Explanation

(a) In adiabatic process, the relation between temperature (T) and pressure(p) is
$\frac{T^{\gamma}}{P^{\gamma - 1}} = constant$
Where$\ \gamma$ is ratio of specific heats.
Given, $T_{1} = 27℃ = 27 + 273 = 300\ K,$
$p_{1} = p,\ p_{2} = \frac{p}{8},\ \gamma = \frac{5}{3}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{1}}{T_{2}} = \left( \frac{p_{1}}{p_{2}} \right)^{\frac{\gamma - 1}{\gamma}}$
$\Rightarrow \ \ \ \frac{T_{1}}{T_{2}} = \left( \frac{8}{1} \right)^{\frac{\frac{5}{3} - 1}{5/3}}$
$\ \ \ \ \ = (8)^{0.4} = 2.297$
$\Rightarrow T_{2} = \frac{T_{1}}{2.297} = \frac{300}{2.297}$
$\ \ \ \ \ \ \ \ \ \ \ = 130.6\ K \approx 131K$
$\Rightarrow \ \ T_{2} = 131 - 273$
$\ \ \ \ \ \ \ \ \ \ \ \ \ = - 142℃$