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NEETPhysicsKinetic Theory of Gases

At -73 ^ C , the root mean square (rms) speed of Helium gas molecules is v . At what temperature will the rms speed of Hydrogen gas molecules be 100 % more than v ?

Options

  1. A527 ^ C
  2. B127 ^ C
  3. C400 ^ C
  4. D1327 ^ C

Correct answer

B. 127 ^ C

Step-by-step solution

The rms speed of a gas is given by v = 3RT M . For Helium ( M_ He = 4 g/mol ): Initial temperature, T_ He = -73 + 273 = 200 K v = 3R(200) 4 = 150R For Hydrogen ( M_ H ₂ = 2 g/mol ): The target speed is 100 % more than v , which means the new speed is v + v = 2v . v_ H ₂ = 2v = 2 150R = 4 150R = 600R Equating this to the formula for Hydrogen's rms speed: 3RT_ H ₂ 2 = 600R Squaring both sides: 3T_ H ₂ 2 = 600 T_ H ₂ = 600 2 3 = 400 K Converting back to Celsius: T_ H ₂ = 400 - 273 = 127 ^ C Answer: 127 ^ C

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