Page 195 - Advanced thermodynamics for engineers

9.2 STATE EQUATION FOR IDEAL GASES 181

Enthalpy or internal energy data are generally presented in tabular or graphical form. The two
commonest approaches are described in Section 9.3 below. First, it is useful to consider further the
terms involved.

9.2.2 THE SIGNIFICANCE OF u 0,M AND h 0,M
As previously discussed, u 0,m and h 0,m are the values of molar internal energy, u m , and molar enthalpy,
h m , at the reference temperature, T 0 .If T 0 ¼ 0 then, for an ideal gas,

u 0;m ¼ h 0;m (9.14)
If T 0 s0, then u 0,m and h 0,m are different. Most calculations involve changes in enthalpy or internal
energy, and if the composition during a process is invariant the values of h 0,m or u 0,m will cancel.
However, if the composition changes during a process it is necessary to know the difference
between the values of u 0,m or h 0,m for the different species at the reference temperature. This is
discussed below.
Obviously u 0,m and h 0,m are consequences of the ideal gas assumption and the Eqn (9.3)

h ¼ hðTÞþ h 0
contains the assumption that the ideal gas law applies down to T 0 .If T 0 ¼ 0, or a value outside the
superheat region for the gas being considered, then the gas ceases to be ideal, often becoming either
liquid or solid. To allow for this it is necessary to include latent heats. This will not be dealt with here,
but the published data do include these corrections.

9.2.3 ENTROPY OF AN IDEAL GAS – THIRD LAW OF THERMODYNAMICS
The change in entropy during a process is defined as
<dp
dh m
ds m ¼ (9.15)
T p
If the functional relationship h m ¼ h m (T) is known then Eqn (9.15) may be evaluated, giving
Z T
dh m p
s m s 0;m ¼ < ln (9.16)
T p 0
T 0
where s 0,m ¼ value of s m at T 0 and p 0 .
It is convenient to take the reference temperature, T 0 , as absolute zero. It was previously
shown that

dh m c p;m ðTÞdT
dh m ¼ c p;m ðTÞdT and hence ¼ : (9.17)
T T

dh m
Consider :
lim T
T/0