QJEEM17Pha45a: JEE Main 2017 Physics - Class 11 JEEM17Pha45a Solution: N moles of a diatomic gas in a cylinder are at a temperature T. …

Initial kinetic energy of N mole of diatomic gas,

K_i = N$$\frac{5}{2}$$ RT

Kinetic energy of n mole of monoatomic gas
= n $$\frac{3}{2}$$ RT

When n mole of diatomic gas converted into monoatomic gas then remaining diatomic gas = (N $$-$$ n)

Find kinetic energy,

K_F = (2m)$$\frac{3}{2}$$RT + (N $$-$$ n)$$\frac{5}{2}$$ RT

= $$\frac{1}{2}$$ nRT + $$\frac{5}{2}$$ NRT

$$\therefore$$ Change in kinetic energy,

$$\mathrm{\Delta }$$K = K_f $$-$$ K_i = $$\frac{1}{2}$$ nRT