IB Physics HLThermodynamicsPaper 1 & 2Second Law~10 min read
Second Law of Thermodynamics
The first law says energy is never lost — but it happily allows things that never happen: a cold drink un-cooling, a smashed cup leaping back together. The second law is the referee that rules those out. It says which way real changes actually go, and it wears three different disguises that all mean the same thing: disorder wins.
📚 What you need to know
Entropy form: the total entropy of an isolated system (and of the whole Universe) always increases in any real process
This sets the natural direction of every change — the “arrow of time”
Clausius form: heat cannot spontaneously flow from a colder body to a hotter one (only if you do work, e.g. a fridge)
Kelvin form: you cannot take heat from a single reservoir and turn it entirely into work — some must always be dumped as waste heat
All three forms are equivalent — break one and you break them all
Together they set a hard limit on how efficient any heat engine can be
The entropy form: disorder always wins
The deepest version of the law is about entropy. In any real process, the total entropy of an isolated system never goes down — it increases (or, for a perfect reversible ideal, stays exactly the same). Zoom right out to include everything, the “Universe”, and its entropy is only ever climbing.
The total entropy of the Universe only ever rises. That one-way climb is why time has a direction — you remember the past, not the future, and cups smash but never un-smash.
Keep the two laws straight: the first law says energy can’t be created or destroyed; the second says it always spreads out and becomes less useful. Energy is still all there after a cup smashes — it’s just been shared out into heat and sound and can’t be gathered back. That “spreading out” is the second law at work.
The Clausius form: heat flows one way
The most everyday face of the law is about heat. Left alone, heat always flows from hot to cold — a hot cup warms your hands, never the reverse. It never flows the other way on its own.
Heat drifts from hot to cold by itself (that’s what raises total entropy). The reverse — cold to hot — never happens spontaneously.
The magic word is spontaneously. A fridge or a heat pump does move heat from cold to hot — that’s its whole job — but only by doing work (using electricity). The second law doesn’t forbid moving heat “uphill”; it forbids getting it for free.
WE 1
An inventor claims to have built a sealed box that, with no power supply, keeps a room warm by drawing heat out of the colder air outside. Why is this impossible?
It breaks the Clausius form of the second law.Heat can’t move from the cold outside to the warm room spontaneously. A real heat pump can do it — but only by using work (power). With no power supply, the device is impossible.
The Kelvin form: you can’t win it all
The third face is about engines. Suppose you have a hot reservoir full of thermal energy and you want to turn it into useful work. The Kelvin form says you can’t convert all of it. No matter how clever your engine, some heat must always be thrown away to a colder reservoir. That leftover is the “waste heat” every real engine produces.
WE 2
The ocean holds an enormous amount of thermal energy. Why can’t a ship simply pull heat from the sea and turn all of it into motion, needing no fuel?
It breaks the Kelvin form of the second law.You can’t take heat from a single reservoir (the sea) and convert it entirely into work. An engine also needs a colder reservoir to dump waste heat into — and it can only ever use the difference, never the whole lot.
Putting it together: which engines can exist?
The two practical forms act like bouncers, turning away any machine that’s too good to be true. Picture three engines running between the same hot and cold reservoirs:
Only the third engine is allowed. The first tries to send heat cold→hot for free (breaks Clausius); the second turns all its heat into work with no waste (breaks Kelvin); the third takes heat from the hot side, does work, and dumps the rest to the cold side — obeying the second law.
WE 3
Three proposed engines run between a hot and a cold reservoir. A: heat flows from cold to hot with no work put in. B: it takes heat from the hot reservoir and converts it all to work. C: it takes heat from the hot reservoir, does some work, and releases the rest to the cold reservoir. Which can exist?
Only C can exist.A breaks the Clausius form (heat can’t go cold→hot for free). B breaks the Kelvin form (you can’t turn all the heat into work). C dumps waste heat to the cold reservoir, so it obeys the second law.
Entropy form Universe’s S rises
same law…
Clausius form no free cold→hot
…same law
Kelvin form no 100% engine
💡 Top tips
Three forms, one law. Pick whichever fits the question — entropy, heat flow, or engines.
“Spontaneously” is the key word in the Clausius form: fridges are fine because they do work.
No engine is 100% efficient (Kelvin) — there’s always waste heat to a colder reservoir.
Isolated system ⇒ entropy can’t fall — it rises, or stays put for a perfect reversible change.
These limits set the maximum possible efficiency of any heat engine — which we’ll pin down soon.
⚠ Common mistakes
Saying heat can never flow cold→hot — it can, if you do work (fridge, heat pump)
Believing a 100%-efficient engine is possible — the Kelvin form forbids it
Confusing “an isolated system’s entropy can’t fall” with “entropy can never fall anywhere” — it can, locally
Forgetting the three forms are equivalent — a machine that breaks one breaks all
Thinking the second law breaks energy conservation — it doesn’t; energy is still conserved, just less usable
Quick recap: The second law comes in three equivalent forms. Entropy: the total entropy of an isolated system (and the Universe) always increases. Clausius: heat won’t flow cold→hot on its own. Kelvin: you can’t turn all the heat from one reservoir into work. Together they forbid “too-good-to-be-true” machines and cap how efficient any heat engine can be.
Excellent — you’ve met the law that governs the direction of everything. It also tells us no engine can be perfect, which raises the obvious question: how good can an engine be, and how do gases behave step by step to make one work? To answer that we first need the toolkit of individual gas changes — the thermodynamic processes — which is where we head next.
Want this to actually click before the exam?
Book a free meeting and let’s work through the tricky bits together.
