The ratio of specific heats ( C _ P C _ V ) in terms of degree of freedom (f) is given by :

Correct answer: B. (1 + (2)/(f)) From Mayer's relation C _ P = C _ V + R and C _ V = (f)/(2)R Ratio of specific heat, γ = C _ P C _ V = 1 + (R)/((f)/(2)R) = 1 + (2)/(f)

JEE Main 202225 JuneEvening Shift

Exam: JEE Main
Year: 2022
Date: 25 June
Shift: Evening Shift
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main 2022 · 25 June · Evening Shift · Physics · Kinetic Theory of Gases

The ratio of specific heats ( C _ P C _ V ) in terms of degree of...

The ratio of specific heats

\left(\dfrac{{C}_{P}}{{C}_{V}}\right)

in terms of degree of freedom

\left(f\right)

is given by :

Options

A $\left(1 + \dfrac{f}{3}\right)$
B $\left(1 + \dfrac{2}{f}\right)$
C $\left(1 + \dfrac{f}{2}\right)$
D $\left(1 + \dfrac{1}{f}\right)$

Correct answer

B. $\left(1 + \dfrac{2}{f}\right)$

Step-by-step solution

From Mayer's relation ${C}_{P} = {C}_{V} + R$ and ${C}_{V} = \dfrac{f}{2}R$

Ratio of specific heat,

$\gamma = \dfrac{{C}_{P}}{{C}_{V}} = 1 + \dfrac{R}{\dfrac{f}{2}R} = 1 + \dfrac{2}{f}$

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