In everyday language, we often use “spontaneous” to mean “fast” or “sudden”, but in thermodynamics, the word has a precise meaning: a spontaneous process is one that, once started, can occur as written without continuous input of energy from the surroundings. (Be careful not to confuse this term with how we describe the equilibrium position of a reaction, as “reactant-favored” or “product-favored”.) Water evaporating from a glass, iron rusting in air, perfume diffusing through a room—these all happen spontaneously, even if some of them happen slowly.

What ties these changes together is the Second Law of Thermodynamics, which states that in any spontaneous process, the total entropy of the universe increases:

ΔS_universe = ΔS_system + ΔS_surroundings > 0

This does not mean the entropy of the system always increases. Water freezing into ice is a decrease in entropy for the water itself, but because the process releases heat to the surroundings, and that heat increases the entropy of the surroundings, the overall change can still be positive. In fact, at constant temperature, we can quantify the surroundings’ entropy change from the heat flow:

[latex]\Delta S_{surroundings} = \dfrac{-q_{system}}{T}[/latex]

This equation reminds us that heat lost by the system becomes entropy gained by the environment. When the total change, sum of change for system and surroundings, is positive, the process is thermodynamically allowed.

So, entropy does not dictate that things fall apart or get messier. It simply reflects the tendency of systems to evolve toward configurations where energy is more widely spread, because there are more ways to exist in those states. In the language of probability, high-entropy states are more likely, not because they’re disordered, but because there are more microstates that correspond to them.

Entropy and Thermodynamic Stability

Entropy is not just about predicting change—it also tells us something about a system’s stability. Systems that have low energy (enthalpically favorable) and high entropy (widely dispersed energy) are especially stable. They have settled into a configuration where both driving forces (minimizing potential energy and maximizing dispersal) are satisfied.

Vaporization of water offers a clear example of how entropy affects stability. When water molecules escape from the liquid phase into the gas phase, they gain a tremendous amount of freedom to move, rotate, and spread out. That represents a big increase in entropy. But to make that happen, the system has to absorb energy to break the intermolecular attractions holding the liquid together. At low temperatures, the benefit of gaining more ways to disperse energy (via increased entropy) isn’t enough to justify that energy cost. So, vaporization does not occur spontaneously. But as the temperature increases, so does the system’s ability to make use of that energy, to spread it across many more accessible motions in the gas phase. Eventually, the tendency toward greater energy dispersal becomes strong enough to “pay for” the energy input required. At that point, vaporization becomes spontaneous.

This interplay between enthalpy and entropy governs how systems respond to temperature and other conditions. It helps explain why some processes only occur above or below certain thresholds, and why others are always favorable no matter the context.

Looking Ahead: Free Energy

Entropy of the universe gives us deep insight into how a process evolves, but entropy of the system does not tell the whole story. To determine whether a process will occur under specific conditions, we need a way to combine enthalpy and entropy of the system. That is where the concept of Gibbs free energy comes in. In the next day, we will learn how chemists use Gibbs energy to model spontaneity, equilibrium, and the direction of chemical change.