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

\(=k T=1.38 \times 10^{-23} \times 571=787.98 \times 10^{-23} J\)