When a 60.0-g sample of metal at 100.0 °C is added to 45.0 g water at 22.60 °C , the final temperature of both the metal and the water is 32.81 °C . The specific heat of water is 4.184 J/g · °C . Calculate the specific heat of the metal.

Strategy

Because of the law of conservation of energy, the energy lost by the metal will be gained by the water. We will determine the amount of heat (q) gained by the water and assume that this is the amount of heat lost by the metal. Knowing that quantity, we can determine C_s for the metal, because we also know ΔT for the metal. Thus, this will be a two-step calculation.