A mass of 31.5 g of an unknown solid initially at 180.0 °C is added to an ideal constant-pressure calorimeter containing 100.0 g of water (Cs, water = 4.184 J/(g °C)) initially at 20.0 °C. After the mixture reaches thermal equilibrium, the final temperature is recorded to be 30.32 °C. What is the specific heat capacity of the unknown solid?
Express your answer to three significant figures.
The law of conservation of energy states that energy can neither be created nor destroyed. However, energy can be transferred from one object to another, and it can assume different forms. A good way to understand and track energy changes is to define the system under investigation. For example, the system may be the chemicals in a beaker, or it may be the iron reacting in a hand warmer. The surroundings are everything with which the system can exchange energy. If we define the chemicals in a beaker as the system, the surroundings may include the water in which the chemicals are dissolved (for aqueous solutions), the beaker itself, the lab bench on which the beaker sits, the air in the room, etc.
When two substances with different temperatures are combined, thermal energy flows as heat from the hotter substance to the cooler substance. If we assume that the two substances are thermally isolated from everything else, then the heat lost by one substance exactly equals the heat gained by the other, according to the law of energy conservation. If we define one substance as the system and the other as the surroundings, we can quantify the heat exchange as
qsys = − qsurr
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