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Time taken by growth of ice to a thickness x when temp. falls to -T 0 C is given by: t=( ρL/2KT )x 2 Can you pls explain from where has the formula come???

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???

Grade:12th Pass

1 Answers

APURV GOEL
39 Points
9 years ago

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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