Question

The ratio of the heat capacities $C_p/C_V$ for one mole of a gas is $1.67$. The gas is

• A. $He$
• B. $H_2$
• C. $C{O}_2$
• D. $C{H}_4$

Answer 1

Answer: (A)

The ratio of molar heat capacities at constant pressure to that at constant volume is represented by $\gamma$ .
The value of $\gamma$ gives information about the atomicity of gases.
If$\frac{C_p}{C_V}=1.67,$ gas will be monoatomic.
If$\frac{C_p}{C_V}=1.40,$ gas will be diatomic.
If$\frac{C_p}{C_V}=1.33,$ gas will be triatomic.
As given in question, $C_p/C_V$ for one mole of a gas is $\mathrm{1.67.}i.e$.
$\frac{C_p}{C_V}=\gamma =1.67$
$\therefore$ It will be a monoatomic gas.
Thus, from the given options,
He is a monoatomic gas.