## Isentropic process

Isentropic expansion of an ideal gas was treated in Sect. 3.5. Here, the same process is analyzed without the restriction of ideality. Equation (6.23b) is divided by dv while holding s constant, which produces the relation:

To illustrate the effect of gas nonideality on property changes during an isentropic expansion, the right hand side of Eq (6.30) is evaluated for a Van der Waals gas obeying the equation of state in the form given by Eq (2.5):

Substituting the above EOS into Eq (6.28) yields:

In the limit of low pressure, the specific heats are independent of p (or v) and their difference is the gas constant. The nonideal gas effect on Cv is given by the first equality of Eq (6.26). For the Van der Waals EOS (d 2p/dT2)v = 0, so Cv is not a function of v. Substituting R = CP0 - CV0 , setting Cv = CV0 and using the symbol y for CP0/CV0, the above equation becomes:

Integrating between states 1 and 2 gives:

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