Question

The thickness of ice in a lake is $5cm$ and its atmospheric temperature is $-{10}^{o}C$. Calculate the time required for the thickness of ice to grow to $7cm.$ Thermal conductivity of ice = $4\times {10}^{-3}cal/c{m}^{-1}{s}^{-1}{C}^{-10}$; density of ice $0.92g/c{m}^3$ and specific latent heat of fusion for ice $=80cal/g.$

Answer 1

Here, $x_1=5cm,x_2=7cm;T={10}^{o}C,k=4\times {10}^{-3}cal/c{m}^{-1}{s}^{-1}{C}^{-10};L=80cal/g,\rho =0.92g/c{m}^2$
Using $\Delta t=\frac{\rho L}{2KT}(x_2^2-x_1^2)$
We have the required time $\Delta t$ as
$\Delta t=\frac{92\times {10}^{-2}}{2\times 4\times {10}^{-3}cal/c{m}^{-1}{s}^{-1}{C}^{-10}}\frac{g}{c{m}^3}\times \frac{80}{{10}^{o}C}\frac{cal}{g}(7^2-5^2)cm$
$=\frac{92\times 80\times 24}{8}s=22080s=6.13h$