## 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 $?