c
\({T_1}{V^{\gamma  - 1}} = {T_2}{\left( {32V} \right)^{\gamma  - 1}} \Rightarrow {T_1} = {\left( {32} \right)^{\gamma  - 1}}.{T_2}\)

\(For\,diatomic\,gas,\,\gamma  = \frac{7}{5}\,\,\,\,\,\,\therefore \gamma  - 1 = \frac{2}{5}\)

\(\therefore {T_1} = {\left( {32} \right)^{\frac{2}{5}}}.{T_2} \Rightarrow {T_1} = 4{T_2}\)

\(Now,\,efficiency = 1 - \frac{{{T_2}}}{{{T_1}}} = 1 - \frac{1}{4} = \frac{3}{4} = 0.75.\)