One mole of a gas having $\gamma=\frac{7}{5}$ is mixed with one mole of a gas having $\gamma=\frac{4}{3}$ The value of $\gamma$ for the mixture is ( $\gamma$ is the ratio of the specific heats of the gas)

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Aicharya · Accepted Answer

$\mathrm{n}_1=1$ mole, $\mathrm{n}_2=1 \mathrm{~mole}, \delta_1=\frac{7}{5}, \delta_2=\frac{4}{3}$ $\begin{aligned} & 	herefore \frac{\mathrm{n}_1+\mathrm{n}_2}{\delta_{	ext {mix }}-1}=\frac{\mathrm{n}_1}{\delta_1-1}+\frac{\mathrm{n}_2}{\delta_2-1} \ & \Rightarrow \frac{1+1}{\delta_{	ext {mix }}-1}=\frac{1}{\frac{7}{5}-1}+\frac{1}{\frac{4}{3}-1}\end{aligned}$ $\begin{aligned} & \Rightarrow \frac{2}{\delta_{\operatorname{mix}}-1}=\frac{5}{2}+\frac{3}{1} \doteq \frac{11}{2} \ & 	herefore \delta_{\operatorname{mix}}=\frac{15}{11}\end{aligned}$

One mole of a gas having $\gamma=\frac{7}{5}$ is mixed with one mole of a gas having $\gamma=\frac{4}{3}$…

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