Question

Consider an object falling into a black hole (with these characteristics), which then decreases the entropy of the whole universe minus the black hole. This lost entropy can then be found in an increase of entropy of the black hole, which must depent on mass alone.

Because we can throw every object into a black hole, this means that the entropy of the entire universe depends on mass alone, which I don't think is logical as entropy increases with a different order of the same mass.

What went wrong here? Either there exist no black hole with these characteristics, or there is some mistake in my reasoning.

Answer 1

The misunderstanding here involves the assumption that entropy is solely based on mass. Entropy is also a measure of disorder, and the black hole's entropy is related to the area of its event horizon, not just mass. The second law of thermodynamics, which notes that total entropy can never decrease in an isolated system, and concepts around the heat death of the universe, indicate that entropy has dimensions beyond mere mass aggregation.

Step-by-step explanation:

The student has made an error in reasoning by assuming that the entropy of the universe minus the black hole decreases when an object falls into a black hole. An important concept to remember is that entropy is a measure of disorder, and the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. The act of a black hole increasing its entropy due to accreting mass is in line with this law since the entropy of a black hole is related to the area of its event horizon, which increases with mass. However, entropy is not solely dependent on mass; it is also tied to the degree of disorder and the energy transfer within the system.

Furthermore, entropy can indeed increase in the entire universe as energy becomes less available for doing work. For instance, the heat death of the universe hypothesizes a state of maximum entropy where all energy is distributed evenly and no work can be performed. This state would not be reached simply by agglomerating mass into black holes, but through a process of universal thermal equilibration.

The idea of entropy depending solely on mass arises from a misunderstanding of black hole thermodynamics and the broader principles of entropy as it applies to the entire universe, which includes considerations beyond just mass and encompasses disorder and irreversible processes. The student should re-evaluate their understanding of entropy, especially considering that it does not simply equate to mass but involves a more complex interplay of variables and the overarching second law of thermodynamics.