Question

Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at -9.4°C and the bottom of the pond at 4.0°C. If the total depth of ice + water is 1.7 m, how thick is the ice? (Assume that the thermal conductivities of ice and water are 0.40 and 0.12 cal/m·C°·s, respectively.)

Answer 1

answer) we have the formula for heat conduction per unit time

Q//t=A/d............1)

let for ice the thickness =d

now using eqn 1 and comparing both their heat conduction we have ( water and ice)

At/d=Ab/1.7-d

A cancels out

1.7-d/d=bottom*/top

1.7-d/d=4*0.12/9.4*0.4

1.7-d=0.1277 d

1.7=d+0.1277 d

1.1277d=1.7

d=1.5 m

so the answer is 1.5 m or 1.51 m