For a diatomic gas, if $\gamma_1=\left(\frac{C p}{C v}\right)$ for rigid molecules and…

For a diatomic gas, if $\gamma_1=\left(\frac{C p}{C v}\right)$ for rigid molecules and $\gamma_2=\left(\frac{C p}{C v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)
  1. $\gamma_2=\gamma_1$
  2. $2 \gamma_2=\gamma_1$
  3. $\gamma_2 \lt \gamma_1$
  4. $\gamma_2 \gt \gamma_1$

Solution

For rigid diatomic molecules
$\begin{array}{ll}
& f=5 \\ \therefore & \gamma_1=\frac{7}{5}=1.4
\end{array}$
For non-rigid diatomic molecules
$\begin{array}{ll}
& f=5+2=7 \\ & \gamma_2=\frac{9}{7}=1.28 \\ \therefore & \gamma_1>\gamma_2
\end{array}$

Asked in: JEE Main 2025 (22 Jan Shift 2)

Practice more Thermodynamics questions on Aicharya