EQUATIONS OF STATE Ideal Gas

(Only valid for gas at low pressure conditions)

RTPv =

Van der Waals

( ) RTbvvaPor

va

bvRTP =−⎟

⎠⎞

⎜⎝⎛ +−

−= 22

Relation with Z = compressibility factor:

RTva

bvb

RTPvZ −

−+== 1

c

c

c

c

PRTband

PTRa

86427 22

==

For mixtures:

∑∑ == iiii bxbandaxa

Van der Waals EOS, in term of Z:

( ) 01 23 =−++− ABAZZBZ

with ( )2RTaPAand

RTbPB ==

Redlich-Kwong

( )bvvTa

bvRTP . +

−−

= 50

Relation with Z = compressibility factor:

v/bv/b

RT/bTR/a

v/bRTPvZ

.

+⎟⎟⎠

⎞⎜⎜⎝

⎛−

−==

111 522

c

c

c

.c

PRT.band

PTR.a 0867042780 522

==

For mixtures:

∑∑ == iiii bxbandaxa

Redlich-Kwong EOS, in term of Z:

( ) 0223 =−−−+− ABZBBAZZ

with ( )2RTaPAand

RTbPB ==

Peng-Robinson

( )( ) ( )bvbbvv

Tabv

RTP−++

−−

=

Relation with Z = compressibility factor:

( )( ) ( )( )RTv/bbbv

Tav/bRT

PvZ−++

−−

==11

1

( ) ( )c

c

c

c

PRT.bandT

PTR.Ta 07780457240 22

== α

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−−++=

cTT...T 12699205422613746401 2ωωα

For mixtures:

∑∑ == iiii bxbandaxa

Peng-Robinson EOS, in term of Z:

( ) ( ) ( ) 0231 32223 =−++−−+−+ ABBBZBBAZBZ

with ( )2RTaPAand

RTbPB ==

Benedict-Webb-Rubbin (BWR)

( ) ( )22

23632

2

1 dexpT

dcddadabRTdTCARTBRTdP o

oo γγα −+

++−+⎟⎠⎞

⎜⎝⎛ −−+=

Relation with Z = compressibility factor:

( )23

2252

21 dexp

RTdcdd

RTad

RTabd

RTC

RTAB

RTPvZ oo

o γγα−

+++⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −−==

where

vd 1= ; Bo, Ao, Co, b, a, c, α, γ are emphirical constants

for each substances.

For mixtures, use appropriate mixing rules such as:

( )[ ] ( )[ ]331331 ∑∑∑ === /ii

/iioiio xbxbBxB αα

Calculations of other properties from EOS