Most substances contract on freezing . However, water does not belong to this category. We know that water expands on freezing. Further , coefficient of volume expansion of water in the temperature range from `0^(@)C` to `4^(@)C` is negative and above `4^(@)C` it is positive . This behaviour of water shapes the freezing of lakes as the atmospheric temperature goes down and it is still above `4^(@)C`.
If the atmospheric temperature is below `0^(@)C` and ice begins to form at t = 0 , thickness of ice sheet formed up to a time 't' will be directly proprotional to

Options

A. `t^(4)`
B. `t^(2)`
C. `t`
D. `t^(1//2)`

Answer

D

Explanation

`(Ldm)/(dt) = (DeltaT .kA)/(x) , dm = rhoAdx`
`(implies L rhoAdx)/(dt) = (DeltakA)/(x) = Lrho(X^(2))/(2) = DeltaTk.t` Thickness , x `alpha t^(1//2)`