Freezing Water with a Reversed Steam Engine

[physicsss]

The steam engine which operates between 500°C and 200°C is run in reverse. How long would it take to freeze a tray of a dozen 37 g compartments of liquid water at room temperature (20°C) into a dozen ice cubes at the freezing point, assuming that it takes 300 W of input electric power to run it? Assume ideal (Carnot) behavior.

The Q that is required to freeze the cube is (37/1000)kg*(4186J/K)(20K)+(37/1000)kg(3.33 x 10^5)

The coefficient of performance of ice is equal to TL/(TH - TL)=QL/(QH-QL), so pluging it the stuff, I get (200+273)/((500+273)-(200+273))= QL/ (300-QL), so I solved for QL and divide the Q needed to melt ice by QL. But my answer is wrong. Why? The 300W is QH, right?

 

[Astronuc]

The Q that is required to freeze the cube is (37/1000)kg*(4186J/K)(20K)+(37/1000)kg(3.33 x 10^5)

First of all, it seems you forgot to multiply by 12, since the problem considers a dozen 37 gram compartments.

Then to freeze one has to reduce the temperature by 20°C and then remove the heat of fusion. It appears you have considered this.

 

[physicsss]

assuming that it takes 300 W of input electric power to run it? Assume ideal (Carnot) behavior.

Do you think this is W(work) or QH?

 

[physicsss]

And thank you for pointing that out. :)