Entropy Calculations for Ideal Gases
For a closed system, the first law provides:
dU = dQ + dW
If the process of change occurs under reversible conditions then the above equation becomes:
d ( H − PV) = TdS − PdV
dH − PdV − VdP= TdS − PdV ............(4.18)
However for an ideal gas: dH = CigpdT .....(4.19)
Thus combining eqns. 4.18 and 4.19:
Integrating between an initial (T0, P0) and any final (T, P):
The last equation provides a direct expression for computing entropy change between two states for an ideal gas.
For the special case of a reversible adiabatic dQ = 0; hence dS= 0. Thus:
For constant CPig , it follows that: .....(4.22)
One may note that eqn. 4.22 provides the same relation as obtained by the Fist Law analysis as in eqn. 3.18.