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**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 = C^{ig}_{p}dT .....(4.19)

Thus combining eqns. 4.18 and 4.19:

.....(4.20)

Integrating between an initial (T0, P0) and any final (T, P):

.....(4.21)

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 C^{Pig }, 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.

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