$2\mathrm{.}5.$B A simple van der Waals fluid is compressed isentropically to half its volume. If the initial

state is $(T_0,v_0),$ find the final temperature, the work required, and the heat flow.

$2\mathrm{.}5.$C One mole of oxygen at $25C$ and $15$atm is compressed iso$-$energetically $($i$.$e$.$ at constant

energy$)$ to $35$atm. Calculate the change in entropy using both a simple ideal gas $(c=$

$\frac{5}{2})$ and a simple van der Waals fluid. The other parameters for the van der Waals

fluid can be found from the critical properties of oxygen, as shown in Section B$.3$ of

Appendix B$.$ Compare the two answers. Why are they different? How does your answer

fit with the definition of entropy, Eqn. $(2\mathrm{.}20)?$