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Kinetic Theory of Gases appeared 26 times across 3 years — 3% of Physics. This question is from Ideal Gas Equation and Temperature.

Year 2026 2025 2024 Total
Questions 6 11 9 26
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The temperature of a gas having 2.0 × 10²⁵ molecules per cubic meter at 1.38 atm (Given, k = 1.38 × 10⁻²³ J K⁻¹) is:

Solution & Explanation

Related Formula

The state equation of an ideal gas in terms of the number of molecules N and Boltzmann constant k is:

PV = NkT

Rearranging to express pressure in terms of number density n = N/V:

P = n k T

Core Logic

Given parameters:

  • Number density, n = (N)/(V) = 2.0 × 10²⁵ molecules/m³
  • Pressure, P = 1.38 atm = 1.38 × 1.01 × 10⁵ N/m²
  • Boltzmann constant, k = 1.38 × 10⁻²³ J K⁻¹
Step 1: Solve for Temperature

Rearranging P = n k T for temperature T:

T = (P)/(nk)

Substitute the values:

T = 1.38 × 1.01 × 10⁵(2.0 × 10²⁵) × (1.38 × 10⁻²³)

Notice that the term 1.38 cancels out from numerator and denominator:

T = (1.01 × 10⁵)/(2.0 × 10²) T = (1.01 × 10³)/(2.0) ≈ (1010)/(2) ≈ 500 K
Pattern Recognition

The numerical values are designed to cancel out smoothly. Spotting the 1.38 cancelation instantly saves valuable calculation time.

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

More Kinetic Theory of Gases Questions — jee_main_2024_29_january_evening

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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%)