Energy transfers · Model
Heating and thermal equilibrium
A sparkler throws sparks at 1500 °C and they do not hurt. A bath at 40 °C can injure a small child. Which holds more energy, and why does the cooler one do more damage?
Start here
1500 degrees, and it does not hurt.
A sparkler throws out sparks at around 1500 °C — hot enough to melt iron. They land on your hand and you feel a pinprick. Meanwhile a bath at 40 °C, barely more than body temperature, will make you flinch and can genuinely injure a small child.
Commit. Which holds more energy, and why does the cooler one do more damage?
The bath, by an enormous margin — tens of millions of joules against a fraction of one. Temperature is a measure of the average kinetic energy of the particles — the energy they have because they are moving. Energy depends on that and on how many particles there are. A spark is a handful of very fast particles; a bath is a hundred kilograms of moderately fast ones. Two different quantities, and this lesson is about never confusing them again.
You already know from the particle unit that heating a substance makes its particles move faster and does not change the particles themselves. That claim comes back here, and it comes back harder — because this time you have to use it to separate two things that everyday language treats as one word.
Two quantities · move each one on its own
Temperature is not the same as energy
Set how much there is, then set how fast its particles are moving. Watch the two readouts move independently — that is the whole point.
How much there is
How fast the particles move
Temperature
Thermal store
The thermal-store bar is logarithmic — the largest setting on this bench holds about 10^11 times the smallest, and a linear bar would leave everything but the bath at nothing.
Temperature moved when you changed the speed and did nothing when you changed the amount. The thermal store moved for both. They are two different quantities, and the spark is the proof: the fastest particles on the bench, and almost no energy at all.
Key fact
Temperature is a measure of the average kinetic energy of the particles — the energy they have because they are moving. The energy in a thermal store depends on that and on how many particles there are.
One-way flow · run each pair
Energy goes one way, and stops when they match
Run each pair and watch the arrow. There is only ever one, and it always points the same way.
no cold travels this way
Energy leaves the drink and enters the ice. One arrow, pointing from the drink to the ice. Nothing at all travels the other way — the drink gets colder because it is losing, not because it is receiving. The ice reaches 0 °C, melts, and the meltwater goes on warming with the drink — which is why the drink ends up colder than the size of the cube suggests.
The spoon is much hotter but tiny, so it loses temperature fast while the water barely warms — there are far more particles in the water, so the same energy shifts its temperature hardly at all. Same one-way flow — and it stops when they match, not when the spoon “runs out”.
Already at the same temperature, so there is no net flow at all and nothing happens — this is thermal equilibrium. Particles are still colliding and still exchanging energy in both directions; the two flows are simply equal. That is exactly the diffusion result from C1, in a new setting.
Think again
“Put ice in your drink and the cold moves out of the ice into the drink.”
There is no such thing as cold. Cold is not a substance, not a store, and not a thing that can travel — it is just a smaller amount of the same thing. Energy moves out of the drink and into the ice, in one direction only, and the drink is left with less. Nothing entered it.
This matters more than it sounds. If cold were a substance you would expect a fridge to make cold and pump it in; instead a fridge takes energy out of the food and dumps it into your kitchen, which is why the back of a fridge is warm and why leaving the door open warms the room rather than cooling it. Watch the flow bench again: there is only ever one arrow, and it always points the same way.
And note what has not changed in either object: the particles are the same size and the same particles throughout. Heating and cooling change how fast they move and nothing else — exactly as the particle model said, now doing work in a new situation.
“A bath is hotter than a cup of tea, because there is far more heat in it.”
Two different quantities are being run together. Temperature is a measure of the average kinetic energy of the particles — the energy they have because they are moving. The energy in the thermal store also depends on how many particles there are. A bath at 40 °C holds far more energy than a cup at 80 °C, and yet the tea is hotter — and it is the temperature, not the total energy, that decides which way the heating goes when you put one in the other.
Key fact
Heating is energy moving from a hotter object to a colder one, and it only ever goes that way. It stops when the two reach the same temperature — thermal equilibrium — not when one has run out of heat.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
Energy in a thermal store always flows from…
Rung 2 · The one that catches people
A mug of tea and a swimming pool are both at 30 °C. Which statement is correct?
Rung 3 · Explain
Explain why a spark at 1500 °C landing on your hand does far less damage than water at 60 °C. Use both temperature and energy in your answer.
Rung 4 · Take it somewhere new
A student leaves the fridge door open on a hot day to cool the kitchen down. Explain what will actually happen, and why. Use the idea that cold is not a substance.
Key note
Temperature and energy are two quantities, not one. Heating runs from hotter to colder until the two match, and cold is not a substance that travels — it is simply less of the same thing.
Going further
For a long time heat was thought to be a substance, called caloric, that flowed out of hot things into cold ones. It was a good model: it explained why heating goes one way, why things reach the same temperature, and why a hot object cools. What killed it was a cannon factory. In 1798 Count Rumford noticed that boring cannon barrels produced heat without limit, as long as the boring continued — and a substance that never runs out is not a substance. Energy was being transferred by the mechanical work of the drill, not poured out of a reservoir. That is the same lesson Testing the model teaches: caloric was not stupid, it was a model that worked until someone found its edge.
Before this lesson
At GCSE this becomes
- Specific heat capacity — the same two quantities, with a number attached to how much energy each kilogram of a substance needs for each degree.
Where to next
Ask Mr Badmus AI
Still picturing cold as something that moves?
Lesson content © MrBadmusAI.