COMEDK2021PhysicsKinetic Theory of Gases

The average energy associated with a monoatomic molecule is

Options

AK_ B T
B1 2 K_ B T
C3 2 K_ B T
D2 K_ B T

Correct answer

C. 3 2 K_ B T

Step-by-step solution

A monoatomic gas molecule has 3 degrees of freedom ( f = 3 ) corresponding to its translational motion along the x , y , and z axes. According to the law of equipartition of energy, each degree of freedom contributes 1 2 K_ B T to the average kinetic energy of the molecule. Therefore, the total average energy E is given by E = f 1 2 K_ B T = 3 1 2 K_ B T = 3 2 K_ B T . Answer: 3 2 K_ B T

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