The thickness of icein a lakeis 5 cm and theatmospherictemperatureis- 10^(@)C. Calculate the timerequired for the thickness of ice to growto 7 cm . Thermal conductivityof ice= 4 xx 10^(-3)cal//cm-s-""^(@)C , density of ice= 0.92 g //cm^(3) and specific latentheat of fusion for ice= 80cal/g.

The thickness of icein a lakeis 5 cm and theatmospherictemperatureis-

1.	The thickness of icein a lakeis 5 cm and theatmospherictemperatureis- 10^(@)C. Calculate the timerequired for the thickness of ice to growto 7 cm . Thermal conductivityof ice= 4 xx 10^(-3)cal//cm-s-""^(@)C , density of ice= 0.92 g //cm^(3) and specific latentheat of fusion for ice= 80cal/g.
Answer» Solution :Here `x_(1) = 5 CM , x_(2) = 7 cm , T = - 10^(@)C , k = 4 XX 10^(-3) CAL//cm -s-""^(@)C , L = 80 cal//g ` and`rho = 0.92 g //cm^(3)` Using`Delta t = (rho L)/(2kT) (x_(2)^(2)- x_(1)^(2))` we have , the required `Delta t ` as` = (92 xx 10^(-2))/(2 xx 4 xx 10^(-3) cakl//cm-s-""^(@)C)(g)/(cm^(3)) xx (80)/(10^(@)C) (cal)/(g)(7^(2) - 5^(2)) cm^(2) = (92 xx 80 xx 24)/(8) s = 22080s` =6.13 hr .