Explanation

(c) Given, $pT^{2}$=constant
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( \frac{nRT}{V} \right)T^{2} =$constant
or $T^{3}V^{- 1} =$ constant
Differentiating the equation, we get
$\frac{3T^{2}}{V}.dT - \frac{T^{3}}{V^{2}}.dV = 0$
or $3.dT = \frac{T}{V}.dV$
From the equation, $dV = V_{\gamma}.dT$
$\gamma =$ coefficient of volume expansion of gas
$=$ $\frac{dV}{V.dT}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \gamma = \frac{dV}{V.dT} = \frac{3}{T}$