Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

By performing the differentiations and eliminating vcr, the constants aand b
are determined to be

(3–23)

The constants aand bcan be determined for any substance from the critical-
point data alone (Table A–1).
The accuracy of the van der Waals equation of state is often inadequate,
but it can be improved by using values of aand bthat are based on the
actual behavior of the gas over a wider range instead of a single point.
Despite its limitations, the van der Waals equation of state has a historical
value in that it was one of the first attempts to model the behavior of real
gases. The van der Waals equation of state can also be expressed on a unit-
mole basis by replacing the vin Eq. 3–22 by and the Rin Eqs. 3–22 and
3–23 by Ru.

Beattie-Bridgeman Equation of State

The Beattie-Bridgeman equation, proposed in 1928, is an equation of state
based on five experimentally determined constants. It is expressed as

(3–24)

where

(3–25)

The constants appearing in the above equation are given in Table 3–4 for
various substances. The Beattie-Bridgeman equation is known to be reason-
ably accurate for densities up to about 0.8rcr, where rcris the density of the
substance at the critical point.

Benedict-Webb-Rubin Equation of State

Benedict, Webb, and Rubin extended the Beattie-Bridgeman equation in
1940 by raising the number of constants to eight. It is expressed as

(3–26)

The values of the constants appearing in this equation are given in
Table 3–4. This equation can handle substances at densities up to about
2.5rcr. In 1962, Strobridge further extended this equation by raising the
number of constants to 16 (Fig. 3–59).

Virial Equation of State

The equation of state of a substance can also be expressed in a series form
as

P
 (3–27)

RT

v



a 1 T 2

v^2



b 1 T 2

v^3



c 1 T 2

v^4



d 1 T 2

v^5

...

P

RuT

v

aB 0 RuTA 0 

C 0

T^2

b

1

v^2



bRuTa

v^3



aa

v^6



c

v^3 T^2

a 1 

g

v^2

beg>v

 2

A
A 0 a 1 

a

v

b¬and¬B
B 0 a 1 

b

v

b

P

RuT

v^2

a 1 

c

v T^3

b1vB 2 

A

v 2

v

a

27 R^2 T^2 cr

64 Pcr

¬and¬b

RTcr

8 Pcr

Chapter 3 | 145

P

Critical point

Tcr

= constant

v

FIGURE 3–58

Critical isotherm of a pure substance

has an inflection point at the critical

state.