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Heat and Thermodynamics question

2023 · 30 Jan · Shift 2 · Q57
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  5. /2023 · 30 Jan · Shift 2 · Q57

Heat and Thermodynamics question

2023 · 30 Jan · Shift 2 · Q57

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A flask contains hydrogen and oxygen in the ratio of 2:12: 12:1 by mass at temperature 27∘C27^{\circ} \mathrm{C}27∘C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:
  1. A
    1 : 1
  2. B
    4 : 1
  3. C
    1 : 4
  4. D
    2 : 1
View written solutionFree

Correct answer: A

  1. Use 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 idea

This expression depends only on temperature, not on:

  • the type of gas,
  • its molecular mass,
  • or the amount of gas present.

Since both hydrogen and oxygen are in the same flask, they are at the same temperature:

T=27∘C=300 KT = 27^\circ C = 300\,KT=27∘C=300K
  1. Average kinetic energies

For hydrogen:

K‾H2=32kT\overline{K}_{H_2} = \frac{3}{2}kTKH2​​=23​kT

For oxygen:

K‾O2=32kT\overline{K}_{O_2} = \frac{3}{2}kTKO2​​=23​kT

Therefore,

K‾H2:K‾O2=1:1\overline{K}_{H_2} : \overline{K}_{O_2} = 1:1KH2​​:KO2​​=1:1
  1. Check options
  • A: 1:11:11:1 ✅
  • B: 4:14:14:1 ❌
  • C: 1:41:41:4 ❌
  • D: 2:12:12:1 ❌

Hence, the correct option is A.

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