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MHT CET202519 Apr 2025Evening ShiftPhysicsKinetic Theory of GasesActual

If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at 47^ C , the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)

Options

  1. A23^ C
  2. B47^ C
  3. C80^ C
  4. D114^ C

Correct answer

B. 47^ C

Step-by-step solution

The root mean square velocity is given by v_ rms = 3RT M , where R is the gas constant, T is absolute temperature, and M is molar mass. Given v_ rms, H ₂ = 4v_ rms, O ₂ with M_ H ₂ = 2 g/mol and M_ O ₂ = 32 g/mol, and oxygen temperature T_ O ₂ = 47^ C = 320 K. 3RT_ H ₂ M_ H ₂ = 4 3RT_ O ₂ M_ O ₂ Squaring both sides and simplifying: T_ H ₂ M_ H ₂ = 16 T_ O ₂ M_ O ₂ Solving for the hydrogen temperature: T_ H ₂ = 16 M_ H ₂ M_ O ₂ T_ O ₂ = 16 2 32 320 = 320 K Converting to Celsius gives 47^ C . Final answer: 47^ C

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