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JEE MainPhysicsKinetic Theory of Gases

An ideal gas is confined in a container of volume V at a pressure P . If the total number of gas molecules in the container is N , the average translational kinetic energy of a single molecule is given by:

Options

  1. A3 2 PV
  2. BPV N
  3. C3PV 2N
  4. D2PV 3N

Correct answer

C. 3PV 2N

Step-by-step solution

The ideal gas equation in terms of the number of molecules N is given by: PV = NkT where k is the Boltzmann constant and T is the absolute temperature. From this, we can write: kT = PV N The average translational kinetic energy of a single gas molecule is given by: E = 3 2 kT Substituting the value of kT from the ideal gas equation, we get: E = 3 2 ( PV N ) = 3PV 2N Answer: 3PV 2N

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