Question

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 diatomic gas get converted into monoatomic gas . What is the change in total kinetic energy of the gas?

Answer 1

we know, molar specific heat of gas at constant volume is $C_v=f\frac{R}{2}$

where f is degree of freedom of gas.

R is universal gas constant.

if number of mole of diatomic gas = N

then , number of mole of monochromatic gas formed by diatomic = 2N

molar specific heat for diatomic = 5R/2

and molar specific heat for monochromatic = 3R/2

now, change in internal energy = heat supplied

= $n_fC_{v_f}T-n_iC_{v_i}T$

= 2N × 3R/2 × T - N × 5R/2 × T

= 3NRT - 5/2NRT

= NRT/2