Derive expressions for (left(frac{partial c_{v}}{partial v} ight)_{T}) for substances obeying the following laws: (a) (p=frac{Re T}{v-b} mathrm{e}^{-frac{a}{Re

Derive expressions for \(\left(\frac{\partial c_{v}}{\partial v}\right)_{T}\) for substances obeying the following laws:

(a) \(p=\frac{\Re T}{v-b} \mathrm{e}^{-\frac{a}{\Re T v}}\)

(b) \(p=\frac{\Re T}{v-b}-\frac{a}{T v^{2}}\)

(c) \(p=\frac{\Re T}{v-b}-\frac{a}{v(v-b)}+\frac{c}{v^{3}}\).

Discuss the physical implication of the results.

\(\left[\frac{p a^{2}}{\Re^{2} v^{2} T^{3}} ;-\frac{2 a}{v^{2} T^{2}} ; 0\right]\)