Explanation

(c) $\mathrm{\Delta}Q = \mathrm{\Delta}U + \mathrm{\Delta}W \Rightarrow \mathrm{\Delta}W = (\mathrm{\Delta}Q)_{P} - \mathrm{\Delta}U = (\mathrm{\Delta}Q)_{P}\left\lbrack 1 - \frac{(\mathrm{\Delta}Q)_{V}}{(\mathrm{\Delta}Q)_{P}} \right\rbrack$
$= (\mathrm{\Delta}Q)_{P}\left\lbrack 1 - \frac{C_{V}}{C_{P}} \right\rbrack = Q\left\lbrack 1 - \frac{3}{5} \right\rbrack = \frac{2}{5}Q$
$\because(\mathrm{\Delta}Q)_{P} = Q$ and $\gamma = \frac{5}{3}$ for monoatomic gas