1. The problem statement, all variables and given/known data A 100g (.1kg) cube o ice at 0dC (d=degrees) is placed in 1kg of water that was originally at 80dC. What is the nal temperature of the water after the ice has melted? Answer: 65.5dC 2. Relevant equations Lf = Q/m Q=(DelT)mC 3. The attempt at a solution At first I looked up the latent heat of fusion for ice which turned out to be 3.35*10^5J/kg. I just randomly decided to say Lf ice=3.35*10^5Jkg, Q/(m ice) = 3.35*10^5J/kg Q = 3.35*10^5Jkg * .1kg (ice) and so determined the amount of energy needed to phase change each kilogram of ice was 3.35*10^6J Then I just tried a bunch of random manipulations of other equations that didn't work and now my paper has so many eraser marks that it's hard to distinguish what I write from the background erase marks. I hypothesized that at the start of the scenario, the 1kg of water had a specific amount of internal thermal energy, but the only way I know to measure internal energy is using the second equation I listed, but I thought that if I could detirmine the amount of thermal energy the 80 degree water had to start with, I could say that the energy in ice was subtracted from that total amount of thermal energy and I could just simply solve or the change in temperature, but as I said, I don't know how to just automatically know at an instantnanous moment what the magnitude of the thermal energy of a substance is, just the amount of heat it gained from changing to a different temperature. Surely all 1kg 80 degee amounts of water have the same magnitude of kinetic energy, it doesn't matter what the starting temperature was. Right off the bat this problem seem contradictory. It makes physically sense that putting an ice cube in would lower the temperature of the water, but somehow I remember and also looked up to confirm that a phase change doesn't change the temperature of the system, just the internal energy. So to begin with I don't know how the temperature could be lowered if that statement is true, assuming the melting point of water is infinitesimally close to a number greater than 0 degrees Celcius, any added energy to the ice will cause it to melt which shouldn't change it's temperature, yet kinetic energy get's taken from the water in order t break apart the crystalline bonds of ice.