Explanation:
In solving the problem of pouring boiling water into an aluminum pan, the following simplifying assumptions were made:
A. The thermal energy of the aluminum doesn't change: This simplifies calculations by assuming that the temperature of the aluminum pan remains constant throughout the process, neglecting any heat transfer to or from the pan.
B. The thermal energy of the water doesn't change: This simplifies calculations by assuming that the temperature of the water remains constant throughout the process, neglecting any heat transfer to or from the water.
C. The heat capacities for both water and aluminum hardly change with temperature in this temperature range: This assumption simplifies calculations by assuming that the specific heat capacities of both water and aluminum remain constant and do not vary significantly with temperature within the given temperature range.
D. Energy transfer between the system (water plus pan) and the surrounding was negligible during this time: This assumption simplifies calculations by assuming that there is no significant heat exchange between the system (water plus pan) and the surroundings, either because the system is well-insulated or because any heat transfer is negligible.
In this scenario, we can conclude that all of the given statements are simplifying assumptions that were made to solve the problem effectively. However, if you're looking for the choice that directly relates to the scenario described, it would be choice D. Energy transfer between the system (water plus pan) and the surroundings was negligible during this time.
The simplifying assumptions made in this scenario are:
A. The thermal energy of the aluminum doesn't change: This assumes that the aluminum pan does not absorb or lose any significant amount of heat during the process, and its temperature remains constant throughout.
B. The thermal energy of the water doesn't change: This assumes that the heat capacity of water remains constant during the process, meaning that no heat is lost to the surroundings or absorbed by the container.
D. Energy transfer between the system (water plus pan) and the surrounding was negligible during this time: This assumption suggests that the system (water plus pan) is well-insulated, and there is minimal heat exchange with the surrounding environment.
Option C is not directly related to the simplifying assumptions made in this specific scenario, as it pertains to the constancy of heat capacities for water and aluminum over a range of temperatures, which may not be relevant to the immediate situation described. Therefore, the correct simplifying assumptions are A, B, and D.
