MF17041: A hot penny is dropped into cold water inside a polystyrene foam cup. Assuming negligible heat loss to the cup and to the surroundings, which of the following statements would be true, if any?

| DSpenny | = | DSwater |
| DSpenny | > | DSwater |
| DSpenny | < | DSwater |
Both entropy changes are negative.
Both entropy changes are positive.

To answer this question, we need to understand the concept of entropy and how it relates to the given scenario.

First, let's define entropy. Entropy is a measure of the randomness or disorder in a system. It is a thermodynamic property and can be increased or decreased during a process.

In the given scenario, a hot penny is dropped into cold water inside a polystyrene foam cup. We are assuming negligible heat loss to the cup and surroundings, which means that the system can be considered closed.

When the hot penny is dropped into the cold water, heat will flow from the penny to the water until they reach thermal equilibrium. As the heat is transferred, there will be changes in the entropy of both the penny and the water.

Now let's analyze the statements given:

1. | DSpenny | = | DSwater |
This statement implies that the change in entropy for the penny is equal to the change in entropy for the water. If the system is considered isolated, this statement is not likely to be true. The reason is that the temperature change for the penny will likely be larger than the temperature change for the water, leading to different entropy changes.

2. | DSpenny | > | DSwater |
This statement implies that the change in entropy for the penny is greater than the change in entropy for the water. This is likely to be true since the temperature change for the penny is expected to be larger compared to the water.

3. | DSpenny | < | DSwater |
This statement implies that the change in entropy for the penny is smaller than the change in entropy for the water. This is unlikely to be true since the heat flow from the penny to the water will lead to an increase in disorder, thus increasing the entropy for both.

4. Both entropy changes are negative.
This statement is not likely to be true since heat is being transferred from the hot penny to the cold water, which will increase the disorder and therefore the entropy of the system.

5. Both entropy changes are positive.
This statement is likely to be true since the heat transfer from the hot penny to the cold water will increase the disorder and therefore the entropy of the system.

In conclusion, statement 2: | DSpenny | > | DSwater | and statement 5: Both entropy changes are positive are the most likely to be true in this scenario.