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)

Pick an option to check your answer.

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Answer & Solution

Correct Answer

(C) \(\gamma_2 \lt \gamma_1\)

Step-by-step Solution

Detailed explanation

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

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