Question

What is the final temperature, in oC, after a 27.0 g piece of ice, at 0oC, is placed in a styrofoam cup with 120 g of water initially at 70.5oC.
Assume there is no transfer of heat to or from the surroundings.

The specific heat of water = 4.184 JK-1g-1
The heat of fusion of ice = 333 Jg-1

Answer 1

gain of heat on melting ice + gain of heat on raising T from 0C to Tfinal + heat lost by 120 g H2O at 70.5C to Tfinal = 0
Each [ ] gives the three processes above.
[mass ice x heat fusin] + [mass melted ice x specific heat H2O x (Tfinal-Tinitial)] + [mass warm water x specific heat H2O x (Tfinal-Tinitial) = 0
Substitute the numbers and solve for the only unknown of Tfinal.