If $\gamma$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

Question

Dr. Abubacker · Accepted Answer

(c) From the Mayer’s formula
$C_{p} - C_{V} = R$ …(i)
and $\gamma = \frac{C_{p}}{C_{V}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \gamma C_{V} = C_{p}$ …(ii)
Substituting Eq. (ii) in Eq. (i) we get
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \gamma C_{V} - C_{V} = R$
$C_{V}(\gamma - 1) = R$
$C_{V} = \frac{R}{\gamma - 1}$

Q. If $\gamma$ is the ratio of specific heats and $R$ is the universal gas constant, then the molar specific heat at constant volume $C_{v}$ is given by

Explanation

Reviewed by Dr. Abubacker

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