For a diatomic gas, if γ1 = (Cp / Cv) for rigid molecules and γ2 = (Cp / Cv) for another diatomic molecules,

Question

For a diatomic gas, if \(\gamma_{1}=\left(\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)\) 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) \(\gamma_{2}=\gamma_{1}\)

(3) \(2 \gamma_{2}=\gamma_{1}\)

(4) \(\gamma_{2}<\gamma_{1}\)

Answer 1

Correct option is : (4) \(\gamma_{2}<\gamma_{1}\) 

\(\gamma=\frac{2}{\mathrm{f}}+1\)

without vibration : \(\mathrm{f}=5: \gamma_{1}=1.4\)

without vibration : \(\mathrm{f}=7: \gamma_{2}=1.14\)

\(\therefore\ \gamma_{2}<\gamma_{1}\)