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Kinetic Theory of Gases appeared 26 times across 3 years — 3% of Physics. This question is from Internal Energy of Gas.

Year 2026 2025 2024 Total
Questions 6 11 9 26
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The internal energy of air in 4m× 4m× 3m sized room at 1 atmospheric pressure will be _ × 10⁶J. (Consider air as diatomic molecule)

Numerical Answer Type:
Enter a numerical value Answer: 12 to 12 +4 marks

Solution & Explanation

Related Formula
  • Ideal Gas Law:

    • P V = n R T

  • Internal Energy (U) of a diatomic gas (f = 5 degrees of freedom):
U = n Cv T = n ((5)/(2) R) T = (5)/(2) P V
Core Logic

Given parameters:

  • Dimensions of the room = 4 m × 4 m × 3 m
  • Volume of air in the room V = 4 × 4 × 3 = 48 m³
  • Room pressure P = 1 atm = 10⁵ N/m²
Step 1: Calculate internal energy

Using the thermodynamic relationship:

U = (5)/(2) P V

Substitute the volume and pressure parameters:

U = (5)/(2) × 10⁵ N/m² × 48 m³ U = 5 × 10⁵ × 24 = 120 × 10⁵ J = 12 × 10⁶ J

Thus, the internal energy is 12 × 10⁶ ~J.

Pattern Recognition

Sees: Internal energy of diatomic gas occupying a macroscopic room volume. Trap: Attempting to calculate thermodynamic variables like temperature or density explicitly. Internal energy is completely determined by pressure and volume via degrees of freedom (U = (f)/(2)PV). Shortcut: A diatomic gas has f=5, so U = 2.5 PV. Putting in numbers, U = 2.5 × 10⁵ × 48 = 120 × 10⁵ = 12 × 10⁶ ~J, leaving a coefficient of 12.

Chapter Mix

Class 11 Physics: Kinetic Theory of Gases

Reference Study Guides

Kinetic Theory Of Gases

More Kinetic Theory of Gases Previous-Year Questions — Page 6

Q31 jee_main_2024_31_jan_morning Kinetic Energy Of Gas Molecules
The parameter that remains the same for molecules of all gases at a given temperature is :
  • A. kinetic energy
  • B. momentum
  • C. mass
  • D. speed

Solution

Related Formula
KE = (f)/(2)kT
Core Logic

The average translational kinetic energy of any gas molecule depends only on the absolute temperature of the gas and is independent of the nature or mass of the gas.

For 1 mole of any ideal gas, the average translational kinetic energy is (3)/(2)RT. Therefore, at a given temperature, the kinetic energy parameter is uniform across all ideal gases.

Pattern Recognition

Temperature is directly proportional to average translational kinetic energy. If T is constant, KE is constant for all gases regardless of mass.

Chapter Mix

Class 11 Physics: Kinetic Theory

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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)