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JEE Main202429 Jan 2024Evening ShiftPhysicsKinetic Theory of GasesActual

The temperature of a gas having 2 . 0 × 10 25 molecules per cubic meter at 1 . 38 atm (Given, k = 1 . 38 × 10 - 23 J K - 1 ) is :

Options

  1. A500 K
  2. B200 K
  3. C100 K
  4. D300 K

Correct answer

A. 500 K

Step-by-step solution

From ideal gas equation, P V = n R T ⇒ P V = N N A R T , where N = total number of molecules ⇒ P = N V R N A T ⇒ P = N V k T ⇒ 1 . 38 × 1 . 01 × 10 5 = 2 × 10 25 × 1 . 38 × 10 - 23 × T ⇒ 1 . 01 × 10 5 = 2 × 10 2 × T T = 1 . 01 × 10 3 2 ≈ 500 K

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