c
For diatomic gas, $\gamma=1.4=\frac{7}{5}$
For adiabatic process, $T V^{r-1}=$ constant
$T_{1} V_{1}^{\gamma-1}=T_{2} V_{2}^{\gamma-1}$
$(300) V_{1}^{\frac{7}{5}-1}=T_{2}\left(\frac{V_{1}}{5}\right)^{\frac{7}{5}}$
$\Rightarrow T_{2}=\frac{300 \times V_{1}^{2 / 5}}{V_{1}^{\frac{2}{5}} \times\left(\frac{1}{5}\right)^{2 / 5}}=\frac{300}{5^{-\frac{2}{5}}}=300 \times 5^{2 / 5}$
$=300 \times 1.903=571$
Mean kinetic energy of rotating molecules
$=k T=1.38 \times 10^{-23} \times 571=787.98 \times 10^{-23} J$