The highest temperature that enables water to freeze

[GasperSavs]

Hi!
I have a little problem with my "sort of" homework. The question is: Determine what is the highest temperature that still allows a puddle of water to freeze if the heat transfer coefficient is given. Count in convective and radiative losses.

I assume that the highest temperature is slightly lower than 273,15K, because there needs to be a difference between the melting point and the surrounding air temperature, so that the heat transfer from the puddle to the surrounding air (removal of latent heat of fusion) is possible, otherwise the water would just stay at 273,15K in liquid form.
The problem is, that I don't have any dimensional properties of the puddle. To determine the amount of heat needed for a phase change i would need to know the mass of the water. And to determine how much energy is lost via convection and radiation, I would need to know the surface area of the puddle.
So my conclusion is that the answer to this question is purely theoretical and cannot be expressed with a number...so my actual question is: Am i wrong?
Thanks for the answers (and sorry for any grammar faults, English is not my first language)

 

[Mapes]

Hi GasperSavs, welcome to PF. If you're missing a value, just use a variable. You may find that it cancels out in the end.

Note that the ambient temperature could easily be above 273 K if you assume that the puddle is outside. In that case the puddle would be radiating heat towards outer space, which is quite cold. Convection would actually add energy to the puddle, but it might not be enough to offset the radiative losses, and as a result the puddle would still freeze. Know what I mean?

 

[GasperSavs]

Thank you, glad to be a part of PF:)

I was just wondering, wouldn't convection actually remove energy from the puddle, since we are trying to lower the temperature of it to freeze, and for convection to happen, wouldn't there be a heat transfer needed from the puddle to the surrounding fluid?
And you were right, some of the variables did cancel out...the puddle's volume and area cancel out, so in the end the only missing data is the average depth of the puddle (or the integral of the sinked surface...sounds fancier:D). I hope the professors assistant will be satisfied with the outcome (not a common on our faculty). But I consider this case closed, thank you for your answer.

 

[Mapes]

I was just wondering, wouldn't convection actually remove energy from the puddle

If the ambient temperature were lower than 273 K, yes. But the puddle could actually freeze even if the air temperature were higher than the melting temperature, as long as the puddle is radiating toward something very cold (like outer space). In this case, the puddle would gain energy via convection, but lose (even more) energy via radiation.

If the puddle is surrounded by walls that are the same temperature as the air, the answer is the trivial 273 K. But this isn't a very interesting result; it's much more instructive about heat transfer to work out the implications when the air and the "walls" can be different temperatures.

 

[GasperSavs]

Okay, I get it now:) And I agree, the result is much more interesting that way, so I'm going to apply these changes to the homework, hope it "works".