A 32.0-g sample of water at 290. K is mixed with 51.0 g water at 310. K. Calculate the final temperature of the mixture assuming no heat loss to the surroundings.

heat loss of warm water + heat gained by cool water = 0

[mass warm water x specific heat x (Tfinal-Tinitial)] + [mass cool water x specific heat x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal.