Question

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

• A. $\gamma R$
• B. $\frac {(\gamma-1)R}{\gamma}$
• C. $\frac {R}{\gamma -1}$
• D. $\frac {\gamma R}{\gamma -1} $

Answer 1

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
$ \gamma C_{V}-C_{V} =R$
$C_{V}(\gamma-1) =R $
$C_{V} =\frac{R}{\gamma-1}$