A layer of ice of thickness is on the surface of a lake

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

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 ice,

l

is the latent heat of fusion, and

\rho

is the density of ice.