JEE Mains · Physics · STD 11 - Kinetic theory of gases
- JEE Mains 2020
- Medium
- MCQ
Consider two ideal diatomic gases \(\mathrm{A}\) and \(\mathrm{B}\) at some temperature \(T\). Molecules of the gas \(A\) are rigid, and have a mass \(m\). Molecules of the gas \(\mathrm{B}\) have an additional vibrational mode, and have a mass \(\frac{\mathrm{m}}{4} .\) The ratio of the specific heats \((\mathrm{C}_{\mathrm{v}}^{\mathrm{A}}\) and \(\mathrm{C}_{\mathrm{v}}^{\mathrm{B}})\) of gas \(\mathrm{A}\) and \(\mathrm{B}\), respectively is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(5:7\)
Step-by-step Solution
Detailed explanation
Degree of freedom of a diatomic molecule if vibration is absent \(=5\)
Degree of freedom of a diatomic molecule if vibration is present \(=7\)
\(\therefore C_{v}^{A}=\frac{f_{A}}{2} R=\frac{5}{2} R\) and \(C_{v}^{B}=\frac{f_{B}}{2} R=\frac{7}{2} R\)
\(\therefore \quad \frac{C_{\mathrm{v}}^{\mathrm{A}}}{C_{\mathrm{v}}^{\mathrm{B}}}=\frac{5}{7}\)
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