Question

For monoatomic gas which is correct?

• A. $C_V=\frac{3}{5}R$
• B. $C_P=\frac{5}{2}R$
• C. $C_P-C_V=2R$
• D. $\frac{C_P}{C_V}=\frac{3}{5}$

Answer 1

Answer: (B)

Monoatomic gas has three translational degrees of freedom. Specific heat at constant volume
$(C_V)=\frac{f}{2}R$ and specific heat at constant pressure $(C_P)$
$C_P=\left(\frac{f}{2}+1\right)R$
For monoatomic gas
$f=3$
$\therefore C_V=\frac{3}{2}R,C_P=\left(\frac{3}{2}+1\right)R=\frac{5}{2}R$
From Mayors formula
$C_P-C_V=R$
$\therefore \frac{5}{2}R-\frac{3}{2}R=R$
and $\gamma =\frac{C_P}{C_V}=\frac{5/2}{3/2}=\frac{5}{3}$