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Heat and Thermodynamics question

2022 · 26 Jun · Shift 2 · Q53
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  5. /2022 · 26 Jun · Shift 2 · Q53

Heat and Thermodynamics question

2022 · 26 Jun · Shift 2 · Q53

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27 ∘^\circ∘ C. The ratio of their average kinetic energy per molecule respectively will be :
  1. A
    3 : 2
  2. B
    9 : 4
  3. C
    2 : 3
  4. D
    1 : 1
View written solutionFree

Correct answer: D

  1. Recall the formula for average kinetic energy per molecule

For any ideal gas, the average translational kinetic energy per molecule is

K‾=32kT\overline{K} = \frac{3}{2}kTK=23​kT

where:

  • kkk = Boltzmann constant
  • TTT = absolute temperature
  1. Key observation

This expression depends only on temperature, not on the type of gas, its molar mass, or the amount present.

Since both argon and oxygen are in the same flask and the mixture is at the same temperature 27∘C27^\circ \text{C}27∘C, both gases have the same value of TTT.

  1. Average kinetic energies of argon and oxygen

For argon:

K‾Ar=32kT\overline{K}_{\text{Ar}} = \frac{3}{2}kTKAr​=23​kT

For oxygen:

K‾O2=32kT\overline{K}_{\text{O}_2} = \frac{3}{2}kTKO2​​=23​kT

Therefore,

K‾Ar:K‾O2=1:1\overline{K}_{\text{Ar}} : \overline{K}_{\text{O}_2} = 1:1KAr​:KO2​​=1:1
  1. Check options
  • A: 3:23:23:2 ❌
  • B: 9:49:49:4 ❌
  • C: 2:32:32:3 ❌
  • D: 1:11:11:1 ✅

Hence, the correct answer is Option D.

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