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JEE MainPhysicsKinetic Theory of Gases

The total translational kinetic energy of 16 g of O ₂ gas is found to be 2493 J . If the universal gas constant is R = 8.31 J/(mol K) , the temperature of the gas is

Options

  1. A-33^ C
  2. B400^ C
  3. C127^ C
  4. D-73^ C

Correct answer

C. 127^ C

Step-by-step solution

The translational kinetic energy of any gas depends only on the number of moles and the absolute temperature, with 3 degrees of freedom for translation. Number of moles of O ₂ , n = Mass Molar mass = 16 g 32 g/mol = 0.5 mol . The translational kinetic energy is given by: E_ trans = 3 2 n R T Substituting the given values: 2493 = 3 2 0.5 8.31 T 2493 = 0.75 8.31 T 2493 = 6.2325 T T = 2493 6.2325 = 400 K Converting the temperature to Celsius: T(^ C ) = 400 - 273 = 127^ C Answer: 127^ C

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