1. The problem statement, all variables and given/known data A 1x106 kg piece of ice is placed into a lake. How much heat is taken from the lake to raise the temperature of the ice from 0 °C to 1x10-20 °C? How much volume does the lake increase by? Latent heat for water is 334x103 J/kg 2. Relevant equations Found in my textbook, cice = 2100 J/kg*K Q = m c ΔT Q = mLf ρwater = 1.0x103 kg/m3 3. The attempt at a solution First I found how much heat is required to raise the temperature of the ice from 0 °C to 1x10-20 °C. Q = mcΔT Q = (1x106 kg)(2100 J/kg*K)(1x10-20 °C - 0 °C) Q = 2.1x10-11 J Then I found how much ice would melt with that amount of heat. Q = mLf m = Q / Lf m = 2.1x10-11 J / 334x103 J/kg m = 6.287x10-17 kg Finally, I found the volume of the water, or ice that melted. ρ = m / V V = m / ρ V = 6.287x10-17 kg / 1.0x103 kg/m3 V = 6.287x10-20 m3 My understanding is the adding heat to ice doesn't increase its temperature and instead melts some of it into water that is at the same temperature. So I'm confused about the part asking how much heat is required to raise the temperature of the ice. I don't know if I took the right approach for this problem. Is it because the temperature change is so small?