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Question: A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measuremen...

A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measurements on this mixture at temperatures below 100 K would indicate that the value of γ\gamma (ratio of specific heats) for this mixture is

A

3/2

B

4/3

C

5/3

D

7/5

Answer

5/3

Explanation

Solution

Below 100 K only translational degree of freedom is considered. Hence γmixture=μ1γ1γ1−1+μ2γ2γ2−1μ1γ1−1+μ2γ2−1\gamma_{mixture} = \frac{\frac{\mu_{1}\gamma_{1}}{\gamma_{1} - 1} + \frac{\mu_{2}\gamma_{2}}{\gamma_{2} - 1}}{\frac{\mu_{1}}{\gamma_{1} - 1} + \frac{\mu_{2}}{\gamma_{2} - 1}} according to question, μ1=μ2\mu_{1} = \mu_{2} and γ1=γ2=1+23=53\gamma_{1} = \gamma_{2} = 1 + \frac{2}{3} = \frac{5}{3}

⇒γmix=γ1=53\Rightarrow \gamma_{mix} = \gamma_{1} = \frac{5}{3}