Title Thermodynamic properties of gaseous propane and ... · as other thermodynamic property values at respective thermodynamic states. In the ... Jforeover, the numerical tables

Title Thermodynamic properties of gaseous propane and propene

Author(s) Watanabe, Koichi; Uematsu, Masahiko; Saegusa, Shogo

Citation The Review of Physical Chemistry of Japan (1976), 46(1): 39-53

Issue Date 1976-06-30

URL http://hdl.handle.net/2433/47027

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

The Review of Physical Chemistry of Japan Vol. 46 No. 1 (1976)

THE REVIGw OF PHYSICAL CttEHlaraY OF JAPAN, VOL. 46, No. 1, 197fi 39

THERMODYNAMIC PROPERTIES Of GASEOUS PROPANE AND PROPENE

By Kotcxt W-ATANAHE. MAS.4HrK0 UEMATSU AND SHOGU SAEGVSA

Based upon the most probable and additional raommended values with respect to the compressibility factor of propane and propene proposed by the High Pressure Data Center of Japan (I3PDCJ), new thermodynamic formu]ations are devised for these sub-stances in their gaseous phases covering the range of temperature from 273.15 K to 523,15 K and pressures up to 30 \IPa for propane and also [hat of temperature from 248.15 K to 498.ISK a¢d pressures up to 60 JfPa for propene, respativeh•. Using the formulated equations of state, the basic correlating iunctians for these hydrocarbons are derived and then the essential thermodynamic properties such as molar volume, enthalpy, entropy and isobaric specific heat capacity tan be calcu]ated.

Introduction

According to the Critical evaluation of the available P-V-T property data, the most probable and

additional recommended compressibility factor values far propane and propene were proposed by Date

and hvasakit> after the discussions at [he HPDCJ organized in the Society of Materials Science, Japan, under the sponsorship of the Agency of Science and Technology. The covered range of the stale para-

meters of this previous work was 248.15-548.15K and pressures up to 30MYa for propane, whereas

248.15-498.15 K and pressures up to bObfPa for propene. As a next procedure of the program of the

HPDCJ, new equations of state [or both propane and propene are formulated based upon these most

probable compressibility factor values for the purpose of calculating the P-V-T property values as well as other thermodynamic property values at respective thermodynamic states. In the present paper,

these new equations of state which can cover the range of temperatures 273.15-523.15 K and of pres-

sures up [0 30MPa for propane. and also that of temperature 248.15-498.15Ii and of pressures up to

bO MPa for propene are described. Jforeover, the numerical tables of the important derived thermo-

dynamic property values are also presented for these two difrerent hydrocarbons.

New Equations of Sfafe

The so-called skeleton table values of the compressibility factor for propane and propene are

composed of the most probable and additional recommended values proposed by the HPDCJ and their

covering ranges are shown in Figs. 1 and 2, respectively. It is needless to say that these skeleton table

(Received Ayril 5, 1976) f) K. Date and H. Iwasaki, TGfs lonrnal, 44, 1 (1974)

2) A. P. Kudchadker, G. H. Alani and B. J. Zwolinski, Chern. Rev., 68 , 659 (1968)


40 F. watanabe, \I. L'ematsu and S. Saegusa

values are accompanied by the estimated uncertainties as in the previous skeleton tables for methaneal,

ethane and ethene•+l. In the present study, both of the most probable and additional recommended

values were used as the basic data sets in devising the new equations of state; in addition to using the

estimated uncertainties mentioned above as the criteria for judging the devised equations.

As shown in Fig. 1, the skeleton table of compressibility factor for propane includes those even in

the liquid phase and therefore those data below 373.15 K were excluded [o be covered by the present

formulation beforehand. IC is also noteworthy that the present equations of state have to be formulated

as a tunction of density and temperature, since they must cover suth wider ranges of [he state para-

C

a

N

1.0~

0.5

~D?~

c - -,,,~b-tip ~5o titi5

_~~.~--;•

N'y O

L_1.~~

C3Hga

C.P.

N N

O

rÌ J

Fig.

00 5 10

p, mo4dm s 1 The most probable and additional recommended <ompressibility factor values for propane

~ most probable values Q additional recommended values

Q critical point (369.8211, 4.250ibIPa, 4.92mo1•dm 3)~)

1.5

n

a

c 1.0 r: N

as

C3 H6

~1t ooy _y~~~~

J~

0 ny =ea

.50

.44

-ao

i !~.

1 zo

•i owPa

Fig. 2 The most probable and additional recommended compressibility fac-tor values for propene

~ most probable values Q additional recommended values 0 critical point (36i.OK, 4.62 b1Fa,

5.54 mo]•dm-s) ~)

3) 4)

0 5 10

P, mo4dm's

J. Osugi, P. Takewki and T. lfaki[a, Tiiit Journal, 41, 60 (1971) R. Date, K 1Vatana6e and Nt. Uematsu, ibid., 43, 92 (1973)


Thermodynamic Properties of Gaseous Propane and Propene 41

meters as shown in Figs. 1 and 2. Although it is well known that the BenediU-W ebb-Robin (BR'R)

equation of state may correlate the P-V-T properties of simple hydrocarbons, it was experienced is

Table 1 Numerical constants in Eqs. (1) and (2) For propane and propene

61

fia

fi3

~~

fib

Qb

fi3

fiB

6g

fi10

all

file

fi13

fil{

filb

filfi

Propane

-4 .090

6.221

-4 .269

6.987

-6.741

2.527

-Z.18i

-1.294

3.186

0

-4 .190

1.i 28

2.448

1.020

3.160

1.451

9899 x 102

3928 x ]0=

9835 x 1011

0632 x (016

6069 x (021

2012 x 1026

i 931 x (035

8332 x 105

4256 x 106

3560 x 1013

3452 x 107

3052 x 101°

5948 x 1015

9572 x L022

4779 x 1012

Propene

1.770

-1 .407

2.815

-1.982

-8.976

5.317

0

-IS67

7.109

-1 .SOi

-7 .422

2.321

-1.61 i

LIiO

-4.218

-4297

6253 x 10+

2709 x 106

5700 x 1010

3817 x 1015

3010 x 1019

8693 x I D2a

4088 x I0~

3220 x 106

1735 x 1011

0764 x 1011

5824 x 108

1961 x 1011

2383 x 1016

4990 x 1072

6459 x 1012

Oli

ulB

419

t!p

Qal

O22

aR3

Oat

QRS

aas

azi

Y

cl

ca

~3

cq

Propane i Propeoe

0

0

-2 .782

- LS48

8.302

0

0

3.341

-4 .064

6.923

-1 .458

1.944

3.6fi3

2.547

-5.7i8

-3.047

3613 x IOto

2512 x lOi+

6178 x lots

9911 x 105

7194 x 108

3929 x lOta

i349x LOtB

4748 x !0+

65 x 108

4l x 10-a

13 x 10-$

05 x 10.8

4.937 -1 .821

~ 2.140 2.560 -2.976

1.138 -].417

0 0 1.048 0 2:479 3.209 4.724

2.714 -2 .328

6880 x lOte

7334 x IOts

9060 x IOu

2341 x lots

8160 x lOte

5003 x 10~r

9285 x ]OTa

8404 x lots

0640 x la

14 x lOt

83 r. 10-~

90 x 30'+

43 x l0-%

Table 2 Average deviations of the-rompressibility

propane and propene from Eq. (I)

[actor values for

Available data sources

\umber of data points Compared

Average deviatioa#

(q)

Propane

Skeleton table values[)

Sage et a7. (1934)m)

Beanie et al. (1937)trt

Deschner et al. (1940)%%~

Lv (I940)ta)

Reamer e/ al. (1949)s~)

Cherney et al. (1946ps1

178

i6

87

147

164

15

0.092

0.944

0.163

O.i00

_xa

0.133

0.359

Propene

Skeleton table valuestl

Farrivgton et ad. (1949)trt 1larchmaa et af, (1949)tr)

il4ichels e! al. (1953)tet

167

194

202

190

O.Oii

0.121

O.i1S

o.0ia

Colculated by the expression given helow:

a(e)~31(Zr.y-Z~„l)/Zr,~l x100

n

inhere Ze.r~=reported compressibility factor values, Zcnt=calculated values by Eq. (Q,

renumber of data points compared. .+ Reported data by Lu are in liquid phases where the present formulation is

effective.

not


42

Table 3-I

R. Natanabe, wI. Uematsu and 5. Saegusa

Calculated values of compressibility factor Z of gaseous propane and

their comparison with the skeleton table values

Pressure Temperature K (°C)

MPa 273.15 298.15 323.15 348.15 373.15

(O1 (251 (507 (751 (1007

0.1 0.97913 0 .98440 0.98787 0 .99028 0.99204

0.97948 0 .98392 0.98737 0 .99000 0.99198-0.035/0.040 0 .049/0.090 0.051/0.040 0 .028/0,040 0.006/0.040

0.5 0 .9119 x0.9398 0.9987 - _ 0.9591

0 .91433 10.93403 0 .99851 0.95911-0 .265/0.35 10.082/0.25 0 .020/0.20 -0.001/0.15 ~

1 ~ 0.8599 0.8927 0.9140 I

X0.85913 0 .89262 0.91599 I

10.069/0.25 0 .009/0.30 -0 .217/0.35 ~_...1

2 I 0 7565 0 8194 ~r ----+I I• the east probable values 1 0 .75956 0.82069 1~____J

1st line skeleton table value, 28T `0. 903/0.50.....y

-0.151/0.50 1I

32nd line calculated value, Z

calII

0.7057 I

0.70516 I

9

3rd line deviation (i)/uncertainty (8)

deviation (8)=[(ZST Zca1)/Zcal)X100

I 0.077/0.30 I I I ~ 0.5380 I 10.53599 ~ L 0.375/0 _30 ~

our precious works> that several additional terms were required [o the original BNR equation in order

to cover wider range of the present interest.

Hence; after several possible additional terms had been tested taking into consideration the. possi-

bility for obtaining a common functional form for both substances, the following functional form which

was developed from the original BWR equation was adopted for the present purpose:

P=RT p+(a~T t az+as/Tz+ a,/T°+a;/Ts+as/Ts+a; /Tsz)pz

+(aeT+ ay+aso/T+aaa/T")pa+(avT+aaa+aia/Tz+ais/ Ts)P'

+{azs+aia/T t a:s lTz=assl Ta)Ps+(ass+as /T+ azs/Tz+azslTa)Ps

+(azaT+¢zs+¢ze/Tz+a.,/T')p°(1+7Pt)eXP (-TPz)~ (I)

where P=pressure is MPa. T=temperature in K, T=(+273.15, t=temperature in 'C on IPTS-bg,

p=molar density in mobcm ', R=molar gas constant in J•K'' mol'', and a,; az,•••,azr; T=numerical constants. The following values were adapted as the atomic weights recommended by Ili PACsI as well as

the molar gas constant recommended by CODATA7~:

C= 12.011 ±0.001 ,

i) AI. Uematsu, S Saegusa, R. R'atanabe and L Tanishita, This Journal, 45, 53 (I97i) 6) Pare and dppl. Chem., 37, i89 (1914)

7) CODAT.9 Ball., ~\"o. I t (1973)

The Review of Physical Chemistry of Japan Vol.

Tpermodynamic Properties of Gaseous Propaae and Propeoe

Ta61e 3-2 (continued)

46 No

33

1 (1976)

Pressure

MPa

O.1

0.5

1

2

3

4

5

6

7

8

9

10

11

12

13

14

TEI[~P2YdGUIE K (°C)

398.15

1125)

923.15

(150)

448.15

(1751473.15

!2001

498.15

(225)

523.15

(250)

0,99339 0.99348

-0 .009/0

x0.9672 10.96699 10.022/0 10 .9328

~ 0.93286 ~ 0.007/0 10:8623 10.86049 10.211/0 I 10,7826 10.78069 10.244/0

~ 0.6894 0.68956

-0 .026/0

10 .5799 ~ 0.57959 10 .054/0 I

10.4479 I D, 44589 10.338/0 L . - - -

0.3726

i 0.37102 10.426/0 10 .3920

~ 0.39113 I o.zz2/o

10.4138 10 .41422

~-0.100/0 10.4372 10.43874

~-0.351/0 10.9635 10.46403 ~-0 .113/0

10.4893 10.48972

L 0.086/0

0.99448 0.99464

.040 -0.016/0.040 _---

0.9727 ~- 0.97300

.10 -0.031/0.10

0.9451 0.99549

.10 -0.041/0.10

0.8893 O. BB867

.10 0.071/0.10

0.8299 o.ez9oz

.10 0.106/0.10

0.7663 0.76589

.15 0.054/0.10

0.6973 0.69864

,30 -0.192/0.10

0.6258 0.62763

.30 -0.292/0.20

I 0.5583

1 0.55763

I 0.120/0.50 I 0.5028

I 0.50290

I -0 .021/0.50

_J 0.4753

0.97533 .40 -o.oa6/o.sD

0.4691 0.46953

.60 -0.092/0.45

0.9741 0.97613

.45 -0.300/0.25

0.4885 0.48944

.30 -0.191/0.20

0:5064 0.50654

.30 -0.028/0.30

0.5272 0.52592

.30 0.244/0.20

0.99539 0.99555

-0.016/0.040

0.9773 0.97770

-0.041/0.10

0.9550 0.95521

-0.022/0.10

0.9096 0.90965

-0 ,006/0.10

0.8629 0.86327

-0.093/0.10

0.8161 0.81607 0.004/0.10

0.7680 0.76817

-0 .022/0,10

0.7198 0.72010

-0 .042/0.15

0.6726 0.67320

-0.089/0:20

0.6284 0.63026

-0 .295/0.40

0.5995 0.59557

-D.lao/o.zs

0.5740 o,s7z7s 0.213/0.15

0.5646 0.5627.4 0.421/0.15

0.5632 0.56153 0.297/0.20

0.5670 0.56775

-0 .131/0.20

0.5785 0.57861

-0 .020/0.15

620 629 9/0.090

13 144 4/0.10

a9 288 2/D. 10

57 582

3/0.15

91 891 2/0.15

27 227 1/0.15

60 611 4/D, 15

04 079 0/0.15

67 690 7/0.15

60 540 9/0.15

85 762 8/0.10

61

513 5/0.10

15 920 5/0.10

24 022 0/0.25

78 769 8/0.35

94 050 1/0.20

0.99

0.99 -0 00

0.

0

98

.98 -o .ol

o. ss

0.96

0.00

OL 92 0.92

-0 .01

0.88

0.88 0.02

0.85 D. BS

O. DS

0.81

0.81 -0 .01

0.78 O,7B

-0,05

0.79

0.74 -0.02

0.71 0.71

0.08

0.68

0.68 0.12

0.66

0.66

0.14

0.65

0.64 0.35

0.64 0.69

0.34

0.63

0.63

0.01

0.63

0.69 -0 .17

0.99691 0.99757 0.99688 0.99737 0.003/0.040 0.020/0.040 -_~

0.9845 I 0.9667 0.98445 I 0.98692 0.005/0.10 I-0.022/0.15

0.9693 ~ 0.9713 0.96903 1 0.97402 0.028/0.10 i-0.279/0.15 0.9389 I 0,9484 0.93858 I 0.94881 0.039/0.15 I-O.Oa_3/0,15

0.9097 ~ 0.9240 0.90876 I 0.92447 0.104/0.151 -0.051/0.15 L

______ 0.8611

0.87970 0.159/0

O.B521 0.05157 0.062/0

0.8244 0.82960 -0.029/0

0.7985 0.79909 -0,074/0

0.7753 0.77547 -0 .021/0

0.7542 0.75425 -0.007/0

0.7364 0.73607 0.044/0

0.7211 0.72156 -0.063/0

0.7107 0.71117 -0 .066/0

0.7046 0.70511 -0 .072/0

0.7023 0.70323 -0.133/0

.ls

.ls

.15

.15

.15

.20

.15

.15

.15

.25

.15

0.9015 - ~ 0.90111 i

0.049/0.15 0.8784 1

0.87684 1 -0.050/0.151 1 0.6567 I 0.85780

-0.129/0.201

0.6375 1 0.83817 1 -0.060/0.201

0.6206 1 0.82015 I

D. 055/0.20 0.6048 i

0.60398

D. 103/0.25 0.7903 1

0.78992 1

0.048/0.25 0.7783 1

0.77826 ~ D. 005/0.151 1 0.7669 1 0.76926 1 -0 .045/0.151

0.7625 I 0.76308 ~ -D. 077/0.20

r------I 0.7596 1 0.75981

~ -0.027/0.20


44 K. Watanabe, bi. Uematsu and S. Saegusa

Table 3-3 (continued)

Pressure Temperature K 1°C1

lYe a 398.15 923.15 448.15 4]3.15 498.15 523.15

11251 (150) (1]51 (2001 1225] 12501

15 ~0. 5157- _

0.5482 _ _ _0.5924 0.6962 0.7016 0.7588~0

. 51563 0.54671 0.59260 0.64 ]4B 0.70514 1 0 .75936

16

0.013/0.30

1 0.5q 1]

0:2]3/0.20 -0.039/0.10

0.5692 0.6[85

-0 .198/0.25

0.65]3

-0 .218/0.

0.]069

151 -0,0]9/0.201I 0.7607

10.54165 0.56861 0.608]2 0.69760 0.7102] I 0.76157

10.009/0.20 0.138/0.25 -0.0.7/0.30 -0.096/0.30 -0.193/0. 20I -0.114/0.20

17 10 .5680 O 5909 0.6265 0.6702 0.71]61 0 7654

10.56]]0 0.590]2 0.65.632 0.6]006 0.]1868

I0.76617

0.051/0.20 0.030/0.30 0.029/0.10 0.021/0.10 -0.094/0. 20~ -0.700/0,2018 10.5942 0.6131 0.6451 0.6846 0. ]286 I 0_]]26

10.59376 0.61366 0.6449] 0.68426 D. ]2903 1 0.]7286

10:0]8/0 .20 -0 .055/0.35 0.021/0.10 0.020/0.25 0.078/0. 151 -0.039/0.20i

19 :0.6205 0.6355 0.6641 0.6992 o.7aos I o.7eza

10.6197-0 0.6]642 0.6643] 0.69977 D. 73970 I 0.78134

10.123/0.30 -0 .145/0.35 -0.040/0.10 -0.081/0.20 0.121/0.201 0.084/0.20

20 10.6466 0.6586 0.6843 D.715d 0.7578

1 0.793]

25

10.69568

i 0.191/0.951 D. 7]30

0.65959 0.68431-0.150/o. 3s -0.00?/0.30

r o.n72-~ D.767e

0.71626-0.069/0.20

o.emz

0.752770.142/0.

0.8309

1 0.791331

zol o.zzn/D.zD

I 0.85580.77917 I 0.7]678 / 0.78833 D. BO]04 0.93@] I 0.8562]

-0.152/0.50 1 0.106/0.401 -0.067/0.25 D.DZO/o.zo o.oe2/o. 201 -0.055/0.20_.._._~

30 r---"L ____~ tnc mst probable valves 1 0.9179

10.91]28

I

I

I1st tine skeleton table valve, ZST `0_068/0 _1J2nd line calculated value, Z

cal3rd line deviation (4)/uncertainty (U: deviation 143 =I/25T Z

eal)/Zea11K100

H= 1.00790.0001 ,

R= 8.31441-r0.0002G J•K-'mot-'.

In the procedure of determining the numerical constants in Eq. (1), the skeleton table values were

introduced as a set of input daza into aleast-square processing and the characteristic behavior of the

computed isobaric specific heat capacity values were also carefully examined. Especially, the reported

experimental values by Biet ei a/.e> for propene in the range of temperature 298.11 K-473.15 K and

pressures up [0 12 MPa were taken into consideration for the present purpose. As a result of these

procedures, the numerical con_~tan[s for both propane and propene in Eq. Q) were fixed on as listed in Table 1.

In case qC computing the isobaric specific heat capacity, the following torrelations for the isobaric

specific heat capacity at [he ideal gas state. C °; devised by Maki[asl were used:

Cp =c,+csTtcsT~+csTa. (2 )

The numerical constanu which appeared in Eq. (2) are also tabulated for both propane and propene

8) I{. Bier, G. Ernst, J, Kunze and G. htaurer, !. Chem. TLermadynarnics, 6. 1039 (19)4) 9) T. Makitn, private communication to the present author

i

I

I

1

i


45Thermodynamic Properties of Gauous-Propane and P ropenc

O OI O O O N O- O O ~ O N N •N`/

1

VÔ O O ~ N ~ ~O /O HO n0 b0 rv0 n0 P SO \ eNVOSm ^n\ rvNN \r n\ nmN ym\ \ o \ Pn\ ~ v \ rn mloP .+.. o.+ NN ..m PPN aa~ ° ~n hp~o Ov~i ., mco omelet o °m°m°o mmo ~mo ma o Om4mo mm°o r~o rro ~~o hro e~oi

000 ooolo Go 000 000 ood oco 000 000 000 000 000 000 GGOI

° oI o 0 0 0 0 0 0 0 0l o .. I .°+ n I

C P p NO .a0 00 40 r0 /O n Y n0 PO O n ~I ry m \ nr\I \ O ^ mn\ mN\ \ nOm rn\ O-~^ Nm\ OP\ nr\ nln(lo NS m TmON m nnm .4 mCN n00 I PP mmNl PS m r^N Po NOI PPS PPOISS.'I PPC O m6S m O S G r O n rr0 000 OOOI000 OOC COC 000 OC-O p00 000 000 000 000 O O O

_ O n I .°. .+ ti r r °~ °~ .°. r0 m01 n0 NO NO VO ~0 PO ~i0 n0 NO nO 00~ \ ~ n\ nr\ .~n\ 6\ mvC ..I~n nnn rOn \ rvm\ n..\ n..\ _ YN1mN y0. I1n .+P ..O mP O 4~~1 Nn nC OPn „ net nnNl n PPO PPOIPmO PPO m00 m0n (-Im-.~1 hrN hf~-N. Om0 VV.. VVN N O~ NNn mn

000 oGclooo 000 000 000 oco ocG 000 GGG Go.G oGG GGG oGo~ °

0 1 ° 0 0 o e o e o 0 o .. I neo I Oo ~ f' '' ~ me N~ no No ~o no mo \ rm\ Or\ NmN rNm v^PP Ocv VnN Onn N/n \m N\ qmP O.ni 1\D mmm PPO rOIN 00 rC"y rr ~m4 PPP PPO PP v PO OIP ~+0.~ mY)O NO 40 000 OOOI000 000 000 O ' ' GOO 000 000 000 000 000 000 1

O I NO .°iI O O O O O N ~ O n N O r OI Ô r O N O T O n O f ~ ~ n O O V O r° mM SnP anPl~ \ Nn\ pe.P NO\ n.\ V.P\ 6P\ .~N°\1 .~O\ n\ PPP mmP P" P ..n I P rrS G rm+S° Mm4 00 /mim n PAS ~aS PPS mm sG O O O ap

DOO OOOI000 GCO 000 °oo Oco 0 000 0 / e00 000 000 Oo0

I

I

I

I

______J

° e~ o o ..~

gory a°~l am\ .no o\ n\ mmo mao~mmo° °m°mo O1r°o mo° 000 000000 000 000 oco

or- °nl .°+ °.

n P~nb\ NOn 4N'. I~I~T N~ hc0 O OOOO 000 I

e

~~H

C 00~ ~,

myry ~ NNO uy'~ 000 O

E y T x 4 N

~ a 9 V O a ~ v ~ V 9 a

V V Ô s ~ V C \ N4 O q a .. ~f

4 V 9 `+ y

y ~ N O V

F a ~ ' Y U V J

9 0 C Y y Y N O

r--- ~i ncl no

"m~u°ieo m

eln ~.y. o oclooo

i~

O

O Pn0 ..off P 0 M N Q. O

O G C

.+ O

n0 P P fV

CGG

N

C O

d

O

O~ O Nq0 NO~ POI VN\ N~~~Vrv~ PP

O 000000 000 0000 OO ~~

O O .1 P O

N \ 0mrv P00

o O O

f'1 ~ ~ a I I~ ~ I IHI I m c b LJ., r

0

0 m n \ ~~o

P P D

O O O

m

e

N O

n ._

.. n

nN c-P

:~ ..

r D

.-I N

/p/

u

N

a E

NNON

N.1N q

Y

6

V

O

C O

n v

L .3

C _~ `n a E 0

.Y

p v e m

u c 4 6 O

d

7

u m

O N 0 m T

a

V

a E 0 ò u

a

u A

V q V

v

F

~~

~I

I

I 1


4fi K. Watanabe, hf. Uematsu and S. Saegusa

Table 4-] (continued)

4vazsu[a

MPa

13

la

15

3E

lJ

lP

19

26

Mk

30

35

49

a5

SO

GO

2aepetahre x 1°cl

398.15

11251

423.15

(3501

448.15

I1J51

4)3.11

1200)

)98.13

(3251

r 0.4496 -1 0:999]6

j-o.o3s/0.35 1 0.4]18 '

0.9]1]9 I 1 0.002/0.20 ' (1.9999 ' OA993i ' u . uo/o.2s I

1 D.svJ I 0.5]]23 1 0.090/0.20 I 1 0.5404 I O. s4029 1 o.ozD/o. zo 1 D.ss33 ' 0 .56394

-G.GZa/D.zG

I 0.s0G3 1 0.56662 1 -o.osc/o.zG

1 o. s6s4 I 0.60990 I •o: ass/o,2o I ~ G.]zs1 I O.J249J I 0.010/0.15 I 0.8382 1 0.81829 1-0.013/0.15 I 0

.9999 1 0.99939

~ -01020/0.15 ' 1

.0588 1 1.0589]

j -0.016/0.15 ' 1

.1665 ' 1.16660

~ -0.000/0.20 ' 1.2]2] ' 1 .2]363

~ 0.006/0.20 1 1.4006 ' 3 .48043 '

0 011/0 20 L _.__.

o. soaz 0.30410

-o. o5s/o.1o

o. slez 0.51825

-0.009/0.16

0.5301 0.534:] -0.069/0.10

0.5523 O.6s229 0.003/0.15

O. Sr1J O.5J116 a.osc/a.zo

0.59E 0.540)6 D.DSJ/o.za

Dsua 0.61086 0.023/0.x0

0.6312 Os333D

-o_ols/0.20

D.6J98 0. 5E252

-0.124/0.15

o.se3o 0.583]6

-0.130/0.1$

0.591 0.59132

-o. ozo/o.ls

r 0.]]59 1

0.]358] 0.000/0.151 0-B9L 0.8:113 I 0.009/0.101

0.9453 I 0.9454) I

-o. ola/D.ld

3. o4J9 ~ 3. o4aso -0.05]/0.15 L1°-01 I

1.1s013 -0.002/420 1.2501 I

1.2501) 1 0.011/0.201

1.44]4 1 1.04]00 1

0.025/0_2)

0.6029 o: soma 0.063/0.16

0.6158 D.6li01 0.129/0.30

0.6309 O.s2965 0.319/0.30

o. s9ss 0.6;552

-0 .003/0. xc

o. GS2o 0.66230

-o. Ges/0.2s

0.6594 0.65645

-0.009/0.10

0.6552 0.65511 0.019/0:10

0.6560 O.fi5591 D.ala/D.lo

O.E6Di O.E6O39 0.031/0.30

O.E5>0 D. [6]31

os]s] D.6T6J0 0.000/0.10

O.68J2 0.68T90 -0 .102/0.10

onooG 0.]0053

_ o.0]s/a.la

408)/0.1 a1 0.]205 I 0.]2133

-0.!15/0.15

0.]266 I O.J266] I

-0.009/O.ls1

0.]394 1 O.J]392 I 0.063/0.301

D.]43a 1 0.]4281 1

0.13]/0.2)

o. izsz_-1 O.J2s9s j D.1W/D.z01

0.]204 I 0.]2001 0.064/0.1 s

0.]1]5 I 0.]1]66 I

-D.azs/41s1

O.Jll6 0.]Laz3 .1

in Table 1.

Comparison of

values and also with

the

the

compressibility factor

experimental data of

values computed

both propanelo-ls7

from Eq. (1) with

and propenels-1s)

the

were

skeleton table

conducted. It

IO) ll) l2) 13) 14) 13) 16) 17) l8)

B. H, Sage, J. G. Schaafsma and W. N. Lacey. /rtd. Eng. Chem., 26, 1218 (1934)

J. 4 Beanie, W.C. Kay and L Kaminsky, I. Am. Chem. Soc., 59, 1589 (1937) N. lV. Deschner and G. G. Brown, Ind. Eng. CGeno., 32, 83fi (1940) J. H. Burgoyne, Roc. Roy. Soc„ A176, 280 (1940) H. H. Reamer, B. H. Sage and W. V. Lacey, Ind. Eng. Chem., 41, 482 (1949) B.J. Cberney, H. Dlarchman and R. York, Jr., ibid., 41, 2613 (1949) P. S. Farringma aad B. H. Sage, ibid., 41, 1734 (1949) H. hiarchman, H. W, Prengle. Jr, aad R.L. DSotard, ibid., 41, 2638 (1949) A. J4ichels, T. Wassenarr, P. Louwerse, R.J. Luabeck and G.J. R'olkers, Physics, 19, 287 (1953)


Thermodynamic Properties of Gaseous Propane and Propene ii

1'a61e 5 Kumerical cons[anls in Fq, (; for propane and propcne

Propane Propene Propane Propene

d.

dy

d.

d;

d;

b,

bz

h b. b;

bs

b~

bB

by

bra

bar

-L18a ssz3xla

1.257 4194x102

-1 .273 70iix 10-~

9.196 8764 x 10_s

2,539 2081 x 10-9

4.650 7610x 30°

-4 .090 9899 x ]OZ

6.211 3928 x 105

-4.269 9835 x 1011

6.987 083tx ]016

-6.741 6069 x 1 O21

2.827 2012 x IOzs

-2 .187 7931 X 1055

-6 .474 1658 x I0~

1.593 2143 x LOB

0

-1 .295 1780 x 1015

-1 .360

2.6i 1

-2.362

-4.521

1.940

-2 .3i i

1.770

-1 .401

2.813

-1 .982

-5 .976

5.317

0

-3 .783

3.334

-7 .i1 i

-3.ill

6591 x I0/

0580 x 102

4147 x 10_z

8282 x 10'5

3623 x 10'8

7028 x 101

6253 x 10°

2709 x 108

1700 x 101°

3811 x 1015

3010 x 1019

8697 x 10zt

7044 x l05

6610 x 108

8673 x 101°

0381 x 1011

biz

baa

ban

bas

bis

baa

bie

bay

by

bar

baz

bza

bza

bas

bas

baa

r

5.76t

-8.161

3.401

1.053

3.638

0

0

-6 .935

-3.696

1.660

0

0

3.341 -4 .064

6.923

-1 .456

1.944

lso7 x loft

OIi2x (00

9827 x I01<

6324x 1022

6947 x 101

9033 x 1018

1023 x 1013

5316 x 1018

9911 x 105

7594 x l06

3929 x 1012

5349 x 1016

4748 x 104

7.751 9414 x 107

-5 .390 6i36 x 1016

3.834 1177 x ]015

-1.406 1663 x l Ozz

-1.074 4115 X ] 0°

1.234 4220 x 1016

-4Si4 3334x1016

5.332 2630x IOz0

1.120 4682 x 1016

->.953 6320x1012

2.277 OOOS x 1020

-2 .835 8570x102z

0

0

4.048 8404 x 1012

0

2.479 0640x 104

should be noted that the comparison with the at•ailahle data was performed only with those taken into

consideration for the establishment of the skeleton tables in the previous work by Date and Iwasaki». The average deviation of these reported experimental data from Eq. (I) are shown in Table 2 and it

can be understood thaz the computed compressibility factor values are in satisfactory agreement with

the skeleton table values and the experimental data which were evaluazed to be found more reliable

by the HPDCPI. The computed compressibility factor values as well as their comparison with the

skeleton [able values are tabulated for propane and propene in Tables 3 and 4, respectively.

I[ is confirmed that Eq. (1) can reproduce satisfactorily the skeleton table values of propane and

propene for the whole temperature ranges assigned within the gaseous phases. But, simply because of the fact that the derived values with respect to the isobaric specific heat capacity are less reliable along

the two bounded isotherms of 298.15Ii and 548.15 K for propane, the effective range of the present

equation of staze for gaseous propane is limited to somewhat narrow region as mentioned previously

and therefore those computedvalues in this limited range of temperature are only given in Table 3.

Oa the other hand, the derived values of the isobaric specific heat capacity foc propene are not reason-

able only along Che isotherm of 373.15 K for supercritical pressures and hence this region is excluded

from the effective range of the proposed equation as shown in Table 4, however the P-V-T hehavior

along this isotherm is completely satisfactory. It may he understood that this kind of behavior is mainly

due to the difficulty of Htting the P-V-T plane alone without considering the tendency of the derived

property values especially in such a vicinity of [be critical isotherm as 373.15 K for gaseous propene.


48 A. R'atanabe, hi. tiematsu and S. Saegusa

Tahle 6-I Calculated values of molar volume, molar enthalpy and molar entropy for Kase0u5 propane

Pressure

.rea

0.1

0.5

1

2

3

4

5

6

7

B

9

10

11

Temperature K (°C)

273.15 (0)

298.15

(25)

323.15 (50)

348.15 175)

373.15 (100)

398.15 (125)

923.15 (1501

498.15

(175]

473.15 (200)

498.15 (225)

923.15 (2501

12

13

14

15

16

1st

2nd

3rd

22245 24391 26529 28657 30776 32886 -1903 -112 .6 1805 3855 6033 8332

-6.115 0.1128 6.285 12.40 18.43 24.40

4533.1 5019.1 5491.2 5951.3 6402.2 -608.9 1362 3474 5706 BO50

-14.38 -8 .038 -1.745 4.446 10.52

2308.3 2567.8 2891.9 3088.1 723.7 2948 5269 7680

-15.21 -8.581 -2.143 4.108

1099.3 1273.0 1424.3 1641 4266 6866

-17 .16 -9_879 -3.129

729.26 861.96 2976 5923

-15 .92 -8.278

415_73 570.69 893.9 4774

-23.02 -12 .93

383.73 3256

-17.93

246.01 1049

-29.26

173.25 -1026

-29 .96

148.13 -2093

-32.95

136.47 -2612

-34.71

129.48 -2970

-35 .94

lz4.ss

line a molar wlume V in em3.mo1 1 -36?B9 line molar enthalpy H in J•mml 1 121

.03 line molaz entropy 8 in J•X 1•mol 1 -7906

-37.67

118.16 -3548

-38.32

115.80 -3659

-38 .90

113.80 -]746

-39.40

312.07 -3815

-39.86

34994 10750 30.29

6806.5 10500 16.50

332fi.4 10180 10.20

1567.7 9098

3.282

972.24 8795

-1 _4x3

673.64 7902

-5.306

491.60 6944

-8 _933

368.03 5840

-12 .55

280.27 4597

-16 _25

221.17 3368

-19 .74

185.81 2388

-22 .53

165.19 1694

-24.58

lsz ze 1201

-26_12

143.50 837.7 -27 .33

137.09 560.3

-28.32

132.16 342.5 -29.15

128.23 168.1 -29.87

124.99 26.34 -30.50

37095 13290 36.11

7286.0

13o7a

22.39

3559.2 12]90 16.18

1694.7 12190 9.469

1072.2 11sfi0 5.066

760.19

10890

1. 6d9

572.46 10160

-1.550

447.20 9375

-4 .426

358.34

8592 -7.179

293.55 7681

-9 .824

246.5]

6845 -12 .29

213.92

fi101

-14.46

190.45 5485

-16.28

174.36 4995

-17.78

162.73 4606

-19.03

154.00 9299

-zo.97

147.21 0041

-20 .97

141.7s 3813

-21.]6

39194

15940

41. Bfi

7721,9

ls]4a

28.19

3787.9 15990 22.05

1821.1 14970 15.49

1165.6 14430

11.28

B 38.20

13860

].996

642.11 13260 5.192

511.93 12640 2.6]3

419.76

lzooa 0.3410

351.79 11350

-1 .851

300.56

10]00

-3.914

267.66 100]0

-5.829

232.17 9496

-7.970

209. BB 8985

-9.116

192.97 esa7

-10.47

179.98 8176

-11. sa

169.81 7865

-12 .67

163.69 7603

-13.57

41289 18]00 47.55

8154.9 lesza 33.92

4013.5 18300 27.83

1943.7 17830 21.39

1254:6

1]360 17.32

910.89 16870 14.20

]05.41 16360 11.58

Sfi9.22 15850 9.2]4

972.81 15330 7.182

401.48 19800 5.247

347_11 1 C270

3.491

304.87 13750 1.752

2]1.69 13260 0.1814

245.9fi 12800

-1.267

224.65 12370

-2. SBB

208.05 11990

-3; 78,2

194.70 11660

-9 .857

183.86 11370

-6.823

43382 21570 53_17

e585.fi 21410 39.57

4236.7 21210 33.53

2063.5 20790 27.19

1340.4

20370

23.22

979. BB 19940 20_21

764.53

19500

17.7]

621.86 19060 15.57

52D, 83

18620

13_69

445.92 18180 11.87

388.56

17740 10_23

393.59 17300 8.705

307.79 16880 7.279

278.84 16480 5.948

255.32 16100 a. na

236.07 15740 3.564

220.20 lsa2o z.so7

2ozoa lslza 1.536


Thermodynamic Properties of Gaseous Propane and Propene

Table 6-2 (continued)

Pressure Temperature x rc1

Moa ]98-15 123.15 448.]5 4]3-15 498.15 Sz3.ls

!1251 1150) 11]51 12001 f 21st (2507

1] 310.55 122.25 13].28 155.06 1]4-95 196.01-3865 -89.94 3660 ]301 11110 I d860

-4G.2fi -31.0] -22 .4fi -14. IB -6.694 0.6451

l8 109.19 119.90 13]-SL 199.55 lfi].52 1fl6.]fi-3911 -185.9 3519 ]193 1089e 14620

-40.66 -01. $8 -23.09 -15.10 -]-4fl3 -0 -1]19

19 10].98 31].85 130-29 144.89 161.21 1]e.fl]-39¢3 -265 .2 3391 ]0]3 10]00 14410

-41 -ai -32 .05 -23.66 -15 .]5 -8.19] -0.9250

20 106.8] 116.01 121.43 140.89 195.88 1]2.10-3966 -730 .8 ]2 B5 G89] 10530 14220

-41.30 -32 .44 -24.11 -1G.34 -8.851 -1 .618

25 102.51 109.26 11].58 126.99 13]-55 198.98-3989 -512 .8 ?955 6413 995] 13560

-C2 _]I -]4.24 -36 .28 -18 .13 -1 L G3 -C Al]

30 126.64

9614

-13 -40

15[ line mler volume u in cn 3•rol-1

2nd line e molar on chalpv ti in S•rol_1

3rd 11ne molar entropy 5 in J.x l .roi 1

39

Basic Correlating Function

i

When density and temperature are chosen as the independent vaziables, [he expressions for pres-

sure and all other thermodynamic properties can be derived directly by the partial differentiation of

a basic correlating function A=.4(p, T), where A is the molar Helmholtz function. In the present study,

the molar Helmholtz function A in J•mol-' is derived from Eqs. (1) and (2) as follows:

A=d,tdxT+d,T'+dsT°+dsT`+dsT•1nT+RT•la p

+(b,T +b~ +b,/T ° +b,/T ` +bs/T °+6s/T °+b,/T'E)p

+(LsT t bs+b,°/T +L„/T''-)p'+(b,aT+L,a+b„/T'+bs/T°)p°

+(b,s+b,r/T+b,e/T°+b,s/T„ip9

+(8P°+b„/T+bYS/7"+b„/T °)ps

+(b„Ttb_s+ba/T'+b„/T`xll7-(P°12+1/r)exp(-rp')]. (3)

The numerical constants in Eq. (3) are given in Table 5. The numerical values of d, and d=in Eq. (3)

are fixed due to the following specified conditions:

(i) Molar entropy, S=0 J•R''mol'' at 298.15K and 0.301325 MPa,

(ii) Molar enthalpy. A=0 pmol'' at 298.15 K and 0 MPa.

Derived Functions


So

Table 7-t

R. R'atanabe, J4. Uematsu and 5. Saegusa

Calculated values of molar volume. molar enthalpy

and molar entropy for gaseous propeae

Pressure

T@a

0.1

0.5

1

2

3

n

5

6

7

8

9

10

11

1?

13

}4

15

is

Temperature x t°ci

298.15

(-25)

273.15 /0I

298.15

(251

323.15 (50)

398.15 1]51

37].15 398_15 1100) (125)

42].15

(1501

448.15

(1751

4]3.15

(2001

498.15

(225)

20110 -3179

-11_13

1st

2nd

3rd

late

line

line

22286 -1691

-5.423

molar

molar

mOlaY

24439 -110 .d o.uzs

4586.6 -190.7 -14.40

2071.9 -1312 -21.93

volume V

enthalpy

enCYOpy

26574 1558 s.4as

SD67.9

1168 -9.73A

2362.7 615.6 -15 .72

959.67 -878.0 -25.02

2x697 3315 10:T2

5532.1 2989

-3.305

262]_3 2595

-9 .969

1153_1 la7s

-17.99

623.07 -69.11 -29_90

in m3•mol 1

H in J•mol 1

5 3n J•K 1•mol 1

30810 32917 5164 7105

15.85 20. BH

5985.3 6431.2 4884 6860

1.950 7.073

2877.1 3117.6 4512 6540

-4 .512 0.7458

1312.1 1455.2 3673 SB47

-11.90 -6.273

776.45 894.82 2649 5053

-37 .37 -11.32

989.29 608.35 1258 4129

-22.75 -15.29

429.50 3009

-19.41

302.88 1562

-23.94

211.82 -227.4 -29.07

162.72 -1725

-33.30

141.27 -2587

-35. B4

130.13 -3101

-37 .47

323.16 -3444

-38.65

118.26 -3693

-39.58

ua. s3 -3882

-4o .3a

111.56 -<071

-al.oo

los.lo -a1s1

-al.se

107.20 -4249

-42.10

39215 13490 35.99

]743.2

13310

21:89

3800.9

13aea

I5.]]

1841.3 12610 9.287

1185.7 32130 S.15fi

e5fi. 89 11620 1.968

660.0]

11100

-o.7zla

529.1]

10560 -3.109

436.2? 10010

-5.29]

767.40

9944 -7.337

315.02 88]8

-9.253

274.56 8322

-11 .05

247.09

7]91

-12_]2

218.53 7298

-14.25

199.26 6852

-15 .63

189.08 6457

-16.87

172.02 6113

-17.9]

162.32 5815

-18.95

37118 31270 30.72

7309.0

11070

17.0]

3582.0

10820

10.86

1717.2

10290

4.253

1094.4 9740

-0 .0279

782.19 9152

-3.400

594.32 8528

-6.314

968.93

7864

-8.973

379.74 7163

-ll.48

313.93

6436 -13.87

26C.69 5]06

-16.16

227.98 5008

-18.25

2on.s1 4377

:20.13

181.Ofi 3837

-21.77

166.39 3379

-23 .17

155.37 3004

-24.37

146.89 2696

-25:39

140.20 2441

-26.28

35019 9140

25.84

6871.9

8921

12.09

3352.0 8690 5.860

1589.1 8042

-0.9174

996.65 7393

-5.41]

700.99 6880

-s.o7e

520.33 5888

-12.38

398.3]

5003 -15.54

310.99 4021

-18.]0

24].]0

2980 -21.81

203.88

1989

-26.fi9

175.39 116fi

-27 .08

ls7.la 537.7 -28.95

145.03 68.30 -30.42

136.53 -ze7.2

-31 .59

130.24 -562.9 -32.Sfi

125.36 -781.8 -33.38

121.44 -958.9 -39 .09

41310 15800 40.31

81]5.3

15690

26.68

4033.4

15430

20.61

1962.5

15010

14.21

1272.3 14570 10.19

sn.al

14130

7.130

720.87

11680

4.588

583.66 13220 2.369

486.27 12760

0.3698

413.97

12290 -Lass

358.62

11830

-3.172

315.33 11370

-4 .765

280,96 10930

-6.253

253.40 10500

-7.639

231.13

loua -s.s2a

213.01 9738

-10.11

198.17 saoz

-11.20

185.92 9098

-12 .19


Thermodynamic Properties of

Table 7-2

Gaseous Propane

(continued)

and Propene 57

Pzescura

NPe

19

]e

19

39

25

30

35

d0

d5

50

60

xemperac~-e K I•CI

198.15

uzs

431.15

usm

9/d.15 395)

49].15 Izaol

499.15 ~zzv

109.]1 -4]31

-az.3i

301.63 -4399

-a 1.06

102.21 -dd55

-a]. as

100.93 -as93

-41 . ]e

95.99] -a619

-d5. ]5

9].502 -asiB

-46.63

09.814 -rile -4]sB

ei.s4o -:i6a

-a8.61

es. 0x6 -La39

-a9.43

8a. x58

-a]31

-50.18

81.680 -a036

-51 _49

110.21 -lla

-l4.]1

115. d] -1x36

-]9. ]B

111.11 -1321

-35.]9

311. os -1411

-lc. xs

301.56 -1681

-18.16

98.641 -1]95

-39.41

ss. aao nel9

-a9s1

92.233 -1]0fi

-41.84

e9.9x6 -1]15

-4x.)5

Bi.9B2 -161fi -41.5]

84. BS1 -1159

-45. W

n;.ao 2230 -2).06

v9.3a 3093 -2].]9

136.59 1901

8.3]

1:3.39 1]]]

-38'.93

lsa.ax 9998

-19.83

la].90 9l3]

-20.62

1a2.4J 914)

-21.J2

1 ]). )9 4984

-21.9]

I6v lim

V in

3na 11ne

x Ln

3cd iine

5 Sn

1]s.]a 882]

-11.10

18].21

8989 -11.9]

199.99 Blil

-1469

193.8] 8181 -19. ]B

mlaz wlwe m •ml 1 ~ mla en[Tilpy 3~m1 1

mlec mtre6+y S•K 1-ml 1

i

i

i

According to the general thermodynamic relations, the pressure P in MPa, the molar entropy S in

J•K'3mo1'r, the molaz enthalpy H in J•mol-', the molar isobaric specific heat capacity C, in J•K'~mol'r and the molar isochoric speci5c heat rapacity C, in J•K'' mol-' can be calculated by the following

expressions:

P=P=(aAl aP)r , (4 )

2(aA/aP)7+P(~~laP`)r

In addition, the compressibility factor Z and the molar volume V in cm'•mol'' can be calculated from

the following expressions, respectively:


52 K_ Watanahe bi. Uematsu and S, Saegusa

Calculated Thermodynamic Properties

By differentiating the new equations of state expressed in the basic correlating functions for gaseous

propane and propene, Eq. (3), all of the thermodynamic properties may be calculated as shown in the

previous seRion. The calculated molar volume; the molar enthalpy and the molar entropy for both

gaseous propane and propene are tabulated in Tables 6 and 7, respectively. With respect to the molar isobaric specific heat capacity for both propane and propene, the calcu-

lated results are shown on CP p diagrams in Figs. 3 and 4. It is also noteworthy that the calculated

Cp values for gaseous propene are in good agreement with the reported experimental data by Bier et

al.e>, wbere they overlap. The average deviation is found as 0.362% with respect to 96 data points

compazed.

1

E

X

300

2~

200

i

~`~~i

isdc; r1' j

usY~

~-3H8

~~

,~o

ioo

so

~t

~-_is~

0 2 4 6 8 70

p, mobdm _3

Calculated molar isobaric specific

heal capacity for propane

O

X

250

200

150

100

Fig. 3

50Q

Fig. 4

~ ~ ,nt 3H

_ I~

~sY III I\insc

2 4 6 8 10 12

o, mal•dm s

Calculated molar isobaric specific

beat capacity for propene

Conclusion

As a part of the activities of the High Pressure Data Center of Japan, new equations of state, Eq.

(1), for both gaseous propane and propene are formulated based upon the most probable and additional recommended compressibility factor values proposed previously by the HPDCJ. The present formu-

lations given as a function of the density and temperature can cover the range of temperature 273.15

K-523.15K and pressures up Co 30MPa for propane, and also that of temperature 248.15 K-498.15 K

and pressures up to 60 MPa for propene, respectively.


Thermodynamic Properties of Gaseous Propane and Propene a3

Based upon the established equations of state, the basic correlating functions given as the molar

Helmholtz function are derived and hence the additional thermodynamic property values such as molar

volume, molar entropy, molar enthalpy and molar isobaric specific heat capacity, are also calculated

and presented.

It was also confirmed that the so-called extended BR'R equations are very effective to cover the

wide range of the state parameters in gaseous region especially for the serial hydrocarbons like ethane,

e[hene. propane and propene in the previous and present studies by the present authors.

Acknowledgment

The present work was discussed by the following members and the cooperator . of [be Working Committee of the High Pressure Dafa Center of Japan:

J. Osagi, Y. Takezaki (Kyoto University);

H. Iwasaki, S. Takahashi. K. Date (Tohoku University);

T. Makita, Y. Tanaka (Kobe University);

I. Tanishita (Ikutoku Technical University;;

A. Nagashima (Keio University),

to whom the authors with to express their sincere appreciation for their valuable suggestions and dis•

cussions.

As for the financial support to the present work, the authors are partially indebted to fhe sponsor-

ship of the Agency oC Science and Technology.

Deparlrnent of Mechmafc¢I Engineering

Aaadty of E>gineering

keno University

Yokohama 223

.lapan

Title Thermodynamic properties of gaseous propane and ... · as other thermodynamic property values at respective thermodynamic states. In the ... Jforeover, the numerical tables

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