Question

If $'C_p'$ and $'C_v'$ are molar specific heats of an ideal gas at constant pressure and volume respectively. If $'\lambda'$ is the ratio of two specific heats and $'R'$ is universal gas constant then $'C_p'$ 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

The Correct Option is 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 E (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 $\frac{\gamma R}{\gamma-1}$