First slide

Law of equipartition of energy

Question

The ratio of the number of moles of a monoatomic to a polyatomic gas in a mixture of the two, behaving as an diatomic gas is : (vibrational modes of freedom is to be ignored)

Moderate

A

2 : 1
B

1 : 2
C

2 : 3
D

3 : 2

Solution

Let the required ratio be n : 1
$Q_{1} = n (\frac{f_{1} R}{2}) ∆ T and Q_{2} = 1 (\frac{f_{2} R}{2}) ∆ T$
and $Q = (n + 1) (\frac{f_{2} R ∆ T}{2})$
$Q = Q_{1} + Q_{2}, So (n + 1) f_{2} = {nf}_{1} + f_{3}$
or $(n + 1) 5 = n (3) + 6 \Rightarrow n = \frac{1}{2}$

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