Question

A process occurs in which the entropy of a system increases by 125 J/K. During the process, the energy that comes unavailable for doing work is zero. (a) Is this process reversible or irreversible? Give your reasoning. (b) Determine the change in the entropy of the surroundings.

Answer 1

The described process with an entropy increase of 125 J/K and no energy becoming unavailable for work is reversible. The change in the entropy of the surroundings for a reversible process is equal in magnitude but opposite in sign to that of the system, resulting in -125 J/K.

Step-by-step explanation:

A student asked whether a process with an entropy increase of 125 J/K, with no energy becoming unavailable for work, is reversible or irreversible, and the change in the entropy of the surroundings.

Answer to (a):

The process described is reversible. If no energy becomes unavailable for work, it means that the energy transfer is completely efficient, which is a characteristic of a reversible process. According to the second law of thermodynamics, in any real (irreversible) process, entropy increases and some energy becomes unavailable to do work. If in this case, the energy unavailable for work is zero, this theoretical scenario would be considered reversible.

Answer to (b):

Since the process is reversible and the system has gained entropy, the surroundings must have lost an equal amount of entropy to maintain the total entropy of the isolated system (system + surroundings). Therefore, the change in the entropy of the surroundings is -125 J/K.

Answer 2

The increase of system entropy by 125 J/K typically indicates an irreversible process. Without more context or data, assuming this scenario takes place in an isolated system, the change in entropy of the surroundings would be zero.

Step-by-step explanation:

To answer part (a) of the question, according to the second law of thermodynamics, a process in which the entropy of a system increases is generally an irreversible process. This is based on the principle that total entropy either remains constant or increases in any process; it never decreases. In this case, where the system's entropy increases by 125 J/K and no energy becomes unavailable for work, the question already implies a peculiar scenario since typically an increase in entropy would result in some energy becoming unavailable for work. This could suggest an idealized, theoretical scenario, perhaps assuming no losses or unintended heat transfer, which is more characteristic of a reversible process. However, without additional context, the standard interpretation would be that this is an irreversible process.

For part (b), determining the change in the entropy of the surroundings without additional information is not straightforward. Assuming this process takes place in an isolated system (where no heat is exchanged with the surroundings), the change in entropy of the surroundings would be zero since there has been no mention of heat transfer. However, in a real-world scenario, additional data related to the surroundings and the process itself would be required to calculate the actual change in entropy of the surroundings.