JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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)
- A \(\gamma_2=\gamma_1\)
- B \(2 \gamma_2=\gamma_1\)
- C \(\gamma_2 \lt \gamma_1\)
- D \(\gamma_2\gt\gamma_1\)
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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