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Entropy Explained
Thermodynamics
Entropy is a measure of how spread out energy is and how many microscopic arrangements a system can have. The second law says the total entropy of an isolated system never decreases, which gives time its direction.
What entropy is
Entropy, symbol S, measures the number of microscopic ways the particles in a system can be arranged while still looking the same on a large scale. A gas spread through a room has many more arrangements than the same gas squeezed into a corner, so it has higher entropy. Entropy also tracks how spread out energy is: energy concentrated in one hot spot can do useful work, but once it has spread evenly as warmth, it cannot. Entropy is measured in joules per kelvin. It is a state function, so its change depends only on the start and end states, not on the path taken between them.
The second law
The second law of thermodynamics states that the total entropy of an isolated system never decreases; in any real process it increases. This is why heat flows from hot to cold, why a dropped glass shatters but never reassembles, and why a hot cup of tea cools instead of getting hotter on its own. Reversible processes are idealised cases in which total entropy stays the same, but all real processes are irreversible and produce extra entropy. The second law does not forbid local decreases in entropy, such as a freezer making ice, but the surroundings must gain at least as much entropy as the system loses.
Where you see it
The second law sets the maximum efficiency of any heat engine, which is why power stations always reject waste heat to a cooling tower or river. It explains why perpetual motion machines of the second kind, which would turn heat from a single reservoir entirely into work, are impossible. In everyday life it is behind the arrow of time: films run backwards look wrong because entropy would have to decrease. It also governs chemistry, where reactions run in the direction that increases total entropy, and biology, where living things maintain order only by taking in low-entropy energy and releasing high-entropy waste heat.
Worked example: entropy change of a reservoir
A reservoir at T = 300 K reversibly absorbs Q = 600 J of heat. Use change in entropy delta S = Q_rev / T. Substitute: delta S = 600 / 300 = 2.0 J/K. The entropy of the reservoir increases by 2.0 J/K. If the same heat were absorbed at 600 K, delta S would be only 600 / 600 = 1.0 J/K, because the same energy is a smaller fractional change at higher temperature.
Common mistakes
- Saying entropy is the same as energy: a system can have high energy and low entropy, or low energy and high entropy.
- Applying the second law to part of a system: a fridge lowers the entropy inside it, but the total entropy including the warm room rises.
- Thinking the second law forbids order: order can grow locally, but only by exporting even more disorder elsewhere.
Practice questions
- A system reversibly absorbs 1200 J at 400 K. What is its entropy change?
Show answer
delta S = 1200 / 400 = 3.0 J/K.
- A gas expands freely into a vacuum. Does its entropy rise or fall?
Show answer
It rises, because the gas has more positions and speeds available to its molecules.
- Can a heat engine turn all its heat input into work?
Show answer
No. A perfect engine would need zero total entropy change, but every real process increases total entropy, so some heat must be rejected.
Frequently asked questions
Is entropy just disorder?
In the everyday sense, yes, it often grows as things become more spread out and disordered, but entropy is precisely a count of microscopic arrangements, not just visible messiness.
Can entropy ever decrease?
No. Local order can increase, for example when water freezes, but only by increasing the entropy of the surroundings by more.