Question

After adding a hot piece of titanium to a cup containing 300.0 mL of 30.0 °C water, the final temperature of the solution is 41.2 °C and the final volume of the solution is 400.0 mL. The density of titanium is 4.50 g/cm3. If no energy is lost to the surroundings, what was the initial temperature of the piece of titanium? (The mass of the water is 300.0g)

Answer 1

heat lost by T + heat gained by water = 0

[mass Ti x specific heat Ti x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0

You have all of the numbers to substitute except for mass Ti. You solve for that from the density. The volume is 100 cc (400 final volume H2O-300 initial volume H2O = 100 mL = 100 cc Ti metal). Use density of mass/volume. You have volume and density, solve for mass.