Final answer:
The equilibrium temperature of a metal and water system is not at the midpoint because the specific heat capacities of metal and water differ, with water typically having a higher specific heat capacity and therefore absorbing more heat without its temperature changing as much.
Step-by-step explanation:
The equilibrium temperature of a combined system of metal and water is not at the midpoint between the initial temperatures because the amount of heat lost by the hot object is equal to the heat gained by the cooler object. This is governed by the principle of conservation of energy. However, metal and water have different specific heat capacities, which means they require different amounts of energy to change temperature by the same amount. Typically, metals have a lower specific heat capacity than water, meaning they change temperature more easily with the absorption or release of heat.
When a 50 gram piece of metal at 100 degrees Celsius is placed in 50 grams of water at 20 degrees Celsius, the water will likely change temperature less than the metal because water's high specific heat capacity allows it to absorb more heat without a significant change in temperature. Therefore, the final equilibrium temperature will be closer to the initial temperature of the water than the metal.