An insulator container contains 4 moles of an ideal diatomic gas at temperature T. Heat Q is supplied to this gas, due to which 2 moles of the gas
are dissociated into atoms but temperature of the gas remains constant. Then
Q=△U=Uf−Ui = [internal energy of 4 moles of a monoatomic gas + internal
energy of 2 moles of a diatomic gas] - [internal energy of 4 moles of a diatomic gas]
=(4×32RT+2×52RT)−(4×52RT)=RT
Note : (a) 2 moles of diatomic gas becomes 4 moles of a monoatomic gas when gas dissociated into atoms.
(b) Internal energy of m moles of an ideal gas of degrees of freedom F is given by U=f2μRT
F = 3 for a monoatomic gas and 5 for diatomic gas.