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NEET
Exam
NEET
Subject
Physics
Chapter
Thermal Properties of Matter

NEET · Physics · Thermal Properties of Matter

Given below are two statements: one is labelled as Assertion (A)...

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The time taken for the ice layer on a freezing lake to double its thickness from xx to 2x2x is exactly equal to the time taken for the ice to initially grow from a thickness of 00 to 3x\sqrt{3}x.
Reason (R): The rate of heat conduction from the water to the surrounding air is inversely proportional to the square of the ice thickness.

In the light of the above statements, choose the most appropriate answer from the options given below:

Options

  1. ABoth Assertion and Reason are true and Reason is the correct explanation of Assertion.
  2. BBoth Assertion and Reason are true but Reason is not the correct explanation of Assertion.
  3. CAssertion is false but Reason is true.
  4. DAssertion is true but Reason is false.

Correct answer

D. Assertion is true but Reason is false.

Step-by-step solution

The time taken for an ice layer to grow from thickness x1x_1 to x2x_2 under a steady sub-zero temperature is given by t=ρL2Kθ(x22−x12)t = \dfrac{\rho L}{2K\theta}(x_2^2 - x_1^2), meaning t∝(x22−x12)t \propto (x_2^2 - x_1^2).

For the thickness to double from xx to 2x2x, the time taken is t1∝(2x)2−x2=3x2t_1 \propto (2x)^2 - x^2 = 3x^2.

For the thickness to grow from 00 to 3x\sqrt{3}x, the time taken is t2∝(3x)2−02=3x2t_2 \propto (\sqrt{3}x)^2 - 0^2 = 3x^2.

Since t1=t2t_1 = t_2, the Assertion is true.

The rate of heat conduction through the ice layer is given by dQdt=KAθx\dfrac{dQ}{dt} = \dfrac{KA\theta}{x}. This shows that the rate of heat conduction is inversely proportional to the thickness xx, not the square of the thickness (x2x^2). Therefore, the Reason is false.

Answer: Assertion is true but Reason is false.
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