Page 197 - Advanced thermodynamics for engineers

9.3 TABLES OF u(T) AND h(T) AGAINST T 183

and

g m ¼ h m ðTÞþ h 0;m T s m ðTÞ < ln p r þ s 0;m

¼ h 0;m Ts 0;m þðh m ðTÞ Ts m ðTÞÞþ<Tln p r : (9.24)

If the terms at T 0 are combined to give
(9.25)
g 0;m ¼ h 0;m Ts 0;m
and the temperature dependent terms are combined to give
g m ðTÞ¼ h m ðTÞ Ts m ðTÞ (9.26)
then
g m ¼ g m ðTÞþ<Tln p r þ g 0;m : (9.27)

0
Often g m (T) and g 0,m are combined to give g , which is the pressure independent portion of the
m
0
Gibbs energy, i.e. g ¼ g m ðTÞþ g 0;m , and then
m
0
g m ¼ g þ<Tln p r : (9.28)
m
0
g is the value of the molar Gibbs energy at a temperature, T, and a pressure of p 0 , and it is a
m
function of temperature alone. The datum pressure, p 0 , is usually chosen as 1 bar nowadays
(although much data is published based on a datum pressure of 1 atm: the difference is not usually
significant in engineering problems, but it is possible to convert some of the data, e.g. equilibrium
constants).
Gibbs energy presents the same difficulty when dealing with mixtures of varying composition as
u 0 , h 0 and s 0 . If the composition is invariant, changes in Gibbs energy are easily calculated because the
g 0 terms cancel. For mixtures of varying composition g 0 must be known. It can be seen from Eqn (9.26)
that if the reference temperature, T 0 , equals zero then

g 0;m ¼ h 0;m ¼ u 0;m (9.29)

9.3 TABLES OF u(T) AND h(T) AGAINST T
These tables are based on polynomial equations defining the enthalpy of the gas. The number of
terms can vary depending on the required accuracy and the temperature range to be covered. This
section will limit the number of coefficients to six, based on Benson (1977). The equation used is of
the form
h m ðTÞ h m h 0;m 2 3 4
¼ ¼ a 1 þ a 2 T þ a 3 T þ a 4 T þ a 5 T (9.30)
<T <T
The values of the coefficients for various gases are listed in Table 9.3, for the range 500–3000 K. If
used outside these ranges the accuracy of the calculation will diminish.