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MHT CET202615 April 2026Evening ShiftPhysicsKinetic Theory of GasesActual

The average translational 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 (N = number of molecules, R = gas constant)

Options

  1. AeVN 2R
  2. B2eVN 3R
  3. CeVN R
  4. D3eVN 4R

Correct answer

B. 2eVN 3R

Step-by-step solution

The average translational kinetic energy of a gas molecule 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 can equate the two expressions: 3 2 k_B T = eV The Boltzmann constant k_B is related to the universal gas constant R and Avogadro's number N (number of molecules per mole) by the relation k_B = R N . Substituting this into the equation gives: 3 2 ( R N ) T = eV Solving for the temperature T : T = 2eVN 3R An

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