An ideal gas is made of polyatomic molecules. | vedclass

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

Question

(A) For a polyatomic gas molecule, the total degrees of freedom $F$ is given by the sum of translational, rotational, and vibrational modes.Given: Tra

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) For a polyatomic gas molecule, the total degrees of freedom $F$ is given by the sum of translational, rotational, and vibrational modes.Given: Translational modes = $3$, Rotational modes = $3$, Vibrational modes = $f$.Each vibrational mode contributes $2$ degrees of freedom (one for kinetic energy and one for potential energy).So, the total degrees of freedom $F = 3 + 3 + 2f = 6 + 2f$.The ratio of heat capacities $\gamma = C_p/C_v = 1 + 2/F$.Given $\gamma = 8/7$, we have $8/7 = 1 + 2/F$.$8/7 - 1 = 2/F \implies 1/7 = 2/F \implies F = 14$.Equating the two expressions for $F$: $6 + 2f = 14$.$2f = 8 \implies f = 4$.

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_p/C_v$ of the gas is $8/7$, then the value of $f$ is:

Similar Questions

For a gas,$\gamma = 7/5$. The gas may probably be

For a gas having $X$ degrees of freedom,what is the value of $\gamma$ (where $\gamma$ is the ratio of specific heats,$\gamma = C_{P} / C_{V}$)?

The temperature of argon,kept in a vessel,is raised by $1^\circ C$ at a constant volume. The total heat supplied to the gas is a combination of translational and rotational energies. Their respective shares are

Derive the equation for the internal energy of a gas in terms of its degrees of freedom.

What is the kinetic energy of $1 \, g$ of $CO_2$ $(O-C-O)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module