A 50g ice cube at 0 degrees celcius is added to a glass containing 400g of water at 45 degrees celcius. What is the final temperature of the system? You may assume that no heat is lost to the surroundings.

In a system, heat that is gained and lost should be conserved. We calculate as follows:

Heat from phase change + sensible heat from the change in tempeture of the ice = sensible heat from the change in temperature of water

mH (fusion) + mCpΔT = mCpΔT

.05 (335) +.050 (4.184) (T - 0) =.4 (4.184) (45 - T)

T = 34.8 °C