Entropy and the second law of thermodynamics

The Second Law of Thermodynamics

Every natural process has a preferred direction — heat flows from hot to cold, gas expands to fill a room, and a bouncing ball eventually stops. The second law of thermodynamics captures this universal tendency: the total entropy of an isolated system can never decrease. It remains constant only when every process within the system is reversible.

A reversible process is an idealized process that can be undone with no net change to the system or its surroundings. Real processes are always irreversible to some degree because of friction, turbulence, or spontaneous heat flow. So in practice, the total entropy of an isolated system always increases over time.

This law does not forbid any particular energy transfer. It restricts the direction. Energy naturally disperses from concentrated regions to spread-out ones. A hot cup of coffee cools down in a room — it never spontaneously heats up by absorbing thermal energy from a cooler room. Both scenarios conserve energy, but only the first satisfies the second law.

MisconceptionStudents sometimes believe entropy means “disorder” in a casual sense. On the AP exam, describe entropy as the tendency of energy to spread or the unavailability of energy to do work — not as “messiness.”

Exam TipUse CED language — energy spreading and unavailability to do work.

BoundaryOnly qualitative treatment of the second law of thermodynamics is required. No quantitative entropy calculations (ΔS = Q/T) are expected.

This is outside the scope of the AP exam.

Entropy as Energy Spreading

Entropy can be understood qualitatively in two complementary ways. First, entropy describes the tendency of energy to spread out. Localized energy — such as thermal energy concentrated in a hot object — will spontaneously disperse into the surroundings until it is distributed as broadly as possible.

Second, entropy describes the unavailability of some of the system’s energy to do work. As energy spreads, it becomes harder to harness. A hot gas concentrated in one half of a container can push a piston and do work. Once that gas has expanded freely to fill the entire container, the same total energy exists, but none of it is available to push the piston further.

Entropy is a state function [a quantity whose value depends only on the current state of the system, not on the path taken to reach that state]. This means entropy depends on the system’s current configuration — its temperature, pressure, volume, and phase — not on how the system arrived there. Two identical gas samples at the same temperature and volume have the same entropy, regardless of their histories.

Maximum entropy occurs when a system reaches thermodynamic equilibrium. At equilibrium, energy is spread as uniformly as possible and no further spontaneous processes can occur. There are no temperature gradients, pressure differences, or concentration imbalances left to drive change.

Examiner InsightAP FRQs often describe a process and ask whether entropy increases, decreases, or stays the same. Always connect your answer to energy spreading or energy becoming less available to do work.

Exam TipJustify entropy changes using energy dispersal, not vague references to “disorder.”

Entropy Changes Through System–Surroundings Interactions

The change in a system’s entropy is determined by the system’s interactions with its surroundings. How entropy behaves depends critically on the type of system.

An isolated system exchanges neither energy nor matter with its surroundings. Such a system spontaneously moves toward thermodynamic equilibrium. Because no energy enters or leaves, the total entropy of an isolated system never decreases — it only increases until equilibrium is reached, at which point it remains constant.

A closed system exchanges energy (but not matter) with its surroundings. Because energy can be transferred into or out of a closed system, the entropy of the closed system itself can decrease.

For example, when a refrigerator removes thermal energy from the air inside, the entropy of the air decreases. However, this decrease is always accompanied by an equal or greater increase in the entropy of the surroundings. The total entropy of the isolated combination (system + surroundings) still never decreases.

This distinction is essential: the second law applies to isolated systems. A local decrease in entropy is allowed for a closed system, but only at the expense of an entropy increase somewhere else.

MisconceptionStudents often claim that entropy can never decrease under any circumstances. The entropy of a closed system can decrease because energy leaves the system. The second law forbids a decrease in total entropy of an isolated system only.

Exam TipSpecify whether you mean the system alone or the system plus surroundings.