heat lost by metal + heat gained by water = 0
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Substitute and solve for the one unknown.
An 8.6 g sample of a metal is heated to 110.0oC and then placed in a coffee cup calorimeter containing 125 g of water at a temperature of 23.00oC. After the metal cools, the final temperature of the metal and water is 26.83oC. Assuming that no heat is lost to the surroundings or has been absorbed by the calorimeter, calculate the specific heat of the metal. The specific heat of water is 4.18 kJ/L.
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