1.3 Real Gases
23
Table 1.1 displays several additional equations of state, and values of parameters for
several gases are found in Table A.3. The parameters for a given gas do not necessarily
have the same values in different equations even if the same letters are used. The
accuracy of several of the equations of state has been evaluated. 2 The Redlich–Kwong
equation of state seemed to perform better than the other two-parameter equations, with
the van der Waals equation coming in second best. The Gibbons–Laughton modification
of the Redlich–Kwong equation (with four parameters) is more accurate than the twoparameter equations.
Table 1.1 Some Equations of State
The letters a and b stand for constant parameters that have different values for different
substances. These parameters do not necessarily have the values for the same substance
in different equations of state.
The Berthelot Equation of State
P +
a
TV 2
m
(V m − b) RT
The Dieterici Equation of State
Pe
a/V m RT (V m − b) RT
The Redlich–Kwong Equation of State
P
RT
V m − b
−
a
T 1/2 V m (V m + b)
The Soave Modification of the Redlich–Kwong Equation of State
P
RT
V m − b
−
aα(T )
V m (V m + b)
where α(T ) {1 + m 1 − (T /T c ) 1/2 } 2 , where m is a constant parameter and where
T c is the critical temperature. See the article by Soave for values of the parameter m.
The Gibbons–Laughton Modification of the Redlich–Kwong-Soave Equation
of State
The equation is the same as the Soave modification, but α(T ) is given by
α(T ) 1 + X(T /T c ) − 1 + Y (T /T c )
1/2
− 1
where X and Y are constant parameters. See the article by Gibbons and Laughton for
values of these parameters.
Other equations of state can be found in the book by Hirschfelder, Curtiss, and Bird,
including the Beattie–Bridgeman equation, with five parameters, and the Benedict–
Webb–Rubin equation, with eight parameters.
2 J. B. Ott, J. R. Goates, and H. T. Hall, Jr., J. Chem. Educ., 48, 515 (1971); M. W. Kemp, R. E. Thompson,
and D. J. Zigrang, J. Chem. Educ., 52, 802 (1975).
23
Table 1.1 displays several additional equations of state, and values of parameters for
several gases are found in Table A.3. The parameters for a given gas do not necessarily
have the same values in different equations even if the same letters are used. The
accuracy of several of the equations of state has been evaluated. 2 The Redlich–Kwong
equation of state seemed to perform better than the other two-parameter equations, with
the van der Waals equation coming in second best. The Gibbons–Laughton modification
of the Redlich–Kwong equation (with four parameters) is more accurate than the twoparameter equations.
Table 1.1 Some Equations of State
The letters a and b stand for constant parameters that have different values for different
substances. These parameters do not necessarily have the values for the same substance
in different equations of state.
The Berthelot Equation of State
P +
a
TV 2
m
(V m − b) RT
The Dieterici Equation of State
Pe
a/V m RT (V m − b) RT
The Redlich–Kwong Equation of State
P
RT
V m − b
−
a
T 1/2 V m (V m + b)
The Soave Modification of the Redlich–Kwong Equation of State
P
RT
V m − b
−
aα(T )
V m (V m + b)
where α(T ) {1 + m 1 − (T /T c ) 1/2 } 2 , where m is a constant parameter and where
T c is the critical temperature. See the article by Soave for values of the parameter m.
The Gibbons–Laughton Modification of the Redlich–Kwong-Soave Equation
of State
The equation is the same as the Soave modification, but α(T ) is given by
α(T ) 1 + X(T /T c ) − 1 + Y (T /T c )
1/2
− 1
where X and Y are constant parameters. See the article by Gibbons and Laughton for
values of these parameters.
Other equations of state can be found in the book by Hirschfelder, Curtiss, and Bird,
including the Beattie–Bridgeman equation, with five parameters, and the Benedict–
Webb–Rubin equation, with eight parameters.
2 J. B. Ott, J. R. Goates, and H. T. Hall, Jr., J. Chem. Educ., 48, 515 (1971); M. W. Kemp, R. E. Thompson,
and D. J. Zigrang, J. Chem. Educ., 52, 802 (1975).