Problem

A layer of ice of thickness

y

is on the surface of a lake. The air is at a constant temperature

-\theta^\circ\text{C}

and the ice water interface is at

0^\circ\text{C}

. Show that the rate at which the thickness increases is given by

\frac{dy}{dt} = \frac{K\theta}{L\rho y}

where,

K

is the thermal conductivity of the ice,

L

the latent heat of fusion and

\rho

is the density of the ice.