Equilibrium and Entropy:

When a system reaches a state of equilibrium, it means that there are no further changes occurring within the system. The system has reached a stable state where all the relevant properties are constant. One of the important properties that occur in equilibrium is entropy.

Entropy:

Entropy is a thermodynamic property that measures the degree of disorder or randomness in a system. It is denoted by the symbol S and is a measure of the system's microscopic configurations. The higher the entropy value, the more disordered the system is.

Maximum Entropy at Equilibrium:

When a system reaches equilibrium, it means that the system has reached a state of maximum entropy. This is because in equilibrium, the system has achieved the highest possible number of microscopic configurations that are consistent with the macroscopic properties of the system.

Explanation:

- In a system that is not at equilibrium, there are still ongoing changes occurring within the system. These changes lead to a decrease in entropy as the system moves towards a more ordered state.
- When the system reaches equilibrium, all the ongoing changes stop, and the system becomes stable. At this point, the entropy of the system is maximized.
- The reason for this is that the system has explored all possible states and configurations, and the entropy is at its highest value.
- In other words, at equilibrium, the system has reached its most disordered or random state.
- This can be understood by considering a simple example of a gas in a container. Initially, the gas molecules are confined to one side of the container, leading to a low entropy state. As the gas molecules spread out and occupy the entire container, the entropy increases. When the gas molecules are uniformly distributed throughout the container, the system is in equilibrium, and the entropy is maximized.
- Therefore, at equilibrium, entropy assumes its maximum value.

Conclusion:

In summary, when a system reaches the state of equilibrium, the property that assumes its maximum value is entropy. This is because equilibrium represents a state of maximum disorder or randomness, where the system has explored all possible states and configurations. Entropy is a measure of this disorder and is at its highest value at equilibrium.