Question

The temperature at the bottom of a pond of depth $L=15m$ is $4^{\circ }$C. The temperature of the air, just above the layer of ice frozen at the pond's surface is $-2^{\circ }$C for the past many days. The thermal conductivity of ice is three times that of water. Find the depth (in m) of unfrozen water below ice?

Answer 1

Let the thermal conductivity of water be $K$ and that of ice be $3K$ and the depth of unfrozen water below ice be $x$.

Then, since same current must flow through two layers.

$\therefore \frac{3KA}{15-x}\left(2\right)=\frac{KA}{x}\left(4\right)$ since temperature of junction will be zero.

Hence, $3x=30-2x$

$x=6m$

Answer is 6.