Delta S universe = Delta S surr + Delta S sys

[Joyce Meng 2J]

I'm confused as to how the delta S of the universe can be greater than or less than zero. In question 4I.7 of the textbook, the entropy for the surroundings and the system are opposites of each other (ie. -73 J/K vs +73 J/K). Is this a special case where the entropy stays the same in the system? If so, what's an example of when entropy would not be the opposite sign for surroundings and the system?

[Nicholas Ryan 2K]

The overall delta S of the entire universe never decreases because energy never flow in the opposite direction. This one-way energy flow causes entropy to increase for the universe as a whole.

[Valeria Perez 3J]

To expand a bit on what the other commenter mentioned, the delta S of the universe cannot be negative because that would violate the second law of thermodynamics. Instead, the entropy of the universe can either be equal to or greater than 0. Oftentimes, the cases where the entropy change of the universe is equal to 0 are actually idealized, unrealistic processes that do not tend to happen in real life, but serve important theoretical purposes(like observing the thresholds of certain values). An increase in the entropy of the universe corresponds to the most common and natural phenomenon, seeing as it implies that the system and surroundings followed the natural spontaneous process to go from lower entropy states to higher entropy states over time, ultimately increasing the universe's entropy. I hope that made sense!