1. The problem statement, all variables and given/known data While forming a 1.5kg aluminum statue, a metal smith heats the aluminum to 2700 degrees C, pours it into a mould, and then cools it to a room temperature of 23.0 degrees C. Calculate the thermal energy released by the aluminum during the process. 2. Relevant equations Q = mc(delta)T Q = mLf Lf aluminum = 6.6 * 10^5 J/kg heat capacity of aluminum : 9.2 * 10^2 3. The attempt at a solution So I already know that I have to find the thermal energy released when the aluminum cools from 2700 degrees to 23 degrees, and I have to add it to the thermal energy released during the change of state. Q = mcT = 1.5(9.2*10^2)(-2677) = - 3 694 260 J Q = mLf = 1.5(6.6 * 10^5) = 990 000 J Q = -3 694 260 + 990 000 = -2 704 260 J I know that the thermal energy released is 2 704 260 J, but I dont understand why you are supposed to add the thermal energy released in the change of state (990 000 J) to the thermal energy released due to the change in temperature. My physics teacher told me that when a substance is cooling from a liquid to a solid, the value of thermal energy should be negative (so basically you subtract), but in this case (the textbook) does not agree. Why is this?