Heat and Thermodynamics 4 Question 23
25. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at $300 K$. The ratio of the average rotational kinetic energy per $O _2$ molecule to per $N _2$ 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:
- Average kinetic energy per molecule per degree of freedom $=\frac{1}{2} k T$. Since, both the gases are diatomic and at same temperature $(300 K)$, 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
$$ =2 \times \frac{1}{2} k T \text { or } k T $$
$\Rightarrow$ Thus, ratio will be $1: 1$.
