Thermodynamics

JEE Main level, single correct, medium

8 of 190

Question 8 of 190

For a diatomic gas, if γ1=(CpCv)\gamma_1=\left(\frac{C p}{C v}\right) for rigid molecules and γ2=(CpCv)\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)

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Answer: (C) γ2<γ1\gamma_2 \lt \gamma_1

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\gt \gamma_2

\end{array}$

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