Time taken by growth of ice to a thickness x when temp. falls to -T⁰C is given by:

t=( ρL/2KT )x² Can you pls explain from where has the formula come???

Assume that a layer of ice of thickness dx is formed at 0 degree celcius and temp falls to -T degreeC below it.

now heat used in conversion of ice =ML

                                                  = AdxΡL, where A is surface area and L is latent heat                 ...........(1)

heat flow rate from ice to water given by dQ/dt = KA(difference in temp)/d

here temp diff is 0-(-T) = T

we get dQ = KATdt/x                                                                                                          ..............(2)

Equating 1 and 2 we get

AdxPL = KATdt/x

(x)dx=(KT/PL)dt

integrate both sides and get your formula.