MHT CET · Physics · Kinetic Theory of Gases
For a gas molecule with 6 degrees of freedom, which one of the following relations between gas constant ' \(R\) ' and molar specific heat ' \(\mathrm{C}_{\mathrm{V}}\) ' is correct?
- A \(\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{3}\)
- B \(\mathrm{R}=\frac{5 \mathrm{C}_{\mathrm{v}}}{4}\)
- C \(\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{2}\)
- D \(\mathrm{R}=\frac{3 \mathrm{C}_{\mathrm{v}}}{4}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{3}\)
Step-by-step Solution
Detailed explanation
For 6 degrees if freedom, \(\mathrm{C}_{\mathrm{v}}=6 \times \frac{1}{2} \mathrm{R}=3 \mathrm{R}\)
\(
\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{3}
\)
\(
\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{3}
\)
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