Heat and Thermodynamics 4 Question 23

25. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. The ratio of the average rotational kinetic energy per O2 molecule to per N2 molecule is

(1998, 2M)

(a) 1:1

(b) 1:2

(c) 2:1

(d) depends on the moment of inertia of the two molecules

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Solution:

  1. Average kinetic energy per molecule per degree of freedom =12kT. Since, both the gases are diatomic and at same temperature (300K), both will have the same number of rotational degree of freedom i.e. two. Therefore, both the gases will have the same average rotational kinetic energy per molecule

=2×12kT or kT

Thus, ratio will be 1:1.



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