# From Hot to Cool: A Change in Entropy

1. Dec 9, 2008

### kristibella

1. The problem statement, all variables and given/known data
In a well-insulated calorimeter, 1.0 kg of water at 20o C is mixed with 1.0 g of ice at 0o C.

What is the net change in entropy Delta Ssys of the system from the time of mixing until the moment the ice completely melts? The heat of fusion of ice is Lf=3.34x105 J/kg.
Note that since the amount of ice is relatively small, the temperature of the water remains nearly constant throughout the process. Note also that the ice starts out at the melting point, and you are asked about the change in entropy by the time it just melts. In other words, you can assume that the temperature of the "ice water" remains constant as well.

2. Relevant equations
Ssys = Sice+Swater
Delta Sice = Qice/T
Qwater = -Qice (amount of heat lost to the ice)
Delta Swater = -Qice/T

3. The attempt at a solution
Delta Sice = (0.001 kg * 3.34x105 J/kg)/(0+273) = 1.22
Delta Swater = -334/(20+273) = -1.14
Delta S sys = 996.59

I think that this could be the correct answer, however, I would just like verification that it is correct. I have gotten the answer 1200, which seems to be a popular answer amongst my classmates, and it was not correct.

Last edited: Dec 9, 2008
2. Dec 9, 2008

### turin

I don't know about your numbers, but your approach looks good. Oh, it looks like you made a mistake inputting the value for Q_water.

3. Dec 9, 2008

### kristibella

Thank you for point it out! I found the correct answer of 0.084 J/K.

Last edited: Dec 9, 2008