\(N\,moles\) of a diatomic gas in a cylinder are at a temperature \(T\). Heat is supplied to the cylinder such that the temperature remains constant but \(n\,moles\) of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

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

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