Question

The ratio $C_p/C_v$ for noble gases is:

• A. $1.67$
• B. $1.33$
• C. $1.42$
• D. $1.84$

Answer 1

The correct option is A $1.67$

The ratio is called the heat capacity.

$C_P$ Expresses the heat capacity (the heat energy required to change a temperature by a certain amount) of a gas held at a constant pressure, $C_V$ the heat capacity of a gas held at constant volume.

To view the ratio (which I usually call the adiabatic index) as a measure of the degrees of freedom of the gas:

${\rm Y}=1+\frac{2}{f}⟷f=\frac{2}{{\rm Y}-1}$

where $\frac{C_P}{C_V}\equiv {\rm Y}$

A monoatomic gas has $f=3⟶{\rm Y}=1+\frac{2}{3}=\frac{5}{3}=1.66$ (the 3 comes from translational motions).
Conclusion: hence the option (A) is correct.