Question

Ice starts freezing in a lake with water at $0^o$C when the atmospheric temperature is $-{10}^o$C. If the time taken for $1$cm of ice to be formed is $12$min, the time taken for the thickness of the ice to change from $1$ to $2$cm will be.

• A. 12 min
• B. less than 12 min
• C. more than 12 min but less than 24 min
• D. more than 24 min

Answer 1

The correct option is D more than 24 min

Time taken by ice to grow a thickness of
$t=\frac{eL}{2K\theta }{y}^2$
Hence time interval to change thickness from $0$ to y, from y to $2$y and so on will be in the ratio.
$\Delta t_1:\Delta t_2:\Delta t_3$
$\therefore =(1-0^2):(2^2-1^2):(3^2-2^2)$
$\Delta t_1:\Delta t_2:\Delta t_3=1:3:5$
According to question $=\Delta t_1<$ terims
$\Delta t_2=3\Delta H$
$=3\times 12=36$min.