Question

If ${}^{\prime }{C}_p^{\prime }$ and ${}^{\prime }{C}_v^{\prime }$ are molar specific heats of an ideal gas at constant pressure and volume respectively. If ${}^{\prime }{\lambda }^{\prime }$ is the ratio of two specific heats and ${}^{\prime }{R}^{\prime }$ is universal gas constant then ${}^{\prime }{C}_p^{\prime }$ is equal to

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

Answer 1

Answer: (A)

Given, that $\frac{C_p}{C_V}=\gamma$...(i)
As we know that from Mayer's relation,
$C_p-C_V=R$
where, $R$ = universal gas constant
Substitute the value of $C_p$ from the above relation in Eq. (i), we get
$\gamma =\frac{C_p}{C_p-R}$
$\gamma \left(C_p-R\right)=C_p$
$\Rightarrow \gamma C_p-C_p=\gamma R$
$C_p(\gamma -1)=\gamma R$
$\Rightarrow C_p=\frac{\gamma R}{\gamma -1}$
Hence, $C_p$ is equal to $\frac{\gamma R}{\gamma -1}$