A polyatomic gas has f vibrational degrees of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a polyatomic gas,the total degrees of freedom $n$ is the sum of translational,rotational,and vibrational degrees of freedom. For a non-linear

Vedclass · Accepted Answer

$\frac{4+f}{3+f}$

Vedclass · Answer

(A) For a polyatomic gas,the total degrees of freedom $n$ is the sum of translational,rotational,and vibrational degrees of freedom. For a non-linear polyatomic molecule,translational degrees of freedom = $3$ and rotational degrees of freedom = $3$. If there are $f$ vibrational degrees of freedom,each contributes $2$ to the degrees of freedom (one for kinetic and one for potential energy). However,in standard physics problems of this type,the specific heat at constant volume $C_V$ is given by $C_V = \frac{f_{total}}{2} R$. Given the structure of the options,the problem assumes $C_V = (3 + f)R$ (where $3$ represents the translational and rotational contributions and $f$ represents the vibrational contribution per mole). Using the relation $C_p = C_V + R$: $C_p = (3 + f)R + R = (4 + f)R$. Therefore,the ratio $\gamma = \frac{C_p}{C_V} = \frac{(4 + f)R}{(3 + f)R} = \frac{4 + f}{3 + f}$.

$A$ polyatomic gas has $f$ vibrational degrees of freedom,then the ratio of the specific heat at constant pressure to that at constant volume will be

Similar Questions

The heat energy required to raise the temperature of $5 \, moles$ of an ideal gas by $5 \, K$ at constant pressure is $600 \, J$. How much heat (in $J$) is required to raise the same mass of the same gas by $5 \, K$ at constant volume? (Take $R = 8.3 \, J/mol \cdot K$)

Obtain the equation for $\gamma = \frac{C_P}{C_V}$ in terms of the degree of freedom $f$.

What is the value of $\frac{R}{C_P}$ for a diatomic gas?

The following sets of values for ${C_V}$ and ${C_P}$ of a gas have been reported by different students. The units are $cal/gm-mole-K$. Which of these sets is most reliable?

The molar specific heat capacity of a diatomic gas at constant pressure is $C$. The molar specific heat capacity of a monoatomic gas at constant volume is

Vedclass Test Series

Exam Paper Generator

Online Exam Module