Isothermal Reversible Expansion

[Victoria_garcia_2L]

For an isothermal reversible expansion can any explain why q=-w and how knowing this might be helpful in understanding the change in entropy?

[TakieraDarrow_2J]

In an isothermal reversible expansion, the heat absorbed (q) by the system is equal in magnitude but opposite in sign to the work done (w) by the system on its surroundings. This relationship is expressed as q = -w. Understanding this relationship helps us comprehend the change in entropy of the system. Entropy measures the disorder of a system. In this type of expansion, the entropy change is directly related to the heat transfer at constant temperature. The relationship shows that the entropy change of the system is directly proportional to the heat transfer and inversely proportional to the temperature. Therefore, grasping the relationship q = -w in an isothermal reversible expansion helps us understand how heat transfer affects the entropy change of the system.

[Ashwin Babu 1I]

It's just the convention of the equation. In the context of an isothermal reversible expansion, the system does work on the surroundings so w>0. However, from the perspective of the system, heat must be absorbed to offset the work done, assuming internal energy stays the same. Thus, q<0. However, instead of worrying about the signs and negatives, just remember that from the perspective of the system, work is done and heat is absorbed. If you think about it in context, it should be easier to follow the sign of each variable.