years of tedious and costly experiment elapsed before he produced a successful engine in 1899. He disappeared in 1913 while crossing the English Channel in a storm.

Max Karl Ernst Ludwig Planck (1858-1947, German) introduced the quantum theory in 1900 for which he won the Nobel prize in 1918. Planck worked on the writings of Clausius in the area of thermodynamics and clarified the concept of entropy. The roots of his Nobel prize quantum theory are in his mastery of thermodynamics.

Hugh Lougbourne CaUendar (1863-1930, English) authored papers on internal combustion engines, thermometric scales, radiation, vapor pressure, and the boiling point of substances. While serving as a professor at several educational institutions (McGill University, University College in London, Imperial College), he directed his primary efforts toward experimentation.

Walther Hermann Nemst (1864-1941, German) was one of the founders of modern physical chemistry, and he also made fundamental contributions to thermodynamics. From 1887 until he retired in 1933, Nernst conducted important research. In 1906 he announced his "third law of thermodynamics" and received the 1920 Nobel prize for it.

Wilhelm Wien (1864-1928, German) was an assistant to Helmholtz. Using ther­modynamic principles, Wien studied thermal radiation (paralleling the work of Planck). For his efforts, Wien won the 1911 Nobel prize in physics.

Constantin Caratbeodory (1873-1950, Greek) was a great mathematician who presented an alternative logical structure of the second law without using the word heat.

Percy Williams Bridgman (1882-1961, American) conducted research on materials at extremely high pressures (l05 atm) and studied their thermodynamic behavior. For this work he received a Nobel prize.

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766 Appendix B

Dates

1600 1650 1700 1750 1800 1850 1900 1950

-Galile - merican Wan

foo--Guerick ~- - ... ... ... • .. -.. -Torricelli _ C N c: ..<:: 3 3

c: E ttl

,.... ttl > CJJ ttl ttl co U U Q)

--Mari otte- c: ,.... 'x c: 3: 3: .... c:

~ ttl 0 aJ Q) c. ~ - Pasca - :l ~ C/l ;; --B oyle- (3

> - Hooke- Q)

0::: - r--Newton -r-- Leibnitz-r-

Amonte ns F hrenheit

I--- Bernoul i-I-Celsius_

- Black-Watt

- Lavoisier-

-r--- Charles --Thompso ---Da ton I

-Seeb eck---G y-Lussac-

--Peltier---Stirling - Carnot-

---Ericss pn • --May ~r_ --deR pchas---Je ule_ -Rank ne_ -Hel rnholtz--Clf usius_

-- homson-r---Thomsen-r--- erthelot-r--- Brayton_ -M xwell---Otto_

- Daimler_

- -van der Waa s-

- -Gibbs-~ Dewar

- - Bo ltzmann-r--van't Hof ---anne ----Cler •

--Diesel r----Pic nck • _Caller dar_ --Ne nst---. WiE in-

Chronology of -Car theodory-personalities in - Bridgman--thermodynamics You x

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Appendix c

Nomenclatu re*

a = acceleration (m/s2) a = specific Helmholtz function

(kJ/kg) A = area (m2) A = Helmholtz function (kJ) C = specific heat (kJ/(kg' K)) c = velocity of light in vacuum

(2.9980 x lOB m/s) C = velocity of sound D = diameter (m) e = specific energy (kJ) E = energy (kJ) f = friction factor F = force (N) 'Y = thrust g = degeneracy g = local acceleration of gravity (m/s2) g = specific Gibbs function (kJ/kg) G = Gibbs function (kJ) h = specific enthalpy (kJ/kg)

h* = Planck's constant (6.625 x 10-34 J . s)

H = enthalpy (kJ) I = moment of inertia J = mechanical equivalent of heat k = cp/c", ratio of specific heats k = fitting loss coefficient K = equilibrium constant m = mass (kg)

* Meaning is determined by context.

Nomenclature 767

Nomenclature and Conversion Factors

rh = mass rate (kg/s) M = Mach number M = molecular weight (kg/kg-mole) n = m/M, number of moles n = mumber of particles n = polytropic index

No = Avogadro's number (6.0220 x 1023 molecules/mole)

q = heat per unit mass (kJ/kg) Q = heat (kJ) Q = heat rate (W) p = pressure (Pa = N/m2) p = probability Ii = momentum

Pr = Wp/k (Prandtl number) R = R/M, gas constant (kN· m/kg· K) R = universal gas constant

(8.3143 J/K mole· K) Re = pVLlfJ. (Reynoias number)

s = specific entropy (kJ/kg· K) S = entropy (kJ/K) t = time (sec)

T = temperature (C, K) u = specific internal energy (kJ/kg) U = internal energy (kJ) v = specific volume (m3/kg) ii = volume per mole (m3/mole) V = volume (m3) V = volume flow rate (m3/s) V = velocity (m/s) w = specific work (kJ/kg)

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768 Appendix C

Nomenclature (Continued)

W = humidity ratio W = work (kJ) W = thermodynamic probability x = quality

Xi = volume fraction X = mole fraction Yi = mass fraction Y = expansion factor z = partition function Z = compressibility factor (3 = coefficient of performance (3 = volumetric coefficient of thermal

expansion [(l/v )/av/aT)p 1

Conversion Factors

Quantity

Acceleration

Area

Density

Energy, work, heat

Flow rate, mass

Flow rate, volume

Force Frequency Gas constant

Length

* E - 01 :::} 10- 1 and so on.

TJ = efficiency TJ = number of degrees of freedom K = Boltzmann constant (1.3807 x 10-23 J/K) K = isothermal compressibility A = wavelength (m) I.t = viscosity (kg/m s) v = frequency (S-I) v = /L/p, kinematic viscosity (m2/s) p = density (kg/m3) 'T = shear stress (N/m2) (J = named temperature

cf> = angle (degrees) cf> = relative humidity w = named frequency

Multiplication Conversion Factor*

ft/sec2 to m/s2 3.048 E - 01 standard gravity m/s2 9.807 E + 00

2 to m2 6.452 In. E - 04 fe to m2 9.290 E - 02 Ibm/fe to kg/m3 1.602 E + 01 slug/fe to kg/m3 5.154 E + 02 Btu (IT) to J 1.055 E + 03 ft-Ibf to J 1.356 E + 00 erg to J 1 E - 07 liter-atm to J 1.013 E + 02 N-m to J 1 E + 00 calorie to J 4.182 E + 00 Ibm/sec to kg/s 4.536 E - 01 Ibm/min to kg/s 7.560 E - 03 Ibm/hr to kg/s 1.260 E - 04 slug/sec to kg/s 1.459 E + 01 fe/min to m3/s 4.719 E - 04 ft2/sec to m3/s 2.832 E - 02 gal (U.S. liquid)/min to m3/s 6.309 E - 05 Ibf (avoirdupois) to N 4.448 E + 00 sec- I to Hz 1 E + 00 Btu/Ibm· R to J/(kg . K) 4.187 E + 03 ft-Ibf/lbm . R to J/(kg· K) 5.380 E + 00 in. to m 2.54 E - 02 ft to m 3.048 E - 01

Source: Adapted with permission from ASME.

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Conversion Factors 769

Conversion Factors

Multiplication Quantity Conversion Factor*

Length mi (U.S.) to m 1.609 E + 03 micron to m 1.000 E - 0.6

Mass Ibm (avoirdupois) to kg 4.536 E - 01 slug to kg 1.459 E + 01

Plane angle degrees to rad 1.745 E - 02 Power Btu (IT)/hr to W 2.931 E - 01

ft-Ibf/sec to W 1.356 E + 00 hp (550 ft-Ibf/sec) to W 7.457 E + 02

Pressure standard atmosphere to Pa 1.013 E + 05 bar to Pa E + 05 Ibf/ft 2 to Pa 4.788 E + 01 Ibf/in. 2 to Pa 6.895 E + 03 mm Hg to Pa 1.333 E + 02 in. Hg to Pa 3.386 E + 03

Rotational frequency min-I to S-I 1.667 E - 02 Specific enthalpy Btu/Ibm to J/kg 2.326 E + 03 Specific entropy Btu/Ibm· R to J/(kg· K) 4.187 E + 03 Specific heat Btu/Ibm· R to J/(kg . K) 4.187 E + 03 Specific internal Btu/Ibm to J/kg 2.326 E + 03

energy Specific volume fe/Ibm to m3/kg 6.243 E - 02 Surface tension Ibf/ft to N/m 1.459 E + 01 Temperature, F to C Tc = (TF - 32)/1.8

measured Temperature, C to K TK = Tc + 273.15

thermodynamic F to K TK = (TF + 459.67)/1.8 R to K TK = TR/1.8

Time hr to s 3.6 E + 03 min to s 6 E + 01

Torque Ibf-in. to N·m 1.130 E - 01 Ibf-ft to N'm 1.356 E + 00

Velocity ft/hr to m/s 8.467 E - 05 ft/min to m/s 5.08 E - 03 ft/sec to m/s 3.048 E - 01 knot (international) to m/s 5.144 E - 01 mile (U.S.)/\1r to m/s 4.470 E - 01

Viscosity, dynamic centipoise to Pa· s 1 E - 03 poise to Pa· s 1 E - 01 Ibm/ft-sec to Pa· s 1.488 E + 00 Ibf-sec/ft2 to Pa· s 4.788 E + 01 slug/ft-sec to Pa· s 4.788 E + 01

Viscosity, kinematic centistoke to m2/s 1 E - 06

stoke to m2/s 1 E - 04

fe/sec to m2/s 9.290 E - 02

Volume gal (U.S. liquid) to m3 3.785 E - 03 fe to m3 2.832 E - 02 • 3 In. to m3 1.639 E - 05

liter to m3 1 E - 03

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770 Appendix C

Multiple Conversion Factors

Btu/hr fe F = 5.6786 W/m2K Btu/hrfe = 3.1546 W/m2 Btu/hr fe = 10.3488 W/m3 Btu/hrft F = 1.7304 W/m K Btu/Ibm = 2.3254 kJ/kg Btu/Ibm· R = 4.186 kJ/kg· K

fe/Ibm = 0.06248 m3/kg Btu/hr = 1.0548 kJ/hr

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Bibliography

Coad, W. J. "Energy Effectiveness Factor." Heating/Piping/Air Conditioning (August 1976).

--. "Second Law Concepts: I." Heating/Piping/Air Conditioning (February 1979). Cravalho, E. G., and Smith, J. L. (Jr). Engineering Thermodynamics. Boston: Pitman,

1981. Eastop, T. D., and McConkey, A. Applied Thermodynamics for Engineering Technologists.

3rd ed. London: Longmans, 1978. Faires, V. M., and Simmang, C. M. Thermodynamics. 6th ed. New York: Macmillan, 1978. Gaggioli, R. A. "The Concept of Available Energy." Chemical Engineering Science

16(1961):87-96. --. "The Concepts of Thermodynamic Friction, Thermal Available Energy, Chemical

Available Energy and Thermal Energy." Chemical Engineering Science 17(1962):523-

530. Gaggioli, R. A., and Petit, P. J. "Second Law Analysis for Pin-pointing the True

Inefficiencies in Fuel Conversion Systems." ACS Symposium Series 21(2)(1976):56-75. This article also appeared in Chemical Technology 1(8)(1977):496-506.

Gaggioli, R. A., and Wepfer, W. J. Available-Energy Costing-A Cogeneration Case Study. Paper presented at A.I.Ch.E. Meeting 1978.

Gibbs, J. W. Collected Works. Vol. 1. New Haven: Yale University Press, 1948. Gyftopoulos, E. P., Keenan, J. H., and Hatsopoulos, G. N. "Thermodynamics." Encyc­

lopedia Brittanica, 1975. Hatsopoulos, G. N., and Keenan, J. H. Principles of General Thermodynamics. New York:

Wiley, 1965. Holman, J. P. Thermodynamics. 3rd ed. New York: McGraw-Hill, 1980. Jones, J. B., and Hawkins, G. A. Engineering Thermodynamics. New York: Wiley, 1960. Keenan, J. H. "A Steam Chart for Second Law Analysis." Transactions ASME

54(1932):195. --. Thermodynamics. New York: Wiley, 1941. Lay, J. E. Thermodynamics. Columbus: Merrill, 1963. Obert, E. F. Thermodynamics. New York: McGraw-Hill, 1948. --. Concepts of Thermodynamics. New York: McGraw-Hill, 1960. Sears, F. W. An Introduction to Thermodynamics, The Kinetic Theory of Gases, and

Statistical Mechanics. 2nd ed. Reading, Mass.: Addison-Wesley, 1953. Tien, C. L., and Lienhard, J. H. Statistical Thermodynamics. New York: Holt, Rinehart &

Winston, 1971. Tribus, M., and Evans, R. Thermoeconomics. UCLA Report 52-63. Los Angeles: UCLA,

1962.

771

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772 Bibliography

Tribus, M., and McIrvine, E. "Energy and Information." Scientific American (September 1971}:121-128.

Van Wylen, G. J., and Sonntag, R. E. Fundamentals of Classical Thermodynamics. New York: Wiley, 1965.

Wark, K. Thermodynamics. 3rd ed. New York: McGraw-Hill, 1977. Zemansky, M. W. Heat and Thermodynamics. New York: McGraw-Hill, 1968.

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Answers to Selected Problems

Chapter 1

1. 155.9 N 3. 129N 5. 0.1 m3/kg 7. 3.16 bar; 316 kPa; 3.12 atm 9. 1.136 bar

11. 0.00237 bar 13. 564.5 m 15. 152.37 kg 17. 295.15 K 19. -218.4 Re 21. -2357 Z 23. -40 25. 35.9 C; 68 C; 149.4 C 31. all exact 33. no; yes; no 35. 962.7 kglhr; 10.13 m/s 37. 297 kg/min; 39. 2 kgls 41. 1.531(103) cm3/sec

Chapter 2

3. Conditions only; 0.056 (R-12); SH, 10 C (R-12); SC, S = 0.5705 (H20); 0.073 (H20); SH, 380 C (H20)

5. S only; a. 8.7776 kJ/kg' K

b. x = 0.4345 c. 7.2345 kJ/kg' K d. 3.6995 kJ/kg . K

7. 313.93 kJ/kg 9. Condition only; 173.8 C

(SC-inlet); 568.SC (SH­outlet)

11. 271.77 kJ/kg; 271.95 kJ/kg 13. S(in) = 0.6125 kJ/kg . K;

T(out) = -6.7 C; h(out) =

188.65 kJ/kg 15. 40.89 kJ/kg 17. 32.5 kJ/kg 19. 125.46 kJ/kg;

0.4211 kJ/kg' K 21. 128.02 kJ/kg 23. 324.79 kJ/kg 25. a. 21 C b. 0.973 c. 40 C

d. 0.953 e. 1.0 27. a. 0.00069 m3, 0.626 kg

b. 0.56548, 2.0738 kg 29. a. 0.439 kg, 3.27 cm2

b. 0.014 kg, 4.9 cm2

33. 6.0479 kJ/kg . K 35. 5.79 kg; 4.21 kg; 84.994 m3 ;

0.002 m3

37. 0.15; 0.0; 0.024 39. 1 kJ/kg' K 41. 2.595 kJ/kg' K;

1.995(10-4) m3/kg· K 43. 2.015 kJ/kg . K

773

47. 3 pt. fit; a = 2476.6 kJ/kg b = 1.0292 kJ/kg . K c = 1636.6 kJ/kg' K2

49. 0.5516 m3/kg; 3590 kJ/kg; 19.9836 m3/kg; 2508.4 kJ/kg . K

51. X - 0.453; 54.5 C; 0.2156 m3/kg; 0.06185 kJ/kg . K; 203.76 kJ/kg' K

53. a. 65 K, 171.5 K b. 356 R, 0.8187 c. 0.5673, 382.7 R

55. 1.047 kJ/kg· K; 0.00099 m3/kg· K

Chapter 3

1. 667.1 kg 3. 12,984 m3/min; 1.288 m2

5. 1856.3 kPa; 696 K; 393 kJ/kg

7. 119 m3/kg 9. 0.27945 m3/kg; 183.1 kJ/kg

11. 17.23 kJ/kg; 0.068 m3/kg 13. 649.8 K; 0.01 kg; 332.6 kJ/kg;

0.217 kJ/kg' K; 235.7 kJ/kg 15. 362K; 1.8916 x 1O-3 kg;

0.0393 kJ; 0.0551 kJ; -1.016(10- 3) kJ/kg' K

17.4.63m/s;0.1319m 19. 1461 m3

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774 Answers to Selected Problems

21. 39.9kJ;5.177 kJ/kg· K; 2.02 kJ/kg· K

23. 39.28 MPa 27. -0.029327 kJ/kg· K 31. -180.1 kJ/kg 39. 0.85; 0.452; 1.04 41. 34% 43. 4.83(10-3) m3/kg; 108% 57. 598.4 K; 284.4 kJ/kg;

0.176 m3/kg 59. 5.658%; 7.715% 61. 0.3338 m3/kg; 8.954 m3/kg;

-593.4 kJ/kg

Chapter 4

1. 781.04 N . m 3. 347.18 N· m 5. 1065 kJ; 412.5 kJ

15. 20.62 kJ 17. -9.67 kJ 19. 291 kJ/kg 21. 1.4706 kJ/kg . K 23. 1.025 kJ/kg· K

Chapter 5

1. a. 795 kJ; 1110 kJ; 795 kJ; 0 b.795kJ;1110kJ;315kJ; 1110 kJ

3. 22.5 kW 7. 1521.2 kJ; 1914.1 kJ

11. 1.245 m3 ; 0.454 m3 ;

439 K; 155.5 kJ 13. a. w = 1051.3 kJ/kg

b. q = 279 kJ/kg c. w = 0 d. q = 4070 kJ/kg

15. 50.9 kJ/kg 17. 71.2 kW; 339.9 A 19. 1.64026(105) kW 21. 8'(}516(104) kJ/hr 23. 589 kg/hr; 7.978 m3/min 25. 150kW . 27. 0.363 29. 1915.6 MW; 2.65(105) kg/hr;

1415.6MW 31. 3.103 kJ/kg 33. 79,420 kW;

-5.001(108) kJ/hr

35. 6.94 kJ/sec 37. 0.152; 0.8993 Klbar 39. 620.8 m/s 41. 2758.2 kJ/kg 43. 60.84 m/s 45. 1239.7 kW; 0.974; 0.0142;

0.01151; 1.93(10-5)

47. 110 C; 0.301 49. 81.78 kJ/kg 51. 11.2 kg 53. 140 kJ 55. 26.6 C 57. -1784.5 kJ 59. 302.8 cm/sec

Chapter 6

1. 1.83; 0.4 3. 1.97 kW 5. 21.1 kW 7. 8.98 m2

9.6kW;429K 11. 68.6 kW 13. 5.06; 151.6 kJ 15. 0.533; 1.877; 0.877 19. 0.514; 367 K 21. 545 K; 0.3188; 0.4679 23. 0.125 kW; 1.192 kW;

1.317 kW 25. 524kW 33. 298.5075; 218.5075

Chapter 7

9. 3; 2 13. No 15. 0.28715 kJ/kg· K 27. 489.9 kJ/kg 29. 14.54; -403.5 kJ/kg;

-60.3 kJ/kg 31. -382.4 kJ; -382.4 kJ 33. -116.6 kJ/kg; -4305.3 kJ;

0.41187 kJ/kg . K 37. -21.15 kJ/kg 39. Ta = 100 K; Tb = 400 K;

Tc = 200 K; AU(bc) = 7K

-500 K; As(ca) = - Tin 2

41. -217.1 kJ/kg; -0.22045 kJ/kg· K; -79.5 kJ/kg

43. 563.5 K; 1.14318 m3/kg;

- 373.8 kJ/kg; 523.3 kJ/kg; 533 kJ/kg

45. 20.24C 47. a. -245.6 kJ/kg; 0

b. -179.5 kJ/kg; 179.5 kJ/kg c. -222.7 kJ/kg; -66.7 kJ/kg

49. 44.84 cm2

51. 435 m/s 53. 142.5 kW; 8.8348 kJ/kg· K;

7.2345 kJ/kg· K; 0.13829 kJ/kg· K claim is possible

57. no 69. 19,978 kW 71. 1037 m/s; 0.171 m 73. 11 ,246 kW 75. O.64kW 77. 0.041 kJ/kg· K 79. 94,173 kW; 0.341; 0.616 81. a. 93 C; 0.762 m3/kg b.

-42.6 kJ/kg c. 42.6 kJ/kg d. 40.2 kJ/kg

85. 77 kW-hr

Chapter 8

1. 4055.4 kJ/kg 3. a. 1.65; 5.56 b. 5.63;

18.1 c. 2.13; 0.632 5. a. 419.7 kJ; 0.663 b.

As(hi) = -0.6585 kJ/kg; As(lo) = 0.6585 kJ/kg

11. 0.877 13. 141.36 MJ/s 15. 646 K 17. 1261.7kg/hr;0.194kW 19. 1.328 kW 21. 1.245 kJ/kg 23. -5.0 kJ/kg; T = 25.25 C 25. 270.13 kW 27. 5.61 kW; 2.39 kW 29. 3.84kW 31. 445.1m/s;6.588cm2

35. 324 C; 550 kPa 37. 6.2(10-4) m2; 0.07 m2

39. 25.3%; 73.13% 41. a. 77,971 kW b. -4.93(108)

kJ/hr c. 0.94 d. 221.5 kW

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e. 0.362 f. 0.3848 43. 0.257; 0.366 45. c.0.637 d. 0.283 47. 4499.3 K; 2071.6 kPa 49. 722 K; 2196 kPa; 3962 K;

12,040 kPa; 1650 K; 558 kPa; 0.585; mep = 1804 kPa

51. 1586 kJ/kg; 321.3 kPa 53. 0.567; 779.4 kJ 55. 48 kW; 15 kg/hr 57. 4.18 kW; 27,631 kJ/hr

0.86; 0.843 59. 0.59 63. 0.398 65. 0.334 71. 1.73 73. 19,108 kJlhr; 62.53 kJ/hr' K;

53 kJ/hr· K 75. 10 kW; 2.5; 105,665 kJlhr 77. 5.34 79.3.77;2.77 81. 0.962; 0.294; 3.71, 5.1 kW

3.7; 4994 kJlhr; 2.7;

9.68 kJ/hr Watt

85. 11.6 kW; 111,508 kJ/hr

Chapter 9

1. 0.29; 0.079 3. 118.8 kW; 2014 kW; 3.9 m 5. 0.466 7. 720.5 kJ/kg; 0.228 9. 0.35; 0.099

11. 0.509 13. 0.308 15. 0.318 29. 6.582(109) kJ/min 31. 383.25 kPa; 171.25 kPa;

2.442(103) kW 33. 1.17(104) kW 35. 4,160kW 37. 2.18 kW; 0.98 41. 41,800 kW; 650 kW;

0.069 kg/hr; 51247 kg/hr 43. l.27kW

Chapter 10

1. 230.8 kJ/kg; 24.6 kJ/kg; 301.4 kJ/kg; 206.2 kJ/kg;

Answers to Selected Problems 775

206.2 kJ/kg; 206.2 kJ/kg; 0 3. 0.51(106) kglhr; 7.33 kJ/kg;

2.9 kJ/kg; 28.1 kJ/kg; 2.48 kJ/kg; 193.5 kJ/kg; 288.2 kJ/kg; 0.0254; 0.0379; 186.1 kJ/kg

5. 426 kJ/kg; -116 kJ/kg; -60 kJ/kg; -69 kJ/kg

9. 45.01 kJ/kg 21. 5490.5 kg/hr; 0.501; 0;

4478.8;40,431;33,237.2; 2715

23. 2073 kW; 914 kW; 1198 kW; 994 kW; 0.7625; 0.92; 80 kW

25. 33.2kW

Chapter 11

15. 8.9666 kJ/kg· K 17. 41 kJ 19. 190.45 kJ 21. -399.6 kJ/kg· K 27. 2288.3 kJ/kg

Chapter 12

1. 52.59 kPa; 196.8 kPa; 171 kPa

3. 147.4 kg; 32.6 kg/kg' mole 5. 0.6203 kJ/kg . K

13. 0.394; 0.0085 kg/kg 11. 75 C; 0.54 kg

15. 18.4 C; 70.3 kJ/kg; 0.0112 kg/kg

17. Humidity ratio or relative humidity; 0.0033; 0.0058; 0.016; 0.0157; 46 (R.H.); 0.0052; 0.001; 0.011; 47 (R.H.); 0.0234

19. Humidity ratio or relative humidity; 0.0087; 0.006; 0.0155; 0.0207; 60 (R.H.); 0.005; 0.001; 0.0115; 45 (R.H.); 0.227

21. 2.77 Pa 23. 0.0088 kg/kg; 11.8 C;

0.524 kg 25. 1.43 kg/min

-6182 kJ/min 27. 0.49; 5 C; 0.0054; 47.2 kJ/kg;

58.6 kJ/kg; 11.4 kJ/kg; 0.25

29. 35.6C 31. 0.467; 71.27 kJ/kg air;

0.864 m3/kg 33. 230.5 kPa; 214 m/s 35. 3.26(106) kJlhr; 583.7 kg/hr;

2.41(106) kJlhr; 1.52(106)

kJ/hr; 12.3 C 37. 46C 39. 51.71 kJ/kg

0.0070 kg/kg 41. 27 C; 0.0112; 0.48;

74.4 kJ/kg; 16 C 43. 28.2 C; -2.77 kg 45. 23.3 C; 17.8 C 47. 14,498 kg/hr; 18.3 C; 14.4 C

0.5 49. 24.8 C; 18.1 C; -25.9 tons 51. 12.5 C; 0.53 53. 17.3 C; 0.0025 kg 55. 0.452; 24.1 C; 0.463 57. 0.0177 kg/kg; 11 C; 0.32 61. 16,089 kJ/hr; 7839 kJ/hr

31.5 kg/min; 70% 63. b. h only; 91.6; 68.2; 73.9;

56.8 d. 322.8 m3/min e. -31.3 tons f. 69.8%(sens) g. 34.1%

65. 19.5 C; 0.01403 kg/kg; 64.7 kJ/kg; 0.872 m3/kg

67. 38.9 C; 0.0088 kg/kg; 3514.5 kg/hr; 874.6I/s; 26.5 kW; 109 kg/hr

69. 78.7 kW (22.4 tons); 241.7 kg/hr; 42.7 kW; 34.5 kW; 12.2 C

71. 28,230 kJ/hr (loss); 0.28; 35.28 m3/min; 14%

75. 41,778 kJ/hr; 76,910 kJ/hr; 87.1 C/day

Chapter 13

1. 8.0 kg air/kg C 5. 14.55 kg air/kg fuel;

1.34 kg water/kg fuel; 17 kPa; 56.6 C; 5.94%; 11.04%; 83.02%

7. 13.25 kg air/kg fuel; 34.4 C 9. 1O.48m3air/m3fuel; 110.1%;

10.1% 11. 0.58kg; 13.3kPa; 15.1%;

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776 Answers to Selected Problems

23.69 m3/kg 13. 17.49 kg air/kg fuel 15. Wet 11.5%; 11.65%;2.49%;

74.4%; Dry 12.95%; 2.82%; 84.2%; 48.9 C

17. 45.095 kllkg 12.41 kg/£ 19. 37,854.3 kllkgr; 68.4 kllkgr 21. a. $23,404 b. $26,298 23. see 14-11

Chapter 14

1. 0.15 m3/min; 1.41 kg/min; 1.l9kW

3. 6.1 5. 0.484 m3/min 7. 4.2 kW; 2.2 9. 247.5 kllkg; 271 kllkg;

77 kllkg; 0.49 kW 11. 103.3 kllkg

13. 1.742 kllhrlW; 5.634; 2.098 kW/ton; 19.07 kllhrlW; 5.298; 0.665 kW/ton

15. 4.64 m3/min 27. h only (kllkg); -127.9;

390.8; 1639.8; 69.8; 1395.6; 169.8

29. 2.28 33. 11,338 m/min; 20.4 C

-58C 35. -2.8 C 39. 198 tons 41. 249 tons; 2847 tons;

19.3(104) m3/hr

Chapter 15

11. 304.3 K; 347.9 m/s; 432.5 kPa; 0.00473 m2;

626.7 kPa

13. 317.5 m/s; 374.6 m/s 15. 5.54 cm2 ; 6.22 cm2

17. 0.00595 m2

23. 0.508; 175.1 m/s 25. 25.1 C 27. 161.6 kPa 29. 39.9kW 31. 2.124 kg/s 35. 242.6 cm/s

Chapter 16

1. 5.65(10-21 ) llmolecule; 1.3267(10-26) kg/molecule; 5.3068(10-26) kg/molecule;. 922 m/s; 461 m/s

3. 101.7 kPa 7. 0.18892

19. 7; -12 23. =e-!07

Page 68: Appendices - Springer LINK

A Absolute temperature scale, 185 Absorption refrigeration

ammonia, 295, 555 aqua-ammonia, 560 lithium-bromide, 556

Activity, 515 Adiabatic

compressibility, 220 flame temperature (T,), 505 process, 24, 112,466

Air, 445, 487, 492 tables, 758

Air/fuel ratio (A/F), 494 Air standard cycle, 268, 567 Amagat's law, 438 Annual cycle energy system

(ACES), 174,537 Availability, 372, 391 Avogadro's law, 439

B Beatti-Bridgeman,76 Benedict-Webb- Rubin

(B-W-R), 76, 426 Bernoulli equation, 142,596,

608,618 Berthelot, 75, 80 Boiler, 246, 547 Boltzmann constant (K), 21, 182,

652,676 Bose-Einstein, 648, 665,

676,698 Bottoming cycle, 337 Boundary layer, 595

Index

Brayton cycle, 268, 311, 323, 330,342

Breeder, 345 Brown cycle, 304 Bulk modules, (8), 89

C Callendar,75 Carnot cycle, 164, 167, 178,

309,536 Characteristic function, 420 Clapeyron equation, 422 Clausius

equation of state, 74, 87 gas, 74, 76,416,445 inequality, 178, 191 statement, 176

Closed system, 6, 110, 121,376 Coefficient of performance (1];

COP), 162,290,373 Cogeneration, 336 Combined cycles, 333 Combustion, 481

efficiency of, 518 Combustor, 250 Compressed air energy storage

(CAES),333 Compressed liquid (sub-cooled),

39,45 Compressible flow tables, 643 Compressibility, 88

chart, 77, 82 factor (Z), 77, 80, 444

Compressor, 224, 232, 240, 539, 630,638

777

Condenser, 246, 543 Control

surface, 129 volume, 7, 129,207

Conservation of energy, 121, 138, 183

Conservation of mass (continuity), 30, 137,230, 594,598,609,618

Conversion tables, 767 Criterion of equilibrium, 432 Critical constants, 759 Critical point, 40, 44, 81 Curtis, 637 Cycle, 23, 122,261,519 Cyclic relations, 86, 93

o 0, d,~, 10 Darsy-Weisbach, 614 Dead state, 394 Debye temperature (6D ), 690 Degeneracy, 664, 681 Degree of saturation, 448 Degrees of freedom, 653 Density (p), 9, 11,44,431 Detonation, 482 Dew point temperature (Td)'

449 Diesel, 281, 313 Dieterici, 74, 104 Diffuser, 251, 301, 603 Discharge coefficient (Cd)' 611 Dissociation, 507 Dry-bulb temperature (T), 447 Duel cycle, 304

Page 69: Appendices - Springer LINK

778 Index

E EER, 162, 537 Effectiveness (E), 330, 389 Efficiency (T]), 373

blade, 636 Brayton, 268, 311, 326 Carnot, 167, 183, 309 combustion, 518 compressor, 224, 540 cycle definition, 160,223,263,

373,388 diesel, 281, 313 Ericsson, 284, 303 heat engine, 160,309 heat pump, 161,288,309,536 nozzle, 224 Otto, 278, 312 process, 223 Rankine, 263, 310 refrigerator, 161,288,309 second law, 374, 389 Stirling, 284, 303, 391 turbine, 223, 262

Einstein's theory of solids, 689 Ejector, 577 Energy, 2, 101

available, 372 biomass, 358 geothermal, 358 hydroelectric, 358 of ideal gas, 66 internal (U), 20 solar, 351 wind, 355

Enthalpy (H) of combustion, 488, 496 definition, 21,143,412,429,

441,679 of formation, 499 of ideal gas, 66 of reaction, 496

Entropy (S) definition, 2, 21,178,185,191,

207,379,412,427,431,441, 674,676 .

of ideal gas, 68 principle of increase, 203 and probability, 21, 182,673

Equation of state Beattie-Bridgeman, 75 Benedict-Webb-Rubin,76,

426 Berthelot, 75 Callendar,75 Clausius, 74, 76 definition, 45, 62, 85, 426 Dieterici,74 ideal gas, 62, 650 Linde, 76 Martin-Hou, 76, 429 Redlich-Kwong, 74 Saha-Bose,75 van der Waals, 74 vitial, 76, 426

Equilibrium, 22, 39, 422, 508, 667 constant (KJ, 508, 512 neutral, 433 state, 23 thermal, 22

Ericsson cycle, 283, 303 Euler equation, 142,596 Evaporators, 547 Excess air, 493 Expansion valve, 552 Explosion, 482 Extensive property, 10

F Fan, 232, 240 Fanno line, 613, 619, 622 Fermi-Dirac, 649, 666, 677, 694 First law of thermodynamics, 121,

183,497 for cycle, 122, 175 for open system, 129 for process, 123

Fission, 345 Flammability, 490 Flow work, 107, 130, 376 Freon (R-12) tables, 737 Friction factor (f), 615 Fuel/air cycle, 519 Fuels, 483 Fundamental relations, 93 Fusion, 350

G Gas

constant (R), 64, 442, 760 photon, 698 turbine cycle, 268

Geothermal power, 358 Gibbs

function, 21,412,422,434, 508,679

paradox, 442 Gibbs-Dalton law, 437, 441 Gravimetric analysis, 439

H Head, 614 Heat (Q)

available, 377 capacity (C), 113, 163 definition, 2, 26, 112 exchanger, 244, 548, 618 latent, 54 sensible, 54

Heat engine definition, 159,309 efficiency (T]HP), 160,309

Heat pump definition, 161,287,292,529,

534,563 efficiency, (T]HP; COP h)' 162,

168 Heating value, 250, 485, 496,

500,518 Heisenberg uncertainty principle,

679 Helmholtz function (a), 21,412,

434,508,678 Hero's turbine, 632 Humidity

ratio (W), 448, 551 relative (<1»,449

Hydraulic diameter, 594

Ice point, 15, 18 Ideal gas, 104,231,602,617,622,

760 definition, 62, 71, 148,416,651 enthalpy, 66 entropy, 66, 68, 196 equation of state, 62 internal energy, 66, 148, 489

Ignition temperation, 489

Page 70: Appendices - Springer LINK

Impulse stage, 234, 631, 634 Increase of entropy principle, 179 Inequality of Clausius, 178, 191 Intensive properties, 11 Internal energy ( U)

available part, 375 definition, 20, 47,116,143,429,

441,678 ofidealgas,66,148,489

Inversion curve, 230 Irreversibility, 372, 379 Irreversible process, 164, 203 Isentropic, 23, 600, 608

compression ratio, 280, 282 Isothermal compressibility (K),

89,105,144,200,220,415

Jet ejector, 577 propulsion, 624

Joule-Thomson coefficient (1-\-), 228,415

K Kelvin-Planck statement, 176 Kinetic energy, 20, 116

available part, 376 Kinetic theory of gases, 649

l Lagrangian multipliers, 658, 667,

698 Last work (LW), 227, 379 Latent heat of transformation

(hft ),47,54, 115,423,710 Laval turbine, 631 Law

of additive volumes, 438 of atmospheres, 686 of corresponding states, 80 first, 121, 129, 175, 183,497 of mass action, 507 of partial pressures, 437 second, 175, 183, 191,374,389 Stefan-Boltzmann, 700 third, 183 Wien's displacement, 699

Le Chatelier equation, 490 Leduc's law, 438 Lenoir cycle, 304 Linde, 75

M Mach number (M), 251, 594, 599 Magnetohydrodynamics (MHD),

340 Martin-Hour, 76, 426, 429 Mass (m)

action law, 507 conservation, 30 fraction, 439

Maxwell-Botzmann, 648, 665, 674,689

Maxwell's relations, 412 Maxwell's velocity distribution,

659 Mean effective pressure (MEP),

280,283 Mechanical equivalent of heat

(J), 122 Modular integrated utility system

(MIUS),239 Mixture, 437 Mole, 491, 510 Mole fraction, 439, 449 Mollier diagram, 48 Most probable speed, 661

N Nernst theorem, 185 Newton's second law, 8, 106,613,

624,632 Newtonian fluid, 593 Nitrogen tables, 756, 757 Nomenclature, 767 Normal shock, 620 Nozzle, 138,224,251,301,

603,610 Nuclear power, 344

o Ocean thermal energy conversion

(OTES), 368 Open system, 6,106,129,207 Orface plate, 610 Otto, 277, 312

p Partial pressure, 437 Partition function (z), 673, 678 Path function, 23, 28, 123, 192 Pauli exclusion principle, 695

Index 779

Perpetual motion machine (PMM)

first kind, 129 second kind, 176 third kind, 176

Phase, 37 diagram, 42, 64

Photon, 698 Photovoltaic, 354 Pitot tube, 610 Planck's constant (h*), 680 Point function, 23, 28, 192,412 Pollution, 523 Polytropic process, 23, 53, 113,

149,608 Porous plug, 228 Potential energy, 20, 116

available part, 376 Power, 103 Pressure (P)

absolute, 16 critical, 40, 81 definition, 11, 678 gauge, 12 partial, 437 reduced,81 saturation, 39, 710

Prime mover, 338 Principle of the increase in

entropy, 179,203 Principle of equipartition, 653 Process

adiabatic, 25 definition, 23 indicator, 25 irreversible, 25 isentropic, 24, 600, 608 isobaric, 23, 43 isochoric, 23 isometric, 23 isothermal, 23, 43 polytropic, 23, 149 quasi-static, 23 reversible, 24, 112, 163,378,

507 throttling, 228

Products of combustion, 493, 498,506,520

Property, 10, 65 extensive, 10 independent, 38 intensive, 10 reduced,81

D.~~.,I";~~ t;')A

Page 71: Appendices - Springer LINK

780 Index

Psychrometrics, 437, 446, 462 charts, 453

Pump, 232, 237, 369 Pure substance, 38

Q Quality (x), 40, 46

R Ramjet, 627 Rankine cycle, 257, 308, 337 Rateau, 637 Rayleigh line, 619 Reactants, 498, 520 Reaction stage, 234, 631, 637 Real gas, 444 Reciprocal relation, 86, 93 Reciprocating engine, 339 Redlich-Kwong, 74 Reduced properties, 81 Refrigerant-12(R-12), 52, 429

tables, 737 Refrigeration cycle, 272, 287,

529,553,567 Refrigerator

definition, 161,309,462, 582 efficiency, 162, 168, 309

Regeneration, 264, 287, 317, 323 Reheat, 269,308,324 Relative humidity (<1», 449 Reservoir, 163 Reversible process, 24, 112, 163,

378,507 Reynolds number (Re), 594, 614 Richardson - Dushman equation,

698 Rocket, 627

S Sackur-Tetrode equation, 684 Saha-Bose,75 Saturated

liquid, 39, 45 vapor, 39, 45

Saturation pressure, 39, 449 temperature, 39

Second law of thermodynamics, 175, 183

Clausius statement, 176 closed system, 191 corollaries, 177 efficiency, 374, 389 Kelvin-Planck statement, 176 open system, 207 statistical, 181

Sensible heat, 54 Shock,620 Solar powt;r, 296, 351, 368, 582 Sound velocity, 594, 598 Specific heat (c), 67, 689, 693,760

cp and c,., 53, 66, 150, 197,415, 430,441,653,679

electron, 694 mean, 56 polytropic, 53

Specific volume (v), 10,46 Stagnation, 253, 597 State of system, 10,22 Steady-state/steady-flow process,

107, 132, 207 Steam

charts, 48 generator, 246, 547 point, 14, 17 tables, 45, 47, 710 turbine, 339

Stefan-Boltzmann law, 700 Stirling, 283, 303 Stirling's approximation, 667,

674,676 Stoichiometric, 492 Subcooled liquid, 39, 44 Superheated vapor, 39, 44 System

closed, 3, 6 isolated,3 open,6

T T ds relations, 196 Temperature (T)

adiabatic flame, 505 critical, 40, 81 Debye ( = 60 ), 691 dew point, 449 dry bulb, 447 Einstein (6E ), 690 equality, 14 flame, 515 ignition, 489 reduced,81 saturation, 39, 710 scale, 15, 187 wet bulb, 447

Theoretical air, 493 Thermal expansion, 88, 105, 144,

200 Thermal energy storage (TES),

336 Thermochemistry, 496 Thermocouple, 19 Thermodynamic

equilibrium, 14,22 probability, 21, 182,664,673 relations (T ds), 196

Thermodynamics definition, 1 macroscopic, 1, 664 microscopic, 1, 181,664

Third law of thermodynamics, 185

Throat, 603 Throttling process, 228, 254, 551 Thrust, 625 Ton of refrigeration, 289 Topping cycle, 336, 342 Triple point (line), 16, 40, 43 Turbine, 136,224,232,330,338,

629 Turbojet, 620

U Unavailable energy, 373 Uniform-state/uniform-flow, 133,

208,230 Units, 8 Unity bracket, 8, 9 _ Universal gas constant (R), 63,

651

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V Valve, 228, 254, 551 van der Waals, 74, 78, 90, 95,

104,158 van't Hoff equation, 509, 513 Vapor compression refrigeration,

289,361,395,530,534 Vapor generator, 246, 547 Vapor pressure curve, 40 Velocity, 594, 598

of particles, 656, 660 of sound (C), 594, 598 space, 657

Venturi, 157,610 Virial coefficients, 76, 426 Viscosity (fl.), 593 Volume fraction, 439 Volumetric

analysis, 440 coefficient of thermal

expansion (a), 415 Vortex tube, 574

Index 781

W Wet-bulb temperature (T*), 447 Wien's displacement law, 699 Wind energy, 355 Work (W)

Z

definition, 102,227,378 flow, 107, 130 mechanical (shaft), 103, 107,

130

Zeroth law of thermodynamics, 14