The time it takes for a system to reach equilibrium when applying heat or a change in volume depends on various factors and can vary significantly depending on the specific system and conditions involved. It is not strictly a linear proportion or purely probabilistic.
When considering the number of particles in a volume, decreasing the number of particles can indeed affect the time it takes for equilibrium to be reached, but the relationship is not necessarily linear. In systems with a small number of particles, the behavior can become more probabilistic, as the behavior of individual particles starts to play a more significant role.
In general, when the number of particles is decreased, there are fewer collisions and interactions occurring within the system, which can lead to a slower attainment of equilibrium. However, the specific details of the system, such as the nature of the particles, their interactions, the presence of external forces, and other factors, can all influence the time required for equilibrium.
Additionally, the concept of equilibrium itself can vary depending on the context. In some cases, it may refer to thermal equilibrium, where the system has reached a uniform temperature. In other cases, it may refer to chemical equilibrium, where the concentrations of reactants and products have stabilized. Each of these equilibria involves different dynamics and may be influenced by different factors.
Therefore, while decreasing the number of particles can generally affect the time it takes to reach equilibrium, the relationship is complex and depends on multiple factors. It is essential to consider the specific characteristics of the system in question to make more accurate predictions about the time required for equilibrium to be reached.