Final answer:
In reversible processes, the system's entropy change is equal in magnitude but opposite in sign to that of the surroundings. The universe's entropy increases when Tsys > Tsurr and remains constant when Tsys ~ Tsurr.
Step-by-step explanation:
The question concerns the concept of entropy changes (dS_system and dS_surrounding) during a reversible process in the context of thermodynamics. In a reversible process, any entropy lost by the system is gained by the surroundings, and vice versa, due to heat transfer (represented by the arithmetic signs of drev). The magnitudes of entropy change are equal, but they have opposite signs, because the process can be perfectly reverted.
When the temperature of the system (Tsys) is greater than that of the surroundings (Tsurr), although the magnitudes of entropy change (|dS|) are the same for both, the value for the surroundings will be more significant due to the lower temperature. Thus, the entropy of the universe (dS_univ) increases, as heat naturally flows from a hotter to a cooler region, aligning with the second law of thermodynamics.
However, if the temperature of the system and surroundings are effectively the same, the magnitudes of their entropy changes will be essentially identical (dS_system ~ dS_surrounding), rendering the entropy of the universe unchanged, signaling that the system is at equilibrium.