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## ProblemEdit

Here are two facts about a substance:

• The entropy is the following function of $T$ and $V$:
$S = R{{V_0 } \over V}\left( {{T \over {T_0 }}} \right)^{\alpha - 1}$
• At constant temperature $T_0$ the work the substance does on its surroundings as it expands from $V_0$ to $V$ is
$\left. W \right|_{T_0 } = RT_0 \ln {V \over {V_0 }}$

(a)Find the Helmholtz free energy F, assuming that it is zero at the state values specified by the subscript 0.

(b)Find the equation of state of this stuff. Is there a point in parameter space where it is ideal?

(c)For this part we’ll simplify the algebra by assuming that $\ln {V \over {V_0 }} = 1$ and also $\alpha = 1$. At what temperature $T'$ would the system do twice as much work in going from $V_0$ to $V$ as it does at $T = T_0$?