For a gas having ' $\mathrm{X}$ ' degrees of freedom, ' $\gamma$ ' is $\left(\gamma=\right.$ ratio of…

For a gas having ' $\mathrm{X}$ ' degrees of freedom, ' $\gamma$ ' is $\left(\gamma=\right.$ ratio of specific heats $\left.=C_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}\right)$
  1. $\frac{1+X}{2}$
  2. $1+\frac{X}{2}$
  3. $1+\frac{2}{X}$
  4. $1+\frac{1}{X}$

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 $\mathrm{f}=\mathrm{X}$, $\therefore \quad \gamma=\frac{X+2}{X}=1+\frac{2}{X}$

Asked in: MHT CET 2023 (09 May Shift 1)

Practice more Kinetic Theory of Gases questions on Aicharya