Entropy

Entropy (S) is a measure of disorder. The more ways particles can be arranged while still giving the same overall state, the higher the entropy.

Some examples to build intuition:

• 5 students all seated in alphabetical order = low entropy (very few ways to do this).
• 5 students scattered around the room = high entropy (many possible arrangements).
• A neat brick wall = low entropy. A pile of rubble = high entropy.
• Sealed bottle of perfume = low entropy (molecules localised). After it diffuses through a room = high entropy.

In a chemical system:

• Solids: particles fixed in place → very ordered → LOW entropy.
• Liquids: particles can move around but stay close → medium entropy.
• Gases: particles fly freely → HIGH entropy.

So melting and boiling both INCREASE entropy. Freezing and condensing DECREASE it.

For a chemical or physical change, ask:

• Does the state change toward more 'free' particles? (solid → liquid, liquid → gas, solid → gas). YES → entropy INCREASES.
• Does the number of gas molecules increase? (e.g. CaCO₃ → CaO + CO₂ produces a gas → entropy increases).
• Is solid being dissolved into solution? Usually YES → entropy increases (a regular lattice becomes scattered ions).
• Are two substances mixing? YES → entropy increases.

Decreases in entropy:

• Gas → liquid → solid (e.g. condensation, freezing).
• Forming a precipitate (free ions in solution becoming an organised solid).
• Polymerisation (many small molecules → one big chain).

The 2nd law says the entropy of the WHOLE UNIVERSE (the system AND the surroundings) must INCREASE for any spontaneous change. So sometimes a system's entropy can DECREASE locally, but only if the surroundings' entropy increases by more.

Why can you scramble an egg but never unscramble it? Why does ink diffuse through water but never spontaneously gather back into a drop? Why does a hot drink cool down but never spontaneously heat itself?

Because all those reverse processes would VIOLATE THE SECOND LAW: they'd DECREASE the universe's entropy. The forward processes (scrambling, diffusing, cooling) all INCREASE entropy.

Even if individual particle collisions are reversible at the microscopic level, the statistics of many particles ALWAYS make the disordered state vastly more likely. That's why time has a direction in our experience — the arrow of time is the direction in which entropy increases.

A famous question: doesn't life create order? Plants build sugar molecules from CO₂ and H₂O; bodies build complex proteins. Yes — but they do this at the expense of MORE entropy increase elsewhere (heat dumped to surroundings, food chemical energy degraded). The local order is paid for by global disorder.

MYP criterion D extension: discuss whether the universe is heading for a 'heat death' — a state of maximum entropy where nothing further can happen. This is a real cosmological prediction (trillions of years away), based on the 2nd law applied to the whole cosmos.