Heat Capacity - Heat Capacity And The Law Of Conservation Of Energy

Calculations using heat capacity can be used to determine the temperature change that will occur if two objects at different temperatures are placed in contact with each other. For example, if a 50 g piece of aluminum metal (Cp = 0.9 J/g C) at a temperature of 100°C is put in 50 g of water at 20°C, it is possible to calculate the final temperature of the aluminum and water. The aluminum will cool down and the water will warm up until the two objects have reached the same temperature. All of the heat lost by the aluminum as it cools will be gained by the water. This is a result of law of conservation of energy, which states that energy can neither be created or destroyed. The heat lost by the metal will be
and the heat gained by the water will be

These two equations are equivalent since heat lost equals heat gained; the final temperature of the mixture will be 27. 8°C. This final temperature is much closer to the initial temperature of the water because water has a high heat capacity and aluminum a low one.