Specific heat, latent heat, and temp

[jaded18]

The system, originally at T_A = 21.0 Celsius, is placed in a freezer, where energy is removed from it in the form of heat at a constant rate. The figure shows how the temperature of the system takes t_1 = 10 min = 600 s to drop to 0 Celsius, after which the water freezes. Once the freezing is complete, the temperature of the resulting ice continues to drop, reaching temperature T_B after an hour.

http://session.masteringphysics.com/problemAsset/1013967/12/1013967B.jpg

If the cooling power remains constant, what will be the temperature of the system T_B after it has been in the freezer for exactly 1 hour? This temperature is off scale on the figure.

also: latent heat of fusion (ice to water phase change at 0 Celsius) = 333.7J/g
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I know that after the water cools to 0 Celsius and freezes, the time that remains before the one hour mark is 722 sec and that the constant cooling power is 36.6J/s which I got by determining how much energy that has to be transferred out of the system as heat Q to lower its temperature to 0 =(2.20*10^4) and dividing it by 600s.

So... that means that in addition to 2.20*10^4 J that was required to bring the T from 21 to 0, we have to consider the energy for phase change (Q=mL=250(333.7)) and also the energy that I calculated to be 26425.2 J in the very beginning with the cooling power and time.

I feel like I'm going around in circles. Help?

 

[Shooting Star]

I have just one confusion. You have to find the temp of the whole thing after two hours from the start at 21 C?

 

[jaded18]

no, I thought I said ONE hour...

 

[Shooting Star]

(You mentioned “system T_B after it has been in the freezer for exactly 1 hour?” Hence the confusion.)

You cannot get the absolute value of heat transfer rate because you haven’t specified the mass.

Take the mass to be m, sp heat of water to be s, sp heat of ice to be s2, time for water to cool to zero t1; time for water to freeze is t2 –t1, and time for ice to cool to T_B be t3. Initial temp of water is T_A=21 C, final temp of ice is (-T_B). L is the latent heat of fusion.

If the rate of heat taken away is constant, then,

ms(T_A)/t1 = mL/(t2-t1) = ms2*(T_B)/(t3-t2)

m cancels out. s2 is reqd. t2 can be found from the 1st two eqns.