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

Question

Dr. Abubacker · Accepted Answer

(c) Below $100\ K$ only translational degree of freedom is considered. Hence
$\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, $\ \mu_{1} = \mu_{2}$ and $\gamma_{1} = \gamma_{2} = 1 + \frac{2}{3} = \frac{5}{3}$
$\Rightarrow \gamma_{mix} = \gamma_{1} = \frac{5}{3}$

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

Explanation

Reviewed by Dr. Abubacker

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