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NEET2023PhysicsKinetic Theory of GasesActual

The temperature of a gas is - 50   ° C . To what temperature the gas should be heated so that the rms speed is increased by 3 times?

Options

  1. A223   K
  2. B669   ° C
  3. C3295   ° C
  4. D3097   K

Correct answer

C. 3295   ° C

Step-by-step solution

RMS speed is given by, v = 3 R T M . Therefore, v ∝ T . Given: Initial temperature, T 1 = - 50 + 273   K = 223   K Let, initial speed be v , then final speed will be v + 3 v = 4 v . Now, 4 v v = T 2 T 1 ⇒ T 2 = 16 T 1 = 3568   K = 3568 - 273   ° C = 3295   ° C

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