A radiation detector is filled with a mixture of 90 % argon and 10 % methane, by moles…

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A radiation detector is filled with a mixture of $90\ \%$ argon and $10\ \%$ methane, by moles. Treat methane as rigid. Find $C_v$ of the mixture. How much heat does $1.5\ \text{mol}$ of the mixture need to warm by $40\ \text{K}$ in a sealed rigid case? Find $\gamma$ too. Take $R = 8.31\ \text{J/(mol K)}$ .

Need a reminder? The key ideaShow

From equipartition, $C_v = \tfrac{f}{2}R$ , $C_p = C_v + R$ and $\gamma = 1 + \tfrac{2}{f}$ . A polyatomic gas with $v$ active vibrations has $C_v = (3 + v)R$ . A mixture has $C_v = \dfrac{\sum n_iC_{vi}}{\sum n_i}$ . A solid has $C = 3R$ , so $c = 3R/M$ .

\displaystyle C_v = \tfrac{f}{2}R

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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