Question:
The correct relation between the degrees of freedom f and the ratio of specific heat \(\gamma\) is :
The correct relation between the degrees of freedom f and the ratio of specific heat \(\gamma\) is :
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Use \(C_v = \frac{f}{2}R\), \(C_p = C_v + R\) and \(\gamma = C_p/C_v\).
Updated On: Nov 4, 2026
- \(f = \dfrac{2}{\gamma - 1}\)
- \(f = \dfrac{2}{\gamma + 1}\)
- \(f = \dfrac{\gamma + 1}{2}\)
- \(f = \dfrac{1}{\gamma + 1}\)
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The Correct Option is A
Solution and Explanation
By equipartition, \(C_v = \dfrac{f}{2}R\) and \(C_p = C_v + R = \left(\dfrac{f}{2} + 1\right)R\).
\(\gamma = \dfrac{C_p}{C_v} = \dfrac{f/2 + 1}{f/2} = 1 + \dfrac{2}{f}\).
So \(\gamma - 1 = \dfrac{2}{f}\), i.e. \(f = \dfrac{2}{\gamma - 1}\).
Answer: (1) \(f = \dfrac{2}{\gamma - 1}\)
\(\gamma = \dfrac{C_p}{C_v} = \dfrac{f/2 + 1}{f/2} = 1 + \dfrac{2}{f}\).
So \(\gamma - 1 = \dfrac{2}{f}\), i.e. \(f = \dfrac{2}{\gamma - 1}\).
Answer: (1) \(f = \dfrac{2}{\gamma - 1}\)
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