# Q & A: Melting Takes Time

Q:
Is there a formula of any kind in who you can calculate the below? A Container measuring 6 x6 12 feet has been filled with water. The container has then been refrigerated to 20 degrees Celsius until all the water has been frozen into solid ice. The container containing the solid ice cube, will now be placed in a room measuring a constant temperature of +20 degrees. Q. How many Days / Hours / Minutes / Second will it take for all the ice to melt into water? Looking forward to your reply. Kind Regards Claude
- Claude (age 19)
Sydney - Australia
A:
Claude -

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

(published on 10/22/2007)

## Follow-Up #1: water to ice and back again

Q:
In the item: Melting Takes time, Tamara & Mats state: 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. My questions are: 1) Is the formula just the opposite to turn water into ice? 2) How much energy is required to turn ice into water?
- Veronicah Hampton (age 42)
New Zealand
A:
Veronica-

1. Yes, the heat released as water turns to ice is just the same as that soaked up as ice turns to water. Also, the heat required to raise the temperature is the same as the heat released as the temperature is lowered (assuming that the temeperature change is made by simple heating and cooling).

2. The energy required is the same as what we called the heat required. "Heat" is defined, in most books which attempt to be precise, as the energy that flows between two bodies due to the temperature difference between them. So actually you could get the energy needed to melt the ice into it via other means than heat, and it would ultimately have the same effect. For example, a light shining on the ice at the right infrared wavelengths to be absorbed by the ice would gradually dump energy in. That would melt the ice just as well as "heat" flowing in from a slightly warmer object.

By the way, if you read over other answers in this site, you will find "heat" used with several meanings, including "total amount of internal thermal energy." That's definitely not standard scientific usage, but it is a common informal meaning.

Mike W

(published on 10/22/2007)