Final answer:
The final equilibrium temperature in a calorimetry problem where a hot metal is placed in cooler water is t1 > t3 > t2, where t3 is the equilibrium temperature between the initial temperatures t1 (metal) and t2 (water). The correct answer to the question is D) t1 > t3 > t2.
Step-by-step explanation:
This is because when a heated piece of metal at a temperature t1 is placed into a calorimeter containing water and a stirrer at a cooler temperature t2, heat will flow from the metal to the water until thermal equilibrium is reached. The final equilibrium temperature t3 will be somewhere between t1 and t2, where t1 is higher than t3, and t3 is higher than t2. This is due to the fact that the piece of metal will lose heat to the water until both reach the same temperature.
In the process of calorimetry, two bodies at different temperatures are brought into contact and exchange heat until they reach a common temperature. Water typically has a higher specific heat, meaning it requires more heat to increase its temperature as compared to many other substances, such as metals. Therefore, in a mixed system, the final equilibrium temperature tends to be closer to the original temperature of the water than to that of the metal.
Hence, D is the correct option.