Your question is very similar to another one that we recently
received, and the answer is about the same. The equations used to
calculate this sort of thing are definitely out there. But they are
fairly complex and may require more information than you have.
Equations like this will tell you the rate at which heat (measured in
calories) will be transferred.
Now, two things have to happen before the ice is melted:
1) You need to warm the ice up from -20 degree C to 0 degrees C.
The amount of heat required to do this will depend on the mass of the
ice (which you can figure out) and on the specific "heat capacity" of
ice, which is 2000 Joules/kg/degree C.
2) Once you have ice at 0 degrees C you want to melt it so you end
up with water at 0 degrees C. To do this you need to supply A LOT more
heat. For water, this "latent heat of fusion" is 335000 Joules/kg.
This makes it very simple to figure out exactly how much heat is
required to melt the ice. The tricky part is figuring out how long this
takes, since the time will depend on how good the surroundings of the
ice are at transferring heat to it. If you actually want to figure this
all out, you will have to account for the 3 different ways that heat
can be transferred: convection, conduction, and radiation. And, to make
things more complex, you'll need to use some calculus because some of
the variables (such as the surface area of the block) will change as
the block melts. For the equations themselves, I would suggest that you
take a look at a thermodynamics textbook, because they are more complex
than I can really begin to get into here.
-Tamara & Mats
(republished on 07/25/06)