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Heat and Thermodynamics question

2023 · 1 Feb · Shift 1 · Q61
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  5. /2023 · 1 Feb · Shift 1 · Q61

Heat and Thermodynamics question

2023 · 1 Feb · Shift 1 · Q61

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
The average kinetic energy of a molecule of the gas is
  1. A
    proportional to volume
  2. B
    dependent on the nature of the gas
  3. C
    proportional to absolute temperature
  4. D
    proportional to pressure
View written solutionFree

Correct answer: C

  1. For an ideal gas, the average translational kinetic energy of one molecule is given by

Kˉ=32kT\bar{K} = \frac{3}{2}kTKˉ=23​kT

where:

  • kkk = Boltzmann constant
  • TTT = absolute temperature

  1. From this formula, we see that the average kinetic energy depends only on TTT.

  2. Now check the options:

  • A: proportional to volume
    Incorrect, because Kˉ\bar{K}Kˉ does not depend on volume directly.

  • B: dependent on the nature of the gas
    Incorrect, because for ideal gases the average kinetic energy per molecule depends only on temperature, not on the type of gas.

  • C: proportional to absolute temperature
    Correct, since Kˉ∝T\bar{K} \propto TKˉ∝T

  • D: proportional to pressure
    Incorrect, because it is not directly proportional to pressure.

  1. Therefore, the correct option is:

C\boxed{\text{C}}C​

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