2. Pure Substances

8/19/2019 2. Pure Substances

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Properties of Pure Substances


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2

Homogeneous Substance

A substance that has uniform thermodynamic properties throughout is said to be

homogeneous.

Pure Substance A pure substance has a homogeneous and invariable chemical composition and may

exist in more than one phase.

Examples:

1. Water (solid, liquid, and vapor phases

2. !ixture of liquid "ater and "ater vapor#. $arbon dioxide, $%2&. 'itrogen, '2

. !ixtures of gases, such as air, as long as there is no change of phase.

)et*s consider the results of heating liquid "ater from 2+°$, 1 atm "hile eeping thepressure constant. -irst place liquid "ater in a pistoncylinder device "here a fixed

"eight is placed on the piston to eep the pressure of the "ater constant at all times.

As liquid "ater is heated "hile the pressure is held constant, the follo"ing events

occur.


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#

Process 1-2

/he "ater is in compressed liquid, or subcooled liquid condition.

0n the compressed liquid region, the properties of the liquid are

approximately equal to the properties of the saturated liquid state at

the temperature.

Process 2-3

At state 2 the liquid has reached the temperature at "hich it begins to boil, called the

saturation temperature, and is said to exist as a saturated liquid. roperties at the

saturated liquid state are noted by the subscript f and v 2 v f . 3uring the phase

change both the temperature and pressure remain constant. At state # the liquid and

vapor phase are in equilibrium and any point on the line bet"een states 2 and # has

the same temperature and pressure.


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&

Process 3-4

At state & a saturated vapor exists and vapori4ation is complete. /he subscript g

"ill al"ays denote a saturated vapor state. 'ote v 4 = v g .

/hermodynamic properties at the saturated liquid state and saturated vapor state are

given in /able A& as the saturated temperature table and /able A as the saturatedpressure table. /hese tables contain the same information. /he saturation pressure

is the pressure at "hich phase change "ill occur for a given temperature. 0n the

saturation region the temperature and pressure are dependent properties5 if one is

no"n, then the other is automatically no"n.


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Process 4-5

0f the constant pressure heating is continued, the temperature "ill

begin to increase above the saturation temperature, 1++ °$ in this

example, and the volume also increases. 6tate is called a

superheated state because / is greater than the saturation

temperature for the pressure and the vapor is not about to

condense. /hermodynamic properties for "ater in the

superheated region are found in the superheated steam tables,

/able A7.

88.89 ≅

/his constant pressure heating process is illustrated in the follo"ing figure.


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7

0f all of the saturated liquid states are connected, the saturated liquid line isestablished. 0f all of the saturated vapor states are connected, the saturated vapor

line is established. /hese t"o lines intersect at the critical point and form "hat is

often called the steam dome;. /he region bet"een the saturated liquid line and the

saturated vapor line is called by these terms: saturated liquidvapor mixture region,

"et region (i.e., a mixture of saturated liquid and saturated vapor, t"ophase region,

and


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9

2 1+++ a

1 1++ a

88.71o$

198.==o$


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=

/he region to the left of the saturated liquid line and belo" the critical temperature is

called the compressed liquid region. /he region to the right of the saturated vapor

line and above the critical temperature is called the superheated region. 6ee /able A

1 for the critical point data for selected substances.

At temperatures and pressures above the critical point, the phase transition from

liquid to vapor is no longer discrete.


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8

he P-V-T Surface for a !eal Substance

>eal substances that readily change phase from solid to liquid to

gas such as "ater, refrigerant1#&a, and ammonia cannot be treated as

ideal gases in general. /he pressure, volume, temperature relation, or

equation of state for these substances is generally very complicated, and

the thermodynamic properties are given in table form. /he properties of

these substances may be illustrated by the functional relation F (P ,v ,T +,

called an equation of state.


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1+

P-V-T Surface for a Substance

that contracts upon free"ing

P-V-T Surface for a Substance

that e#pands upon free"ing


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11

Propert$ ables

0n addition to the temperature, pressure, and volume data, /ables A& through A=

contain the data for the specific internal energy u the specific enthalpy h and the

specific entropy s. /he enthalpy is a convenient grouping of the internal energy,

pressure, and volume and is given by

H U PV = +

/he enthalpy per unit mass is

h u Pv= +

We "ill find that the enthalpy h is quite useful in calculating the energy of mass

streams flo"ing into and out of control volumes. /he enthalpy is also useful in the

energy balance during a constant pressure process for a substance contained in a

closed pistoncylinder device. /he enthalpy has units of energy per unit mass, ?@g.

/he entropy s is a property defined by the second la" of thermodynamics and is

related to the heat transfer to a system divided by the system temperature5 thus, theentropy has units of energy divided by temperature.


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12

Saturated %ater ables

6ince temperature and pressure are dependent properties using the phase change, t"o

tables are given for the saturation region. /able A& has temperature as the

independent property5 /able A has pressure as the independent property. /hese t"o

tables contain the same information and often only one table is given.

-or the complete /able A, the last entry is the critical point at 22.+7& !a.

-or the complete /able A&, the last entry is the critical point at #9#.8o$.

Saturation pressure is the pressure at "hich the liquid and vapor phases are in

equilibrium at a given temperature. Saturation temperature is the temperature at

"hich the liquid and vapor phases are in equilibrium at a given pressure.

/he subscript fg used in /ables A& and A refers to the difference bet"een the

saturated vapor value and the saturated liquid value region. /hat is,

u u u

h h h

s s s

fg g f

fg g f

fg g f

= −

= −

= −

/he quantity hfg is called the enthalpy of vapori4ation (or latent heat of vapori4ation.


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1#

Temp.,

T °C

Sat.Press.,

P sat

kPa

Specific volume,m3/kg

Internal energy,kJ/kg

Enthalpy,kJ/kg

Entropy,

kJ/kg⋅K

Sat. liquid,v

f

Sat.vapor,v

g

Sat.liquid,u

f

Evap.,u

fg

Sat.vapor,u

g

Sat.liquid,h

f

Evap.,h

fg

Sat.vapor,h

g

Sat.liquid,

s f

Evap., s

fg

Sat.vapor,

s g

0.01 0.611 0.001000 !06.00 0.00 !3".# !3".# 0.00 !$00.# !$00.# 0.0000 #.1$$6 #.1$$6

$ 0.%!$ 0.001000 1".03 !1.0! !360.% !3%1.% !1.0! !"%#.1 !$10.1 0.063 %.#"% #.0!"#

10 1.!!% 0.001000 106.3! "!.0! !3"6.6 !3%%. "!.0! !".! !$1#.! 0.1$11 %."%% %.%###

1$ 1.06 0.001001 .%%$ 6!.#% !33!.$ !3#$.$ 6!.#% !"6$." !$!%.3 0.!!"$ %.$$$# %.%03

!0 !.33# 0.00100! $.6! %3.#1 !31%." !"0!.3 %3.#1 !"$3.$ !$3." 0.!#6$ %.36#6 %.6661

!$ 3.10 0.001003 "3.3"0 10".%3 !30".3 !"0#.1 10".%3 !""1. !$"6.$ 0.36! %.1%#$ %.$$6

30 ".!" 0.00100" 3!.%# 1!$.3 !!#0.! !"1$.# 1!$." !"!#.% !$$$.6 0."36% %.01$! %."$!0

3$ $.6!# 0.001006 !$.!0$ 1"6.63 !!6.0 !"!!. 1"6.6" !"1.# !$6".6 0.$0$1 .%"66 %.3$1

"0 .3%$ 0.00100% 1#.$1$ 16.$3 !!61.# !"!#." 16.$3 !"06.0 !$3.$ 0.$!" .6%3! %.!$$6

"$ #.$#$ 0.001010 1$.!$1 1%%."3 !!". !"36.1 1%%."" !3#".0 !$%!." 0.63%6 .$!" %.1633

$0 1!.3$ 0.00101! 1!.0!6 !0#.33 !!33." !""!. !0#.3" !3%!.0 !$#1.3 0.03% .310 %.0"%

$$ 1$.6 0.00101$ #.$63# !30.!" !!1#.1 !""#.3 !30.!6 !36#.% !600.1 0.6%0 .!!1% .#%#%

& & & & & & & & & & & & &

%0 "."! 0.0010!# 3."0$3 33".# !1"6.6 !"%1.6 33$.0! !30%.0 !6"3.0 1.0$6 6.$3$$ .6111

%$ $.% 0.00103! !.%!61 3$$.#6 !131.# !"%.% 3$6.0! !!#$.3 !6$1." 1.13"6 6."0%# .$"3$

#0 0.1% 0.001036 !.3$#3 36.# !11.0 !"#".0 3.0" !!%!.$ !6$#.6 1.1#!# 6.!%$3 ."%!

#$ %".61 0.0010"0 1.#%0% 3#%.00 !10!.0 !$00.1 3#%.0# !!6#.6 !66.6 1.!$0" 6.16" ."1$1

100 101."! 0.0010"3 1.6!0 "1#.06 !0%.0 !$06.0 "1#.1 !!$6." !6$.6 1.30! 6.0"0 .3$"!

& & & & & & & & & & & & &

& & & & & & & & & & & & &

360 1%666 0.001%#$ 0.006#$0 1!6.16 6!$. !3$1.# 161.$3 !0.1 !"%1.6 3.#16$ 1.133 $.0$3

36$ 1#%!! 0.00!01$ 0.00600# 1.!! $!6." !303.6 1%1.16 60$.$ !"!!. ".000" 0.#"%# ".#"#3

30 !10"" 0.00!!1 0.00"#$3 1%"".$3 3%$.6 !!30.1 1%#1.1# ""3.1 !33".3 ".111# 0.6%#0 ".%00#

33.#$ !!06" 0.003106 0.003106 !01$.% 0 !01$.% !0%".3 0 !0%".3 "."00 0 "."00

able &-4 Saturated 'ater-emperature table


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1&

able &-5 Saturated 'ater-Pressure table

Press. P kPa

Sat. Temp.,

T sat

°C

Specific volume,m3/kg

Internal energy,kJ/kg

Enthalpy,kJ/kg

Entropy,

kJ/kg⋅K

Sat.liquid,v

f

Sat.vapor,v

g

Sat.liquid,u

f

Evap.,u

fg

Sat.vapor,u

g

Sat.liquid,h

f

Evap.,h

fg

Sat.vapor,h

g

Sat.liquid,

s f

Evap., s

fg

Sat.vapor,

s g

0.611 0.01 0.001000 !06.00 0.00 !3".# !3".# 0.00 !$00.# !$00.# 0.0000 #.1$$6 #.1$$6

1.0 6.# 0.001000 1!#.1# !#.30 !3$$.! !3%".$ !#.30 !"%"." !$13. 0.10$# %.%6#0 %.#"#

1.$ 13.0! 0.001001 %.#6" $".6# !33%.1 !3#!.% $".6# !"0.1 !$!". 0.1#$6 %.631" %.%!0

!.0 1.$0 0.001001 66.##0 3."3 !3!$.$ !3#%.# 3."3 !"$#.$ !$3!.# 0.!606 %."6!1 %.!!

!.$ !1.0% 0.00100! $".!"! %%."! !31$." !"03.% %%."! !"$1.0 !$3#." 0.311% %.330! %.6"!1

3.0 !".0% 0.001003 "$.6$" 100.#% !306.# !"0.# 100.#% !""3.# !$"".% 0.3$"3 %.!!!! %.$6$

".0 !%.#6 0.00100" 3".#1 1!1.3# !!#3.1 !"1".$ 1!1.3# !"3!.3 !$$3. 0."!!" %.0$10 %."3"

$.0 3!.% 0.00100$ !%.1%$ 13.$ !!%!.1 !"1#.% 13.$ !"!3.0 !$60. 0."6! .#16 %.3#3%

.$ "0.!# 0.00100% 1#.!33 16%." !!61.1 !"!#.% 16%.$ !"0$.3 !$".0 0.$63 .63% %.!$01

10 "$.%1 0.001010 1".60 1#1.# !!"$." !"3.! 1#1.%1 !3#!.1 !$%3.# 0.6"#! ."##6 %.1"%%

1$ $3.# 0.00101" 10.0!0 !!$.#3 !!!!.1 !""%.0 !!$.#" !3!.3 !$#%.3 0.$"# .!$!! %.001

!0 60.06 0.00101 .6"%1 !$1."0 !!0".6 !"$6.0 !$1."! !3$.$ !60%.# 0.%3!0 .0$! .#03

!$ 6".#6 0.0010!0 6.!03" !1.#3 !1#0." !"6!." !1.#6 !3"$.$ !61.$ 0.%#3! 6.#30 .%30!

30 6#.0# 0.0010!! $.!!% !%#.!" !1%.$ !"6. !%#.! !33$.3 !6!".6 0.#""1 6.%!3" .6$

"0 $.%6 0.0010!6 3.##33 31.$% !1$%.% !"6.3 31.6! !31%." !636.1 1.0!61 6.6"30 .66#1

$0 %1.3! 0.001030 3.!"03 3"0."# !1"!. !"%3.! 3"0.$" !30". !6"$.! 1.0#1! 6.$01# .$#31

$ #1.6 0.00103 !.!1! 3%".36 !111.% !"#6.1 3%"."" !!%.0 !66!." 1.!13! 6.!"!6 ."$$%

100 ##.61 0.0010"3 1.6#"1 "1."0 !0%%.! !$0$.6 "1.$1 !!$.$ !6$.0 1.30!% 6.0$6! .3$%#

1!$ 10$.# 0.0010"% 1.3$0 """.!3 !06%.% !$13.0 """.36 !!"0.6 !6%".# 1.3"1 $.#100 .!%"1

& & & & & & & & & & & & &

& & & & & & & & & & & & &

!0,000 36$.$ 0.00!03% 0.00$%6! 1%$.%" $0#.0 !!#".% 1%!6.$# $%$.$ !"1!.1 ".01"6 0.#16" ".#310

!1,000 36#.%3 0.00!!0 0.00"##" 1%"1.6! 3#1.# !!33.$ 1%%.# "$0." !33%." ".101 0.00$ ".%06

!!,000 33.1 0.00!03 0.0036"" 1#$1.6$ 1"0.% !0#!." !011.1! 161.$ !1!.6 ".!#"! 0.!"#6 ".$"3#

!!,06" 33.#$ 0.003106 0.003106 !01$.% 0 !01$.% !0%".3 0 !0%".3 "."00 0 "."00


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1

(ualit$ and Saturated )iquid-*apor +i#ture

'o", lets revie" the constant pressure heat addition process for. 6ince state # is a

mixture of saturated liquid and saturated vapor, ho" do "e locate it on the /v

diagramB /o establish the location of state # a ne" parameter called the quality x is

defined as

saturatedvapor

total

mass

mass

g

f g

m x

m m= =

+

/he quality is 4ero for the saturated liquid and one for the saturated vapor (+ C x C 1.

/he average specific volume at any state # is given in terms of the quality as follo"s.$onsider a mixture of saturated liquid and saturated vapor. /he liquid has a mass mf

and occupies a volume V f . /he vapor has a mass mg and occupies a volume V g .


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17

We noteV V V

m m m

V mv V m v V m v

f g

f g

f f f g g g

= +

= +

= = =, ,

mv m v m v

vm v

m

m v

m

f f g g

f f g g

= +

= +

>ecall the definition of quality x

xm

m

m

m m

g g

f g

= =

+

/henm

m

m m

m x

f g =

−

= −1

'ote, quantity 1 x is often given the name moisture. /he specific volume of thesaturated mixture becomes

v x v xv f g = − +' (1

/he form that "e use most often is

v v x v v f g f = + −' (


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0t is noted that the value of any extensive property per unit mass in the saturation

region is calculated from an equation having a form similar to that of the above

equation. )et Y be any extensive property and let y be the corresponding intensive

property, Y/m, then

' (

)*ere

f g f

f fg fg g f

Y y y x y ym

y xy y y y

= = + −

= + = −

/he term y fg is the difference bet"een the saturated vapor and the saturated liquid

values of the property y 5 y may be replaced by any of the variables v, u, h, or s.

/he follo"ing application is called the )ever >ule. /he )ever >ule is illustrated in thefollo"ing figures.

x y y

y

f

fg

=

−


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1=

Superheated %ater able

A substance is said to be superheated if the given temperature is greater than the

saturation temperature for the given pressure.

0n the superheated "ater /able A7, / and are the independent properties. /he

value of temperature to the right of the pressure is the saturation temperature for the

pressure.

/he first entry in the table is the saturated vapor state at the pressure.


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,ompressed )iquid %ater able

A substance is said to be a compressed liquid "hen the pressure is greater than the

saturation pressure for the temperature.

3ata for "ater compressed liquid states are found in the compressed liquid tables,/able A9. /able A9 is arranged lie /able A7, except the saturation states are the

saturated liquid states. 'ote that the data in /able A9 begins at !a or + times

atmospheric pressure.


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2+

At pressures belo" !a for "ater, the data are approximately equal to the

saturated liquid data at the given temperature. We approximate intensive parameter

y that is v, u, h, and s data as

y y f T ≅ +

/he enthalpy is more sensitive to variations in pressure5 therefore, at high pressures

the enthalpy can be approximated by

h h v P P f T f sat ≅ + −+ ' (

-or our "or, the compressed liquid enthalpy may be approximated by

h h f T ≅ +


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Saturated ce-%ater *apor ableWhen the temperature of a substance is belo" the triple point

temperature, the saturated solid and liquid phases exist in

equilibrium. Dere "e define the quality as the ratio of the mass that

is vapor to the total mass of solid and vapor in the saturatedsolidvapor mixture. /he process of changing directly from the solid phase

to the vapor phase is called sublimation. 3ata for saturated ice and "ater

vapor are given in /able A=. 0n /able A=, the term Subl. refers to the

difference bet"een the saturated vapor value and the saturated solid value.


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/he specific volume, internal energy, enthalpy, and entropy for a

mixture of saturated ice and saturated vapor are calculated similarly

to that of saturated liquidvapor mixtures.

y y y

y y x y

ig g i

i ig

= −

= +

"here the quality x of a saturated icevapor state is

xm

m m

g

i g

=

+


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2#

Ho' to ,hoose the !ight able

/he correct table to use to find the thermodynamic properties of a real substance can

al"ays be determined by comparing the no"n state properties to the properties in

the saturation region. Eiven the temperature or pressure and one other property from

the group v, u, h, and s, the follo"ing procedure is used. -or example if the pressure

and specific volume are specified, three questions are ased: -or the given pressure,

s -

s -

s -

v v

v v v

v v

f

f g

g

<

< <

<

6ome tables may not al"ays give the internal energy. When it is not listed, the

internal energy is calculated from the definition of the enthalpy as

u h Pv = −


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2&

/quations of State

/he relationship among the state variables, temperature, pressure, and specific

volume is called the equation of state. We no" consider the equation of state for the

vapor or gaseous phase of simple compressible substances.

deal 0as

Fased on our experience in chemistry and physics "e recall that the combination of

Foyles and $harles la"s for gases at lo" pressure result in the equation of state forthe ideal gas as

"here R is the constant of proportionality and is called the gas constant and taeson a different value for each gas. 0f a gas obeys this relation, it is called an ideal gas.

We often "rite this equation as

Pv RT =


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2

/he gas constant for ideal gases is related to the universal gas constant valid for all

substances through the molar mass (or molecular "eight. )et R u be the universal

gas constant. /hen,

R R

u=

/he mass, m, is related to the moles, , of substance through the molecular "eight or

molar mass, +, see /able A1.m ! =

/he ideal gas equation of state may be "ritten several "ays.

Pv RT

V P RT

m

PV mRT

=

=

=

DereP absolute pressure in !a, or

a

molar specific volume in

m#

@molT absolute temperature in G

v


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27

6ome values of the universal gas constant are

Hniversal Eas

$onstant, R u=.#1& ?@(mol⋅G

=.#1& a⋅m#@(mol⋅G1.8=7 Ftu@(lbmol⋅>

1& ft⋅lbf@(lbmol⋅>

1+.9# psia⋅ft#@(lbmol⋅>

/he ideal gas equation of state can be derived from basic principles if one assumes

1. 0ntermolecular forces are small.2. Iolume occupied by the particles is small.

/he ideal gas equation of state is used "hen (1 the pressure is small compared to

the critical pressure or (2 "hen the temperature is t"ice the critical temperature

and the pressure is less than 1+ times the critical pressure. /he critical point is that

state "here there is an instantaneous change from the liquid phase to the vaporphase for a substance. $ritical point data are given in /able A1.


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29

,ompressibilit$ actor

/o understand the above criteria and to determine ho" much the ideal gas equation

of state deviates from the actual gas behavior, "e introduce the compressibility factor

! as follo"s.

Pv " R T u=or

" Pv

R T u=

-or an ideal gas ! 1, and the deviation of ! from unity measures the deviation of

the actual P V T relation from the ideal gas equation of state. /he compressibility

factor is expressed as a function of the reduced pressure and the reduced

temperature. /he ! factor is approximately the same for all gases at the same

redu"ed temperature and redu"ed pressure, "hich are defined as

T T T

P P P

R

cr

R

cr

= = a.d

"here P "r and T "r are the critical pressure and temperature, respectively. /he critical

constant data for various substances are given in /able A1. /his is no"n as the

prin"iple of "orresponding states# -igure #1 gives a comparison of ! factors for

various gases and supports the principle of corresponding states.


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2=

When either P or T is unno"n, ! can be determined from the compressibility chart

"ith the help of the pseudo$redu"ed spe"ifi" volume, defined as

v v

R T

P

Ractual

cr

cr

=

-igure A1 presents the generali4ed compressibility chart based on data for a large

number of gases.

/h h t h th diti f hi h ! 1 d th b h id l


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28

/hese charts sho" the conditions for "hich ! 1 and the gas behaves as an ideal

gas:

1.P > J 1+ and T > K 2 or P J 1+P cr and T K 2T cr

2.P > JJ 1 or P JJ P cr

'ote: When P > is small, "e must mae sure that the state is not in the compressed

liquid region for the given temperature. A compressed liquid state is certainly not an

ideal gas state.

-or instance the critical pressure and temperature for oxygen are .+= !a and

1&.= G, respectively. -or temperatures greater than #++ G and pressures less than+ !a (1 atmosphere pressure is +.1+1# !a oxygen is considered to be an ideal

gas.

0f the system pressure is lo" enough and the temperature high enough (P and T are

compared to the critical values, gases "ill behave as ideal gases. $onsider the T v

diagram for "ater. /he figure belo" sho"s the percentage of error for the volume (LMv table N v idealM@v tableOx1++ for assuming "ater (superheated steam to be an ideal

gas.


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#+

We see that the region for "hich "ater behaves as an ideal gas is in the superheated

region and depends on both T and P . We must be cautioned that in this course,

"hen "ater is the "oring fluid, the ideal gas assumption may not be used to solve

problems. We must use the real gas relations, i.e., the property tables.


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#1

ther /quations of State

!any attempts have been made to eep the simplicity of the ideal gas equation of

state but yet account for the intermolecular forces and volume occupied by the

particles. /hree of these are

van der %aals&

' (' ( P a

vv # R T + − =

!

"here

a R T

P # RT

P

cr

cr

cr

cr

= =!

6" %

! !

a.d


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#2

'eattie$'ridgeman&

"here

/he constants a, (, " , )o, 'o for various substances are found in /able #&.

'enedi"t$%e(($Ru(in:

/he constants for various substances appearing in the FenedictWebb>ubin

equation are given in /able #&.

2. Pure Substances

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