How long would it take to freeze?

Question

If you had a body of water (a lake for example) that was 300 yards x 100 yards, and is about 60 yards deep; and the tempature is about -10 Farenhiet;how long would it take for the water to freeze?

Answer 1

While it does depend on the temperature of the water, the dependence is small since the heat of fusion (heat needed to melt or form ice) is large compared to the specific heat. This means that most of the time and heat removal will occur with the water at 32F. The process is governed by the convective coefficient of heat transfer. A reasonable approximation of this is 1 BTU/(ft^2 hr F). The temperature difference is 42 F (from 32 F to -10 F) so the heat transfer is about 42 BTU/(ft^2 hr). Water has a heat of fusion of 144 BTU/lb. A cubic foot of water weighs 62 lbs so it takes:

144 BTU/lb * 62 lbs/ft^3 / (42 BTU/(ft^2 hr)) = 213 hr/ft

So the freezing rate is about 9 days per foot of depth. At 60 yards (180 feet) it takes about 4.5 years to freeze solid.

Keep in mind, this is just an approximation but it is based on reasonable assumptions.

Answer 2

It depends on what the water temperature is to start. If its 50 F, it will take several weeks to start forming a thin layer on top but if it is at 33F, it may start to skin over with ice in a couple days. It might take many months at this temperature to freeze it all completely solid since the ice will start to act as an insulator once it starts forming on top. It probably would be years since the water is so deep and it's possible it never would since the earth below might keep it warm at the bottom.

Answer 3

this is a chemistry/ maybe physics ques.