During the establishment of thermal equilibrium, the total entropy (S) of the system increases until it reaches its maximum value, at which point the system enters a stable thermal equilibrium state. This process is spontaneous and irreversible, and its core driving force is the principle of entropy increase-a direct manifestation of the second law of thermodynamics.
You can understand it this way: When two objects at different temperatures come into contact, heat flows from the higher-temperature object to the lower-temperature object. This process makes the energy distribution more uniform and the system more disordered, thus increasing the total entropy. Once the temperatures are equal, there is no more net heat flow, the macroscopic state of the system is stable, and the entropy reaches its maximum value under this condition, that is, the entropy no longer changes (ΔS = 0).
Key points of entropy change during thermal equilibrium:
In the initial stage of the process: Entropy increases rapidly. The greater the temperature difference and the more intense the heat flow, the more significant the entropy increase. For example, throwing a piece of red-hot metal into cold water instantly produces a large amount of steam and heat mixing, which is a violent entropy increase process.
Approaching Equilibrium: The Rate of Entropy Increase Slows Down
As the temperature difference decreases, the heat transfer rate declines, and the increase in entropy levels off, eventually approaching zero.
Reaching Equilibrium: Entropy is at its Maximum, and the System is Stable
At this point, the system is in a macroscopically static state, but microscopic particles are still in motion-this is a dynamic equilibrium. Although heat no longer flows, entropy has reached its limit and can no longer increase spontaneously.
Entropy Never Decreases in Isolated Systems
If the entire system has no energy exchange with the outside world (such as in a sealed insulated container), the total entropy will only increase and never decrease. This is why "hot coffee automatically heating up" is impossible-that would mean a decrease in entropy, violating the laws of nature.
An intuitive analogy: Ink falling into still water
Imagine a drop of ink falling into still water:
Initial moment: The ink is concentrated, the system is ordered → Low entropy
Diffusion process: The ink spontaneously disperses, becoming increasingly uniform → Increased entropy
Final state: Completely mixed, uniform color → Maximum entropy, reaching equilibrium
This corresponds perfectly to the thermal equilibrium process: temperature difference is like concentration difference, heat transfer is like molecular diffusion, both ultimately leading to maximum disorder.
