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JEE MAIN Physics QUESTION #1000
Question 1
For a diatomic gas, \(\gamma_1 = \left(\dfrac{C_p}{C_v}\right)\) for rigid molecules and \(\gamma_2 = \left(\dfrac{C_p}{C_v}\right)\) for non-rigid diatomic molecules (with vibrational modes). Then which is correct?
  • \(\gamma_2 = \gamma_1\)
  • \(2\gamma_2 = \gamma_1\)
  • \(\gamma_2 < \gamma_1\)✔️
  • \(\gamma_2 > \gamma_1\)
Correct Answer Explanation
For rigid diatomic: \(C_v = \frac{5}{2}R\), \(\gamma_1 = \frac{7}{5} = 1.4\). With vibrational modes: \(C_v = \frac{7}{2}R\), \(\gamma_2 = \frac{9}{7} \approx 1.286\). Since adding vibrational modes increases \(C_v\) more than \(C_p\), \(\gamma_2 < \gamma_1\).