Second Law of Thermodynamics
Entropy measures a system's disorder, and the Second Law says total entropy of a system and its surroundings always increases.
Entropy, represented by the symbol S, is a measure of the disorder or randomness in a system. Entropy also describes how energy is distributed within a system: in a high-entropy state, energy is spread out more evenly; in a low-entropy state, energy is distributed more unevenly. In short, entropy measures the spontaneous dispersal of energy at a given temperature — how widely spread out that energy becomes during a process.
The change in entropy is calculated as:
ΔS = q/T
Key Takeaways
Entropy (S) measures a system's disorder or randomness, and how evenly energy is distributed within it.
The Second Law of Thermodynamics: total entropy of a system and its surroundings always increases in any natural process — systems evolve toward maximum disorder.
Entropy is sometimes called "time's arrow" because its one-way increase distinguishes past from future.
The entropy of the universe is always increasing: ΔS_universe = ΔS_system + ΔS_surroundings > 0.
Spontaneity depends on Gibbs free energy, ΔG = ΔH − TΔS; a process is spontaneous when ΔG < 0. A positive ΔS favors spontaneity but doesn't guarantee it — enthalpy and temperature matter too.
The Second Law of Thermodynamics
The Second Law of Thermodynamics states that in any natural process, the total entropy of a system and its surroundings always increases. This is sometimes called the principle of increased randomness, or the principle of maximum entropy: systems tend to evolve toward a state of maximum disorder.
For example, if a gas is confined to one part of a box and the barrier is removed, the gas molecules spread out to fill the entire box — a more disordered, higher-entropy state.
Entropy as Time's Arrow
MCAT Callout — Entropy as Time's Arrow: Because entropy imposes a unidirectional limitation on how energy moves, it gives us a way to recognize before and after, or new and old. You'd instantly recognize whether a video recording of an explosion were playing forward or backward — the forward direction is the one where entropy increases. This one-way tendency toward disorder is one of the few laws of physics that distinguishes the future from the past.
Entropy and the Universe
A system can be defined as broadly as the entire universe. In that sense, the Second Law claims that the entropy of the universe is always increasing:
ΔS_universe = ΔS_system + ΔS_surroundings > 0
Energy in a closed system will spontaneously spread out, and entropy will increase, unless something hinders that spread.
Entropy and Spontaneity
Entropy also plays a role in determining whether a reaction or process is spontaneous. The Gibbs free energy change (ΔG) — which determines spontaneity — relates to entropy (ΔS) and enthalpy (ΔH) through:
ΔG = ΔH − TΔS
where T is the absolute temperature. A process is spontaneous when ΔG is negative.
MCAT Callout — A Positive ΔS Favors Spontaneity, But Doesn't Guarantee It: Increasing disorder (positive ΔS) drives a system toward spontaneity, since it disperses energy — but whether ΔG actually comes out negative also depends on temperature and enthalpy. A reaction with a favorable (positive) entropy change can still be non-spontaneous if its enthalpy change is unfavorable enough at a given temperature.
Common MCAT Mistakes
Confusing entropy with energy itself. Entropy doesn't measure how much energy a system has — it measures how that energy is distributed or dispersed. A system can have a huge amount of energy that's tightly ordered (low entropy) or spread out (high entropy).
Thinking the Second Law forbids any local decrease in entropy. The Second Law only requires that total entropy — system plus surroundings — increase. A system's own entropy can decrease (like water freezing into ice) as long as the surroundings' entropy increases by more, keeping ΔS_universe positive.
Assuming a positive ΔS automatically means a process is spontaneous. Spontaneity is governed by ΔG = ΔH − TΔS, not ΔS alone. A favorable (positive) entropy change can still fail to produce a negative ΔG if the enthalpy change is unfavorable enough.
Forgetting to include the surroundings when evaluating ΔS_universe. Evaluating whether a process obeys the Second Law requires adding ΔS_system and ΔS_surroundings together — looking at the system's entropy change alone isn't enough to judge overall spontaneity or compliance with the Second Law.
MCAT-Style Concept Check
Question: Liquid water freezes into ice at −5°C, a spontaneous process at that temperature. The entropy of the water itself decreases as it forms an ordered crystal lattice. Which statement correctly explains why this doesn't violate the Second Law of Thermodynamics?
A) The Second Law only applies to gases, not to liquids or solids.
B) ΔS_surroundings must be sufficiently positive that ΔS_universe (ΔS_system + ΔS_surroundings) is still greater than zero.
C) Entropy is conserved overall, so a decrease in the system is always exactly offset by an equal decrease in the surroundings.
D) Freezing is non-spontaneous, so the Second Law doesn't need to be satisfied.
Answer: B
Explanation: The Second Law requires that the total entropy of a system and its surroundings increase, not that every individual system's entropy increase. As water freezes, it releases heat to its colder surroundings, raising the surroundings' entropy by more than the water's entropy drops. The result is ΔS_universe = ΔS_system + ΔS_surroundings > 0, satisfying the Second Law even though the system itself became more ordered.
FAQ
What does entropy measure?
Entropy (S) measures the disorder or randomness of a system, and how evenly energy is distributed within it. Higher entropy means energy is more spread out; lower entropy means it's more concentrated or ordered.
What does the Second Law of Thermodynamics actually state?
It states that in any natural process, the total entropy of a system plus its surroundings always increases — systems tend to evolve toward a state of maximum disorder.
Why is entropy called "time's arrow"?
Because entropy's increase is one-directional, it's one of the few physical quantities that distinguishes the future from the past — you can tell whether a process (like an explosion) is running forward or backward based on whether entropy is increasing.
Does a positive ΔS mean a reaction will happen spontaneously?
Not by itself. Spontaneity depends on Gibbs free energy, ΔG = ΔH − TΔS, where a negative ΔG indicates spontaneity. A positive ΔS favors a negative ΔG, but an unfavorable enthalpy change (ΔH) can still make ΔG positive even when ΔS is positive.
Part of: