Entropy and the Second Law of Thermodynamics

Consider an isolated irreversible system where a hot object interacts with a cold one; both eventually reach the same equilibrium temperature.

Here, energy transfer from the hotter to the colder object increases the overall system’s disorder.

This degree of disorder, or randomness, is measured by entropy, 'S.' These entropy calculations are defined using reversible heat transfers because reversible paths provide a well-defined method to find entropy changes.

An infinitesimal change in entropy equals the infinitesimal energy input divided by the temperature at that moment.

For a system taken reversibly from state A to B at varying temperatures, the entropy change is found by integrating the incremental heat supplied at each stage over the corresponding temperature.

However, in an isothermal reversible process, where temperature is constant, the entropy change equals the heat exchanged divided by the absolute temperature.

Importantly, the total entropy of the universe always increases for any real irreversible process, meaning that all natural and spontaneous processes tend to maximize overall entropy. However, it remains constant for reversible processes.