A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rorational kinetic energy per `O_2` molecules to that per `N_2` molecules is

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. depends on the moments of inertia of the two molecules

Answer

A

Explanation

(a) The law of euipartition of energy states that
'For a dynamical system in thermal equilibrium, the
energy of a system is equally distributed among its
various degrees of freedom and the energy associated
with each degree of freedom per molecule is 1/2k.T. In
this case, `O_2 and N_2` both have two degrees of rotational
kinetic energy and since the temperature is also same,
the ratio of the average rotational kinetic energy is `1:1.`