The ratio of specific heat at constant pressure to specific heat at constant volume $(\gamma)$ for a gas is…

The ratio of specific heat at constant pressure to specific heat at constant volume $(\gamma)$ for a gas is $\left(1+\frac{2}{\mathrm{f}}\right)$ where $\mathrm{f}$ is the number of degrees of freedom of a molecule of a gas. The ratio of ' $\gamma_{d}$ ' for rigid diatomic to ' $\gamma_{\mathrm{m}}$ ' for monoatomic is
  1. $\frac{14}{23}$
  2. $\frac{25}{21}$
  3. $\frac{21}{25}$
  4. $\frac{23}{14}$

Solution

For monoatomic gas \(Y_1=\frac{5}{3}\) For diatomic gas at low temperatures \(\begin{aligned} & Y_2=\frac{7}{5} \\ & \therefore \frac{\gamma_1}{\gamma_2}=\frac{\frac{5}{3}}{\frac{7}{5}}=\frac{25}{21} \end{aligned}\) add this part at last \(\frac{\gamma_2}{\gamma_1}=\frac{21}{25}\)

Asked in: MHT CET 2020 (15 Oct Shift 2)

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