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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.
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