Why do two ideal gases thoroughly mix when combined? What drives the mixing?

The Second Law of Thermodynamics is a fundamental principle that provides deep insight into the natural tendency of energy and matter within the universe. It essentially states that the entropy of an isolated system will either remain constant or increase over time. Entropy can be thought of as a measure of randomness or disorder within a system—the higher the entropy, the more disordered it is.

This law is crucial in understanding spontaneous processes. A spontaneous process is one that occurs without needing to be driven by an external force or energy source. The Second Law implies that any spontaneous change in an isolated system must lead to an equal or greater amount of disorder or entropy. Therefore, when considering the mixing of ideal gases, the law helps us determine why this mixing is a natural, spontaneous process.

It's also the reason why we observe certain phenomena, such as heat flowing from a hot object to a cooler one, rather than the reverse. The Second Law of Thermodynamics traps systems in a forward-moving time flow, always seeking a state of higher entropy or equilibrium, which is a more disorganized, lower energy state.

Spontaneous processes are natural occurrences that take place without external intervention. They are guided by the tendency to move toward a state of greater disorder or randomness, as dictated by the Second Law of Thermodynamics mentioned earlier.

In the context of gas mixing, the spontaneous nature of this process is evident. When two ideal gases are combined, they will spontaneously mix to fill the available space completely. This is because there are many more ways for molecules to be arranged in a mixed state than in a separated state, which translates to a higher entropy. For instance, if one were to open a bottle of perfume in a room, the fragrance would disperse throughout the space; the molecules spread out in search of equilibrium, without any need for mechanical assistance.

The concept of spontaneity also relates to the idea that these processes are irreversible. Once the gases are mixed, they will not spontaneously separate back into their original components. This relates to the increase in entropy: separating the gases would require a decrease in entropy, which violates the Second Law of Thermodynamics without introducing external energy to reverse the process.