Question

At constant volume, the specific heat of a gas is 0.075 $cal{K}^{-1}{g}^{-1}$ and its molecular weight is 40 $gmo{l}^{-1}$. The atomicity of the gas is:
Given: R = 2 cal $K^{-1}mo{l}^{-1}$

• A. Monoatomic
• B. Diatomic
• C. Triatomic
• D. None of the above

Answer 1

The correct option is A Monoatomic

We know that molar heat capacity at constant volume,
$(C_v,m)$ = Specific heat at constant volume $\times$ Molecular weight.

= $0.075\times 40=3cal{K}^{-1}mo{l}^{-1}$....(i)

Also, $C_p–C_v=R$
$\Rightarrow C_p=R+C_v$
= $C_p=2+3=5cal{K}^{-1}mo{l}^{-1}$.....(ii)

Now, $\frac{C_p}{C_v}=\gamma$

Using equation (i) and (ii)
$\gamma =\frac{5}{3}=1.67$
This value shows that the gas is monoatomic.