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JEE Main 202122 JulyMorning Shift

Exam: JEE Main
Year: 2021
Date: 22 July
Shift: Morning Shift
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main 2021 · 22 July · Morning Shift · Physics · Kinetic Theory of Gases

What will be the average value of energy for a monoatomic gas in...

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature

T ?

Options

A $\dfrac{2}{3}{k}_{B}T$
B ${k}_{B}T$
C $\dfrac{3}{2}{k}_{B}T$
D $\dfrac{1}{2}{k}_{B}T$

Correct answer

C. $\dfrac{3}{2}{k}_{B}T$

Step-by-step solution

As per Equi-partition law,

each degree of freedom contributes
$\dfrac{1}{2}{k}_{B}T$ average energy.

In mono atomic gas, $D . O . F .$ $= 3$
$⇒$ Average energy $= 3 \times \dfrac{1}{2}{k}_{B}T = \dfrac{3}{2}{k}_{B}T$

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