Q. 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 ? ($C_p$ and $C_v$ are specific heats of the gas at constant pressure and volume)
A) $\gamma_2=\gamma_1$
B) $2\gamma_2=\gamma_1$
C) $\gamma_2<\gamma_1$
D) $\gamma_2>\gamma_1$
Explanation
[Solution by Dr. Abubacker] Rigid diatomic: $f=5$, $\gamma_1=\frac75=1.40$. With vibrational modes: $f=7$, $\gamma_2=\frac97\approx1.29$. So $\gamma_2<\gamma_1$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.