Heat supplied $=\Delta U=U_{\text {final }}-U_{\text {initial }}$

Total internal energy initially $=\frac{5}{2} N R T$  [Only diatomic gas is present]

Total internal energy when

' $n$ ' moles get dissociated $=\frac{5}{2}(N-n) R T+\frac{3}{2}(2 n) R T$ [diatomic and monoatomic both are present]

$\Delta U=\left\{\frac{5}{2}(N-n) R T+\frac{3}{2}(2 n) R T\right\}-\frac{5}{2} N R T$

Solving this we get

$\Delta U=\frac{1}{2} n R T$

$\therefore$ Heat supplied is $\frac{1}{2} n R T$.