For a gas, $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{V}}}=0.4$, where $\mathrm{R}$ is universal gas constant…

For a gas, $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{V}}}=0.4$, where $\mathrm{R}$ is universal gas constant and $\mathrm{C}_{\mathrm{v}}$ is molar specific heat at constant volume. The gas is made up of molecules which are
  1. rigid diatomic
  2. monoatomic
  3. non-rigid diatomic
  4. polyatomic

Solution

Given: $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0.4$ $\begin{aligned} \mathrm{C}_{\mathrm{V}} & =\frac{\mathrm{R}}{0.4}=\frac{5 \mathrm{R}}{2} \\ \mathrm{C}_{\mathrm{P}} & =\mathrm{C}_{\mathrm{V}}+\mathrm{R} \\ \therefore \quad \mathrm{C}_{\mathrm{P}} & =\frac{7 \mathrm{R}}{2} \\ \gamma & =\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{\frac{7}{2}}{\frac{5}{2}} \\ \gamma & =\frac{7}{5} \end{aligned}$ $\therefore \quad$ The gas is made up of rigid diatomic molecules.

Asked in: MHT CET 2023 (11 May Shift 2)

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