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NEETPhysicsKinetic Theory of Gases

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If a gas at 27^ C is heated such that its rms speed increases by 100 % , its final temperature must be 1200^ C . Reason (R): The rms speed of an ideal gas is directly proportional to the square root of its absolute temperature. In the light of the above statements, choose the most appropriate answe

Options

  1. ABoth (A) and (R) are true and (R) is the correct explanation of (A)
  2. BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
  3. C(A) is true but (R) is false
  4. D(A) is false but (R) is true

Correct answer

D. (A) is false but (R) is true

Step-by-step solution

Reason (R) is a correct statement as v_ rms = 3RT M , which implies v_ rms T , where T is the absolute temperature. For Assertion (A): Initial temperature, T₁ = 27^ C = 27 + 273 = 300 K . Let the initial rms speed be v . If the speed increases by 100 % , the final speed v₂ = v + 100 % of v = 2v . Since v_ rms T , we have v₂ v₁ = T₂ T₁ . 2v v = T₂ 300 4 = T₂ 300 T₂ = 1200 K . Converting back to Celsius, final temperature = 1200 - 273 = 927^ C . The assertion claims the final temperature is 1200^ C , so Assertion (A)

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