From Hot to Cool: A Change in Entropy

[kristibella]

Homework Statement

In a well-insulated calorimeter, 1.0 kg of water at 20^o C is mixed with 1.0 g of ice at 0^o C.

What is the net change in entropy Delta S_sys of the system from the time of mixing until the moment the ice completely melts? The heat of fusion of ice is L_f=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.

Homework Equations

S_sys = S_ice+S_water
Delta S_ice = Q_ice/T
Q_water = -Q_ice (amount of heat lost to the ice)
Delta S_water = -Q_ice/T

The Attempt at a Solution

Delta S_ice = (0.001 kg * 3.34x10⁵ J/kg)/(0+273) = 1.22
Delta S_water = -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.

 

[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.

 

[kristibella]

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