For a diatomic gas, if γ_1=((C p)/(C v)) 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)

Options

A $\gamma_2=\gamma_1$
B $2 \gamma_2=\gamma_1$
C $\gamma_2 \lt \gamma_1$
D $\gamma_2\gt\gamma_1$

Correct answer

C. $\gamma_2 \lt \gamma_1$

Step-by-step 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}

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