Question

Find the number of degrees of freedom of molecules in a gas whose molar heat capacity at constant pressure is equal to $C_P=29\text{J/(mol.K)}$

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is C $5$

We know that,

$C_P=\frac{\gamma R}{\gamma -1}$

$\Rightarrow 29=\frac{\gamma \times 8.314}{\gamma -1}$

$\frac{\gamma -1}{\gamma }=\frac{8.314}{29}=0.287$

$1-\frac{1}{\gamma }=0.287$

$1-0.287=\frac{1}{\gamma }$

$\gamma =\frac{1}{0.713}=1.4$

Now, if $f$ represents the degree of freedom then,

$\gamma =1+\frac{2}{f}$

$1.4-1=\frac{2}{f}$

$f=\frac{2}{0.4}=\frac{20}{4}=5$