The thickness of ice in a lake is 5cm and the atmospheric temperature is -10^(@)C. Calculate the time required for the thickness of ice to grow to 7cm. Thermal conductivity of ice = 4xx10^(-3)cal//cm-s-""^(@)C, density of ice = 0.92g//cm^(3) and latent heat of fusion for ice = 80 cal/g.

The thickness of ice in a lake is 5cm and the atmospheric temperature

1.	The thickness of ice in a lake is 5cm and the atmospheric temperature is -10^(@)C. Calculate the time required for the thickness of ice to grow to 7cm. Thermal conductivity of ice = 4xx10^(-3)cal//cm-s-""^(@)C, density of ice = 0.92g//cm^(3) and latent heat of fusion for ice = 80 cal/g.
Answer» Solution :USING `DELTAT=(rhoL)/(2KT)(x_(2)^(2)-x_(1)^(2))` we have, the required time `Deltat` as `Deltat=(92xx10^(-2)g//cm^(3))/(2xx4xx10^(-3)cal//cm-s-""^(@)C)XX(80cal//gm)/(10^(@)C)xx(7^(2)-5^(2))cm^(2)` = `(92xx80xx24)/8s=22080s=6.13hr`.