Explanation

(c) Specific heat at constant pressure $(C_{p})$ is the amount of heat ($\mathcal{Q}$) required to raise $n$ moles of substance by $\mathrm{\Delta}\theta$ when pressure is kept constant. Then
$C_{p} = \frac{\mathcal{Q}}{n\mathrm{\Delta}\theta}$
Given, $\mathcal{Q}$=70 cal, $n = 2$,
$\mathrm{\Delta}\theta = (35 - 35)℃ = 5℃$
$\therefore$ $C_{p} = \frac{70}{2 \times 5}$=7 cal $mol^{- 1}\ {- K}^{- 1}$
From Mayer’s formula $C_{p} - C_{V} = R$
where $R\ is\ gas\ constant\ ( = 2\ cal\ mol^{- 1})$
$\therefore\ \ \ \ \ \ \ \ 7 - C_{V} = 2$
$\Rightarrow \ \ \ \ \ \ \ \ \ C_{V} = 5\ cal\ mol^{- 1} - K^{- 1}$
Hence, amount of heat required at constant volume $(C_{V})$ is
$\mathcal{Q}^{'} = nC_{V}\mathrm{\Delta}\theta$
$\mathcal{Q}^{'} = 2 \times 5 \times 5 = 50\ cal$