Which one of the following is NOT a correct expression for an ideal gas?…

Which one of the following is NOT a correct expression for an ideal gas? $\left[\mathrm{C}_{\mathrm{p}}=\right.$ Molar specific heat of a gas at constant pressure, $\mathrm{C}_{\mathrm{V}}=$ Molar specific heat of a gas at constant volume, $\gamma=$ Ratio of two specific heats of a gas, $\mathrm{R}=$ Universal gas constant]
  1. $\mathrm{C}_{\mathrm{v}}=\mathrm{C}_{\mathrm{p}}+\mathrm{R}$
  2. $\mathrm{R}=\mathrm{C}_{\mathrm{V}}(\gamma-1)$
  3. $\frac{\mathrm{C}_{\mathrm{v}}}{\mathrm{C}_{\mathrm{p}}}=\frac{1}{\gamma}$
  4. $\mathrm{R}=\frac{\mathrm{C}_{\mathrm{p}}(\gamma-1)}{\gamma}$

Solution

$C_P$ and $C_V$ are related as: $C_P=C_V+R$ Hence expression in (A) is not correct.

Asked in: MHT CET 2021 (24 Sep Shift 2)

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