Question

Ice starts forming in lake with water at $0^{\circ }C$ and when the atmospheric temperature is $-{10}^{\circ }C$. If the time taken for 1cmof ice be 7 hours, then the time taken for the thickness of ice to change from 1 cm to 2 cm is

• A. 7 hours
• B. 14 hours
• C. Less than 7 hours
• D. More than 7 hours

Answer 1

The correct option is D

More than 7 hours

t = $\frac{\rho L}{2k\theta }(x_2^2-x_{1}2)\Rightarrow t\propto (x_2^2-x_1^2)$

$\Rightarrow \frac{t}{t^{\prime }}=\frac{(x_2^2-x_1^2)}{(x_2^{\prime 2}-x_1^{\prime 2})}\Rightarrow \frac{9}{t^{\prime }}=\frac{(1^2-0^2)}{(2^2-1^2)}\Rightarrow t=21hours$