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 x to 2x is exactly equal to the time taken for the ice to initially grow from a thickness of 0 to 3 x . Reason (R): The rate of heat conduction from the water to the surrounding air is inversely proportional to the squ

Step-by-step solution

The time taken for an ice layer to grow from thickness x₁ to x₂ under a steady sub-zero temperature is given by t = L 2K (x₂^2 - x₁^2) , meaning t (x₂^2 - x₁^2) . For the thickness to double from x to 2x , the time taken is t₁ (2x)^2 - x^2 = 3x^2 . For the thickness to grow from 0 to 3 x , the time taken is t₂ ( 3 x)^2 - 0^2 = 3x^2 . Since t₁ = t₂ , the Assertion is true. The rate of heat conduction through the ice layer is given by dQ dt = KA x . This shows that the rate of heat conduction is inversely proportiona