# Time to freeze an X ammount of water

Hello to everyone, first post on these forums.

I have the following problem/question, im somewhat sure how to approach it but i'd like to double check if im going at it the correct way.

The problem is figuring the time it would take to freeze a body of water. Lets say we have a copper mold in the shape of a cube with a volume of 1 cubic decimeter, so 1 liter of water, the top of the square is removed so ice can be extracted. We have a compressor that produces 100W of power and operates on ethylene glycol - antifreeze.
How would you go about solving this problem, which physical properties do i require?
What im loosely thinking :
a) figure out the ammount of energy you need to remove from the body of water for it to become ice - for the sake of the problem lets say that the initial temperature is 20°C and that the final ice temperature is -5°C.
b) figure out the surface over which heat exchange will occur - that includes the surface area of the cube and surface area of the compressor pipes
c) input all the information into the P=W/t formula to get the time.
Thoughts/suggestions?

#### Woody

You seem to be asking the correct questions for this problem,
however there is a lot of "devil in the detail"

Attacking part a)
you need to consider the specific heat capacity of water
then the latent heat of freezing of the water to ice
and finally the specific heat capacity of ice.

You do, however, seem to be missing some steps before part b)
How is your compressor operating on the antifreeze to cool it down?

• topsquark

You seem to be asking the correct questions for this problem,
however there is a lot of "devil in the detail"

Attacking part a)
you need to consider the specific heat capacity of water
then the latent heat of freezing of the water to ice
and finally the specific heat capacity of ice.

You do, however, seem to be missing some steps before part b)
How is your compressor operating on the antifreeze to cool it down?
SOrry for the late response. I'll try to clarify the problem in more details. IM attaching a sketch of the problem as it was presented to me.
So, you have a copper mold cooled by a compressor with copper tubing, 2 pools of water which total 1 liter. The problem seems a bit more complicated
than i initially thought.
So we start with determining the ammount of energy we need to remove from the bodies of water to turn them into ice at -5°C, we use the Q=mc(T1-T2) formula with T1 being 20°C and T2 being 0°C, then we add the crystalization energy required and finally then the Qice=mc(T3-T4) with t3 being 0°C and T4 being -5°C. The addition of the 3 gives us the Qtotal we're looking for.

The next step i assume is finding the heat flow and this is where i run into issues. I assume there are several flows we need to find out, one being from coolant to the copper tubes and the second one being from the tubes to the mold and final from the copper mold to the body of water. For the first one we use the inner radius of the tube to find the inner surface area, for the second one we find the size of contact surface A and for the third we use contact surface B.
We use the q=Q/t= α (T1-T2) / L with L being the width of the surface. I think you need to do the 3 equations as the surface areas differ and with them the heat flow. Im unsure tho what to do or how to combine the 3 q values into 1 or if that is even needed. also im unsure how to determine the temperature of the contact between the copper mold and copper tubing to get the 2nd heat flow.

After this im lost. Lets say you have a compressor with 100W of power and 0,1kg/s mass flow with a random coolant. I dont know which equations or what system to use that includes the specific heat of the coolant and the mass flow of the compressor.[/QUOTE]