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Molar and Specific Heat Capacity

The molar spe...

Question

The molar specific heats of an ideal gas at constant pressure and 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 equal to -

\frac{1 + γ}{1 - γ}

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\frac{R}{(γ - 1)}

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\frac{(γ - 1)}{R}

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γ R

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Solution

The correct option is B $\frac{R}{(γ - 1)}$
$C_{p} - C_{v} = R$
$⟹ \frac{C_{p}}{C_{v}} - \frac{C_{v}}{C_{v}} = \frac{R}{C_{v}}$
$γ - 1 = \frac{R}{C_{v}}$
$∴ C_{v} = \frac{R}{γ - 1}$

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