IB Physics HLThermodynamicsPaper 1 & 2Entropy & Disorder~10 min read
Entropy
The first law tells you energy is never lost — but it doesn’t tell you which way a change will go. A hot drink always cools; it never spontaneously heats up, even though energy would be conserved either way. What decides the direction is a new quantity: entropy, a measure of disorder. Nature, left alone, always drifts toward more of it.
📚 What you need to know
EntropyS measures disorder — the number of ways a system’s particles and their energy can be arranged
More ways to arrange things = more disorder = higher entropy
Order of the states of matter: gas > liquid > solid (a gas is the most disordered)
Melting and boiling increase entropy; freezing and condensing decrease it
Entropy also rises when a substance is heated, when a solid dissolves, or when a gas spreads out (diffuses)
The entropy of an isolated system always increases — that’s the natural direction of change
Entropy can fall locally, but only if the surroundings gain at least as much — the Universe’s entropy never drops
What entropy really is
Entropy sounds abstract, so start with a picture: a bedroom. There’s only one way for it to be perfectly tidy, but a huge number of ways for it to be messy — socks here, books there. Left to chance, the room ends up messy simply because there are so many more messy arrangements than tidy ones. Entropy is exactly that idea for molecules: the more ways you can arrange the particles and their energy, the higher the entropy.
So entropy is a count of possibilities, not a type of energy. A low-entropy system is neat and predictable; a high-entropy one is spread out and jumbled. On the next page we’ll put actual numbers on it — for now, focus on the idea and which way it points.
A handy mental test: “How sure am I about where everything is?” If you can pin the particles down (like atoms locked in a solid), entropy is low. If they could be almost anywhere (like molecules zipping around a gas), entropy is high.
Entropy of the three states
The clearest example is the three states of matter. In a solid, molecules sit in a fixed, regular lattice — you know where each one is, so there are very few arrangements and entropy is lowest. In a liquid, they’re still close but can slide past each other, so there are many more arrangements — medium entropy. In a gas, molecules fly around, far apart, filling all the space, giving an enormous number of arrangements — the highest entropy.
From a neat solid lattice to a jumbled liquid to a wide-open gas, the number of possible arrangements shoots up — so gas > liquid > solid for entropy.
WE 1
Arrange ice, liquid water and steam in order of increasing entropy, and explain your ranking.
Order (lowest → highest): ice < water < steamIce is a fixed lattice — few arrangements, lowest entropy. Liquid water can flow, so more arrangements. Steam spreads through all the space, giving the most arrangements and the highest entropy. It’s the same substance each time — only the disorder changes.
Changing state changes entropy
Because the three states have such different entropies, changing state causes an entropy jump. Go “up” the ladder — melting (solid→liquid) or boiling (liquid→gas) — and entropy rises. Go “down” — freezing or condensing — and it falls. Simply heating a substance also nudges entropy up, because the particles move more vigorously and their energy can be shared out in more ways.
Entropy climbs steadily as a substance warms, then jumps at each change of state. The leap at boiling is the biggest, because turning a liquid into a gas is a huge increase in disorder.
Notice the boiling step is far taller than the melting step. Melting just lets molecules slide around; boiling sets them completely free to fill a whole room. That’s why vaporising something adds so much more entropy than melting it.
WE 2
When steam condenses into liquid water, does the entropy of the water increase or decrease? Explain.
It decreases.Condensing is gas → liquid — the molecules are brought closer and become more ordered, so there are fewer ways to arrange them. Fewer arrangements means lower entropy.
Spreading out raises entropy too
Entropy doesn’t only change with state. Anything that lets particles spread out raises it. Two classic cases: a solid dissolving in a liquid (its particles scatter through the solvent), and a gas diffusing to fill a container. In both, the particles end up more spread out, with more ways to arrange them — so entropy goes up.
Remove the partition and the gas fills the whole box. It spreads out because there are vastly more “spread out” arrangements than “all in one corner” ones — and it never gathers itself back on its own.
That last point is the key to the whole topic. You never see a gas spontaneously bunch back into one corner, or a cooled drink reheat itself. These changes only run one way, and that one-way street is exactly what entropy is tracking.
Reversible, irreversible and isolated systems
Physicists sort changes into two types. A reversible change causes no overall change in entropy — the system and its surroundings could, in principle, return exactly to the start. It’s a perfect, friction-free ideal that never quite happens in real life. Every real process is irreversible: it increases the total entropy, and there’s no getting back to the exact starting point.
This leads to the big rule. An isolated system — one that can’t exchange matter or energy with anything outside — can only have its entropy stay the same or increase, never decrease. So how can a fridge make things colder, lowering their entropy? Because a fridge is not isolated. Its contents’ entropy drops, but it dumps even more disorder (as heat) into the room. Locally entropy fell; overall it rose.
The rule to remember: entropy can decrease in one place, but only if it increases by at least as much somewhere else. Add up everything — the “Universe” — and its entropy always goes up. That statement is so important it becomes the Second Law of Thermodynamics, coming up soon.
WE 3
A hot stone is dropped into a cold lake. State what happens to the entropy of (a) the stone, (b) the lake, and (c) the stone and lake together.
(a) The stone cools → its entropy decreases(b) The lake warms → its entropy increases(c) Together (an isolated system) → entropy increasesThe lake’s gain outweighs the stone’s loss, so the total goes up — which is exactly why heat flows hot → cold and never the other way.
More disorder
more ways to arrange things
More microstates
so…
Higher entropy S
💡 Top tips
Remember the order: gas > liquid > solid.
Up the ladder = entropy up: melting and boiling raise it; freezing and condensing lower it.
Boiling gives the biggest jump — a gas is far more disordered than a liquid.
Isolated system: entropy can only increase (or stay the same for a perfect reversible change).
Local drop is allowed only if the surroundings rise more — the Universe never loses entropy.
⚠ Common mistakes
Thinking entropy is a kind of energy — it’s a measure of disorder (number of arrangements)
Saying entropy can never decrease — it can, locally, as long as the surroundings increase more
Getting the direction of a state change wrong — freezing lowers entropy, it doesn’t raise it
Assuming a fridge “destroys” entropy — it just moves it, dumping more into the room
Forgetting why heat flows hot→cold: because that’s the direction that raises total entropy
Quick recap: Entropy S measures disorder — the number of ways particles and their energy can be arranged. Order of states: gas > liquid > solid. Melting, boiling, heating, dissolving and diffusing all raise it; freezing and condensing lower it. An isolated system’s entropy always increases; a local decrease is only possible if the surroundings gain at least as much.
Great work — you now know what entropy is and which way it points. The natural next question is: how much does it change? Next, in Calculating Changes in Entropy, we put real numbers on it with ΔS = ΔQ/T, and peek at the microscopic version, S = kB ln Ω.
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