Q125 / 150 · MHT CET 2023 (09 May Shift 1) · Physics

For a gas having ' $\mathrm{X}$ ' degrees of freedom, ' $\gamma$ ' is $\left(\gamma=\right.$ ratio of specific heats $\left.=C_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}\right)$

  • A
    $\frac{1+X}{2}$
  • B
    $1+\frac{X}{2}$
  • Correct answer
    C
    $1+\frac{2}{X}$
  • D
    $1+\frac{1}{X}$

Solution

$\gamma$ and degrees of freedom is related by $\gamma=\frac{\mathrm{f}+2}{\mathrm{f}}$ Where $\mathrm{f}$ is the number of degrees of freedoms. Given $\mathrm{f}=\mathrm{X}$, $\therefore \quad \gamma=\frac{X+2}{X}=1+\frac{2}{X}$

Hence, the correct answer is option: 'C'.

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