Question

Molar specific heat at constant volume, for a non-linear triatomic gas is (vibration mode neglected)

• A. $3R$
• B. $4R$
• C. $2R$
• D. $R$

Answer 1

The correct option is A $3R$

For triatomic non linear molecules,

Degrees of freedom, $f=6$

We know ,

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

$\Rightarrow \gamma =1+\frac{2}{6}$

$\Rightarrow \gamma =1+\frac{1}{3}$

$\Rightarrow \frac{C_p}{C_v}=\frac{4}{3}$

Subtracting 1 both sides,

$\Rightarrow \frac{C_p}{C_v}-1=\frac{4}{3}-1$

$\Rightarrow \frac{C_p-C_v}{C_v}=\frac{1}{3}$

We know, $C_p-C_v =R

$\Rightarrow \frac{R}{C_v}=\frac{1}{3}$

Therefore, $C_v=3R$

Hence, the correct option is A.