A chef needs to increase the temperature of a food dish. She thinks she can do this by stacking another dish on top of it. She has three dishes to choose from for the top dish: A, B, and C.

Question

Which one of these dishes would make the food dish the warmest when placed on top of it? As part of your answer, explain how the energy and temperature of both the top dish and the food dish will change when the food dish warms up, and why.

Answer 1

To determine which dish—A, B, or C—would make the food dish the warmest when stacked on top, we need to consider the thermal properties of the dishes, specifically their heat capacity, thermal conductivity, and initial temperature.

1. Heat Capacity and Thermal Conductivity: Each dish has a unique ability to absorb heat and transfer it to the food dish underneath. Dishes with higher heat capacity will be able to retain and transfer more heat energy. Thermal conductivity affects how quickly heat passes from one dish to another.

2. Thermal Energy Transfer: When the top dish is placed on the warm food dish, heat transfer occurs from the warmer substance (the food dish) to the cooler one (the top dish). The rate and amount of that heat transfer will depend significantly on the properties mentioned above.

3. Initial Temperatures: If dish A, B, or C is initially at a higher temperature than the food dish, it will give off heat to the food dish, increasing its temperature until thermal equilibrium is approached. Conversely, if a dish is colder, it will absorb some heat, warming up but possibly lowering the temperature of the food dish.

To maximize the food dish's temperature, the chef should choose the dish that either has:

• Higher initial temperature (if it’s warm, it will warm up the food dish)
• Higher heat capacity (it can absorb and then transfer more heat)
• Good thermal conductivity (it can quickly transfer heat)

In a generalized case without specific temperature values or the specific properties of dishes A, B, and C, we can make the choice based on assumptions:

• If dish A is very conductive and warmer than the food dish: It would raise the temperature effectively.
• If dish B has a high heat capacity but is at room temperature: It will absorb some heat initially.
• If dish C is cold but highly conductive: It will absorb heat quickly, likely lowering the dish's temperature initially.

Conclusion:

The best dish to stack on top would be the one that is both at a higher temperature and ideally has good thermal properties (high heat capacity and thermal conductivity). If we don't know the initial temperatures of the dishes, the chef should opt for the dish that has the highest heat capacity.

Thus, if you're given concrete values for the temperature and properties of dishes A, B, and C, you'd be able to make a more precise recommendation on which dish to use.