Explanation

(c) For adiabatic process, Poisson’s equation is given by
$\ \ \ \ \ \ \ \ \ \ pV^{\gamma} = constant$ ---(i)
Ideal gas relation is
pV=RT
$\Rightarrow \ \ \ V = \frac{RT}{p}$ ---(ii)
From Eqs. (i) and (ii), we get
$p\left( \frac{RT}{p} \right)^{\gamma} = constant$
$\Rightarrow \ \frac{T^{\gamma}}{p^{\gamma - 1}} = constant$ ---(iii)
Where $\gamma$ is ratio of specific heats of the gas.
Given, $p \propto T^{C}$ ---(iv)
On comparing with Eq. (iii), we have
$c = \frac{\gamma}{\gamma - 1}$
For a monoatomic gas $\gamma = \frac{5}{3}$
We have
$C = \frac{\frac{5}{3}}{\frac{5}{3} - 1} = \frac{5}{2}$