advanced physics?

Question

44 grams of water at 16 Degrees C is mixed with 450 grams if ice at -16C. what mass of water freezes? what is the change in entropy of the system? ( The heat capacity of water is 4190 J/Kg , that of ice is 2090 J/Kg, and the heat of fusion of water is 3.34 x 10^5 J/Kg.)

Answer 1

The key formula you need here is E = mCT, where E is energy (or heat), m is mass, C is specific heat capacity, and T is a change in temperature. If F is the heat of fusion, the energy required for a phase change is E = mF.

Call the heat capacity of water Cw and that of ice Ci; you've been given both values. Also, the mass of water is mw and that of ice is mi; again, both are given. The ice can increase from -16C up to 0C and still be ice, so it take in an amount of heat equal to mi*Ci*16. Now consider that, to change from water at 16C to ice at 0C, all of the water must decrease to 0C and then some of it will freeze. The heat lost by the water just by decreasing to 0C would be mw*Cw*16. Then, an unknown amount of the water, m, will freeze, giving up m*F amount of heat. So if we say mi*Ci*16 = mw*Cw*16 + m*F, and m is our only unknown, then m is the mass of water that will freeze.

For entropy, you'll need to look it up in a table that gives specific entropy for water and ice at various temperatures.