The ratio of the specific heats $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma$, in terms…

The ratio of the specific heats $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma$, in terms of degrees of freedom ( n ) is
  1. $\left(1+\frac{1}{n}\right)$
  2. $\left(1+\frac{\mathrm{n}}{3}\right)$
  3. $\left(1+\frac{2}{n}\right)$
  4. $\left(1+\frac{\mathrm{n}}{2}\right)$

Solution

We know $\mathrm{C}_{\mathrm{v}}=\mathrm{n} \times \frac{\mathrm{R}}{2}$
From $C_P-C_V=R$, we get $C_p=C_v+R=\frac{n R}{2}+R=\left(\frac{n}{2}+1\right) R$ $\therefore \quad \frac{C_p}{C_v}=\frac{\left(\frac{n}{2}+1\right) R}{\frac{n R}{2}}=\left(1+\frac{2}{n}\right)$

Asked in: MHT CET 2024 (16 May Shift 2)

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