lndirtn Inst. Sci. 62 (A), Jan. 1980, Pp. 45-49
O Printed in India.
J.
Short Communication
An equation of state for some gases
M. N. CHANDRASHEKARA A N D D. N. SESHADRJ
DepaI'tnlent of Chanical E~sineering,Indiw Insliture of Science, Bangdorc 560 012, India
Receved
011
June 15, 1979; Rewscd on Scptembw
0, 1979
Abstract
An equaii~lof staic proposed by Angus el 01 lras bccn tcsted for seven I.ydrocarbon8and fouv nonbydroc~rbonsat widc ranges of tem!icr,?lurc and pressnre. 11 is found lo be superior Lo the
Bencdict-Wehh-Ruhin eqlration of state.
Key ~vords:
Eqwtion 01 siste, hydrocarbons, non-hYd~'ocirrbons,temperature, pressure
The development of an equilibri~rrnrelation, in the absence of special force fields,
among presswe, temperatwe, and volume is mathenistically fas..inating. Of the several
equations proposed, no single equation of sfate ha%been found ro be applical~lewith
high pre:ision over a wide range or temperati!res and presswes. High prezision eqr!ations have many arbitrary constants whose number depends primarily upon the density
range and in a minor way upon the temperature range. With the improvements in
experimental P-V-T te-hniques the trend in resent years has been towards more complicated equations which can lit the data within the experimental precision.
In this work, a n equation of state first proposed by Angm ct all for ethylene has been
tested for other hydrocarbons. Th-e eq~rationmodified for computer application is
as Collows:
=
:a
N
2 C BIJ
I=,
Jar
TJ-!p7F2
(1)
where Z ic tELe co~npressibilityfaxor, B,, are constants, T is the temperature In " K,
p is the density in molelcc.
The P-V-T data for various hydrocarbons collected from theliierat~crearc fitted to
eqn (1) by the mcthod or leaii squares by minimising the s;~,k'of squares of
45
Table I
J
1
Acetylene
I
2
Constants B,, for acetylene and ethyIeue
3
4
-
Hydrogen
chloride
Ammonia
Sulphur
dioxide .
NzO4-NOzNO-0,
system
205
352
214
118
174
Acetylene
Ethylene
Propylene
Methane
Ethane
Propane
rtButane
122
463
273
405
312
520
No. of
data
points
Substawe
Temp.
rauge
"K
Piessure
range
atm.
Sum of
squares of
deviation
Range and quality of fit for the equation of state
Table El
P.esent
work
.
.
B-W-R
equation
Average absolute
deviation %
Maximum
deviate?
P/;
Sources of Values of
P-V-T
M and A'
data
(references) M
N
48
M.
N . CIIhNDRASfiEKARA AND U . N . SliSllADRI
deviation in compressibility. A compl!!er program Ihr the determi~rationof the con.
stants $, atid the val~teof M and N which lnininiises the strm of squares of deviatioll
has been developed. Fc'r the sol\:!ion or simi?l!aneol!s eqmtions, the usual Ga,~.ss.
elimination tilclhod i s wed. All thc calculations arc perCortned in dovble precision
arithme1i.c thereby rnininlizing the errors in ~'ol!ntl olT and trmcation. The values of
M ant1 N wbi,:h give relatively small valws of the s ~ m
of squl-es 01' dcvistion and the
;tvcr,lge :tbao]a!e cl.wiation is choscn as the best. The constants B,, for tk.c bcs! set o[
Af and N arc given Tor a-clylenc and etliylcnc in 'I'nble 1.
The. range ;tnd q:iality of lit of cqn ( I ) I'or vario1:s sub\i;cnccs arc tab~:lsted m
7'hLe !I".
References
I.
ANGUSS.,
ARMSTRONG,
S. AND
DERLUCK,
K. M.
4. MICHFL~,
A. AND
GELULRMANS, M.
5. MICHELS,
A,, WASSENAI~R,
T., LoUWERSE, P.,
LUNBECE,
R. 1. ANU
WOLKERS,
C. I.
6 . SCHAMP, H. W.
JR.,
MASON, E. A,,
RPXIARDSON, A . C . B.
AND ACTMAN, A.
7. RS.AMER, H. H., OLD%
R. H., SAGB, B. H. AND
LAW,
W. N.
~er&hm
Refiner, 1960, 39, 151
AN EQUATION OF STATE FOR SOME GASES
9. DemER, W. W. AND
BROWN,
hd. E w g . L%ern., 1940, 32, 836.
G . G.
10. REAMER,H. H., SAGE,
hd.Brtgg. Clroa.. 1949, 41, 482.
B, H. AND LACBY, W. N.
11. BEATIIS,J. A., KAN, W. C.
4ND
J . Ant. Chenr. Sac., 1937, 59, 1589.
KAMINSKY,3.
11. PRENGLC,
H. W. JR.,
GREENICANS,
L. H.
YORK,R. JR.
~ N D
13. FRANK, E. V., BKUISE,M.
AND MANGOLD,K.
HIRTH,L. J
Kose, K. A. AND
MCKUTTA,J. J.
14. KANG, T. L.,
IS. S G ~ I N G ~W.
R , G.
SAGE,B. H.
AND
16. SESHA~BI,
D. N. AND
VIS~ANATH,
D. S.
Progress in irrtcn~ationalvereurch urt t h e r m u d ~ ~ t u ~urtd
~ t i ctransport
properties, ASME, Academic Piess, Inc, New York, 1962, p 159.
J . Chenl. 816.g. Drrfu, 1961, 6 , 320.