gas,

\(\mathrm{U}_{\mathrm{i}}=\mathrm{N} \frac{5}{2} \mathrm{RT}\)

Energy associated with \(n\) moles of monoatomic gas

\(=n \frac{3}{2} R T\)

Total energy when \(n\) moles of diatomic gas converted into monoatomic

\(\left(U_{f}\right)=2 n \frac{3}{2} R T+(N-n) \frac{5}{2} R T\)

\(=\frac{1}{2} n R T+\frac{5}{2} N R T\)

Now, change in total kinetic energy of the

gas

\(\Delta \mathrm{U}=\mathrm{Q}=\frac{1}{2} \mathrm{nRT}\)