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MHT CET202616 April 2026Evening ShiftPhysicsKinetic Theory of GasesActual

The average transnational kinetic energy of a molecule in a gas is E₁ . The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is E₂ . The temperature at which E₁ = E₂ possible is (mass of molecule and electron is same) (N = number of molecules, V = Velocity, R = gas constant)

Options

  1. A2VNe 3R
  2. BVNe 2R
  3. C3NeV 2R
  4. D5NeV 3R

Correct answer

A. 2VNe 3R

Step-by-step solution

The average translational kinetic energy of a single molecule in a gas is given by: E₁ = 3 2 k_B T The kinetic energy of an electron accelerated from rest through a potential difference V is: E₂ = eV Given that E₁ = E₂ , we have: 3 2 k_B T = eV T = 2eV 3k_B We know that the Boltzmann constant k_B is related to the universal gas constant R and Avogadro's number N by the relation k_B = R N . Substituting this into the equation for T , we get: T = 2eV 3 ( R N ) T = 2VNe 3R Answer: 2VNe 3R

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