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The molecule of a monatomic gas has only three translational degrees of freedom. Thus, the average energy of a molecule at temperature 'T' is ____________.

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SSC Scientific Assistant Physics Official Paper (Held On: 23 November 2017 Shift 1)
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  1. 3kBT
  2. (3/4) kBT
  3. (1/3)kBT
  4. (3/2)kBT

Answer (Detailed Solution Below)

Option 4 : (3/2)kBT
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Detailed Solution

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CONCEPT:

  • According to kinetic energy theory, if we increase the temperature of a gas, it will increase the average kinetic energy of the molecule, which will increase the motion of the molecules.
    • This increased motion increases the outward pressure of the gas.

The average kinetic energy (KE) or energy (E) of translation per molecules of the gas is related to temperature by the relationship:

      (degree of freedom of a monoatomic gas = 3)

Where K E = kinetic energy, kB = Boltzmann constant and T = temperature.

EXPLANATION:

The average energy of a molecule is given by:

KE = E = (3/2)kBT

So option 4 is correct.

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