The results of Example 18-10 about the flow of heat from a higher to a lower temperature, or the mixing of substances at different temperatures, are characteristic of all natural [that is, irreversible] processes. When we include the entropy changes of all the systems taking part in the process, the increases in entropy are always greater than the decreases. In the special case of reversible process, the increases and decreases are equal. Hence we can state the general principle: When all systems taking part in a process are included, the entropy either remains constant or increases. In other words, no process is possible in which the total entropy decreases, when all systems taking part in the process are included. This is an alternative statement of the second law of thermodynamics in terms of entropy. Thus it is equivalent to the “engine” and “refrigerator” statements discussed earlier.
The increase of entropy in every natural, irreversible process measures the increase of disorder or randomness in the universe associated with that process. Consider again the example of mixing hot and cold water. We might have used the hot and cold water as the high- and low-temperature reservoirs of a heat engine. While removing heat from the hot water and giving heat to the cold water, we could have obtained some mechanical work. But once the hot and cold water have been mixed and have come to a uniform temperature, this opportunity to convert heat to mechanical work is lost irretrievably. The lukewarm water will never unmix itself and separate into hotter and colder portions. No decrease in energy occurs when the hot and cold water are mixed. What has been lost is not an energy, but opportunity, the opportunity to convert part of the heat from the hot water into mechanical work. Hence when entropy increases, energy becomes less available, and the universe becomes more random or ”run down”.
The statement of the second law is in terms of entropy:
“The entropy of a closed system never decreases or equivalently: The change in entropy of the universe is always greater than or equal to zero”: