Final answer:
The question relates to the thermal equilibration of a copper sphere in water, described by thermodynamics. The process involves calculating the final temperature where the system reaches equilibrium using the conservation of energy principle and specific heat capacities.
Step-by-step explanation:
The question involves the concept of thermal equilibration, where a copper sphere is quenched in water. When copper or any material is placed in water of a different temperature, heat transfer occurs until both the material and the water reach thermal equilibrium. This process can be analyzed using the principles of thermodynamics and requires an understanding of specific heat capacities, mass of the involved substances, and the initial and final temperatures of the materials.
Using the formula for heat transfer Q = mcΔT (where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature), we can calculate the final temperature after the system has reached equilibrium. The heat lost by copper will equal the heat gained by water because no heat is transferred to the surroundings. Assuming that the heat transfer between the copper and water is the only process occurring, the final temperature can be found without considering heat loss to the environment or other factors.
For the given example of a 248-g piece of copper initially at 314 °C that is quenched in 390 mL of water at 22.6 °C, the conservation of energy principle implies that the heat lost by the copper must be equal to the heat gained by the water. The calculation of the final temperature will involve setting the heat lost by copper equal to the heat gained by water, and using the specific heat capacities for both substances to solve for the final equilibrium temperature.