Question

For an ideal gas $(\frac{C_P}{C_v}=\gamma )$; of molar mass M, its specific heat capacity at constant volume is:

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

Answer 1

The correct option is B

$\frac{\gamma }{M(\gamma -1)}$

Given $(\frac{C_P}{C_v}=\gamma )$
We know that $C_P-C_V=R$
We have $C_P=\gamma C_V$ then $\gamma C_V-C_V=R$
$\therefore C_V=\frac{R}{\gamma -1}$
$\therefore C_P=\gamma C_V=\frac{R_{\gamma }}{\gamma -1}$
$\frac{\gamma }{\gamma -1}=C_V\times M$
$\therefore C_V=\frac{\gamma }{M(\gamma -1)}$