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

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