Question

Ice starts forming in lake with water at $0^{o}C$ and when the atmospheric temperature is $-{10}^{o}C$. If the time taken for 1 cm of ice to form is 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. 2.3 hours
• D. 21 hours

Answer 1

The correct option is C

2.3 hours

$t=frac\rho L2K\theta (x_2^2-x_1^2)\Rightarrow t\propto (x_2^2-x_1^2)$
$\Rightarrow \frac{t}{t^{\prime }}=frac(x_2^2-x_1^2)(x_2^{{}^{\prime }2}-x_1^{{}^{\prime }2})\Rightarrow \frac{7}{t}=\frac{(1^2-0^2)}{(2^2-1^2)}\Rightarrow t=21hours$