Explanation

(a) For adiabatic process
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ TV^{\gamma - 1} = constant$
${\therefore\ \ \ \ \ \ \ \ \ \ \ \ T}_{1}V_{1}^{\gamma - 1} = T_{2}V_{2}^{\gamma - 1}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{1}}{T_{2}} = \left( \frac{V_{2}}{V_{1}} \right)^{\gamma - 1\ }$
Given , $V_{1} = V,\ V_{2} = \frac{V}{4},\ \gamma = 1.5$
$\therefore\frac{T_{1}}{T_{2}} = \left( \frac{V/4}{V} \right)^{1.5 - 1} = \left( \frac{1}{4} \right)^{0.5} = - \frac{1}{2}$
$\Rightarrow \ \ \ \ \ T_{2} = 2T_{1}$
The change in temperature is given by
$T_{2} - T_{1} = 2T_{1} - T_{1} \Rightarrow T_{1} = 273\ K$