Question

My understanding of the second law is that for an isolated system, the entropy change accompanying any process is non-negative and is zero if and only if the process is reversible. I don't see why this implies that just because the entropy change of a process is positive, it must occur (even kinetically unfavorable processes occur after a long enough time). In other words, why is irreversible and entropically favorable synonymous with spontaneous?

Furthermore, it is often stated that the second law implies that entropy must be at a maximum for an isolated system in equilibrium. However I don't see how the statement that the entropy of a system is non-decreasing implies that entropy must increase to a maximum. Can't entropy remain constant at a non-maximal value as well?

Answer 1

The second law of thermodynamics states that in any spontaneous process in a system, entropy increases or remains constant, and never decreases, while at equilibrium the entropy is at a maximum. However, spontaneous processes may be kinetically slow due to energy barriers. The third law establishes a reference point for zero entropy at 0 K in a perfect crystalline solid.

Step-by-step explanation:

The second law of thermodynamics states that the total entropy of a system either increases or remains constant in any spontaneous process; it never decreases. This fundamental concept implies that irreversible processes, which increase entropy, are considered spontaneous because they align with the natural progression towards a state of maximum entropy.

Conversely, a reversible process is an idealized scenario in which entropy remains constant and the system can return to its initial state. The notion that entropy must reach a maximum in an isolated system at equilibrium is because any deviation from this maximum would imply a possible spontaneous process and further entropy increase, contradicting the idea of equilibrium.

Therefore, while it's theoretically possible for a system to be at a non-maximal constant entropy, in practice, such a system would still tend towards an increase in entropy over time.

Additionally, the second law of thermodynamics is sometimes misconstrued with kinetic favorability, which relates to the rate of a process.

An entropically favorable (spontaneous) process may be kinetically slow if the energy barrier is high, which is why we sometimes observe that processes do not occur even when they are thermodynamically favorable. Spontaneity only describes the thermodynamic favorability based on entropy changes and does not guarantee that a process will occur rapidly.

The third law of thermodynamics helps to establish the concept of absolute zero entropy, where a perfect pure crystalline substance at 0 K has only one possible microstate and thus an entropy of zero. This anchoring point serves to provide a reference for calculating entropy changes in various processes.