According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant γ=(C_p)/(C_v) is ( C_P where C_v are the specific heat capacities of the gas at constant pressure and

Correct answer: C. (4-3 γ)/(γ-1) A polygamic gas has 3 translational, 3 rotational and f vibration modes U=(3)/(2) k_B T+(3)/(2) k_B T+f k_B T U=(3+f) k_B T C_V=(3+f) R C_p=(4+f) R (C_p)/(C_v)=(4+f)/(3+f)=γ 4+f=3 γ+f γ 4-3 γ=f(γ-1) f=(4-3 γ)/(γ-1)

NEET 2024

Exam: NEET
Year: 2024
Subject: Physics
Chapter: Kinetic Theory of Gases

NEET 2024 · Physics · Kinetic Theory of Gases

According to the law of equipartition of energy, the number of...

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant

\gamma=\frac{C_p}{C_v}

is (

C_P

where

C_v

are the specific heat capacities of the gas at constant pressure and constant volume, respectively):

Options

A $\frac{4+3 \gamma}{\gamma-1}$
B $\frac{3+4 \gamma}{\gamma-1}$
C $\frac{4-3 \gamma}{\gamma-1}$
D $\frac{3-4 \gamma}{\gamma-1}$

Correct answer

C. $\frac{4-3 \gamma}{\gamma-1}$

Step-by-step solution

A polygamic gas has 3 translational, 3 rotational and

f

vibration modes

U=\frac{3}{2} k_B T+\frac{3}{2} k_B T+f k_B T

U=(3+f) k_B T

C_V=(3+f) R

C_p=(4+f) R

\frac{C_p}{C_v}=\frac{4+f}{3+f}=\gamma

4+f=3 \gamma+f \gamma

4-3 \gamma=f(\gamma-1) \Rightarrow f=\frac{4-3 \gamma}{\gamma-1}

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