JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Heat & Thermodynamics

The correct relation between the degrees of freedom

f

and the ratio of specific heat

γ

is :

(A) $f = \frac{2}{γ + 1}$
(B) $f = \frac{2}{γ - 1}$ ✓ Correct
(C) $f = \frac{1}{γ + 1}$
(D) $f = \frac{γ + 1}{2}$

Answer: (B)

Solution

A gas with

f

degrees of freedom per molecule has internal energy

U = \frac{f}{2} n R T

, so

C_{V} = \frac{f}{2} R

, and

C_{P} = C_{V} + R = (\frac{f}{2} + 1) R

. The ratio of specific heats is then

γ = \frac{C _{P}}{C _{V}} = 1 + \frac{2}{f}

Rearranging this relation gives

f = \frac{2}{γ - 1}

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option

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