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The molar specific heats of an ideal gas at constant pressure and constant volume are denoted by C_P and C_v respectively. If $γ = \frac{C_{P}}{C_{v}}$ and R is the universal gas constant, then C_v is

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$\frac{(1 + γ)}{(1 - γ)}$

$\frac{(γ - 1)}{R}$

$γ R$

$\frac{R}{(γ - 1)}$

answer is D.

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Detailed Solution

For an ideal gas, $C_{P} - C_{V} = R$

Divide $C_{V}$ on both sides, we get $\frac{C_{P}}{C_{V}} - 1 = \frac{R}{C_{V}}$

As $γ = \frac{C_{P}}{C_{V}}$

$∴ γ - 1 = \frac{R}{C_{V}}$ or $C_{V} = \frac{R}{γ - 1}$

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