Topic 6.3: Heat Transfer and Thermal Equilibrium

Heat transfer: one collision at a time

Our diagrams tell us which way the energy went and how much of it, but they don’t say how it actually got across. For that, we need to watch the molecules. So let’s follow another snowflake down to the water, and keep on going, past the ice crystals, all the way down to the molecules right at its edge.

On one side are the water molecules of the bath, tumbling and jostling past each other, and on the other side are the ice molecules, locked into their crystal, only able to tremble in place. When a fast water molecule slams into the edge of the ice, it knocks some of its energy into the ice molecule it hits, so the ice molecules shake harder and harder, until they break loose and join the liquid.

Look closely, though, because the molecules in the warm water aren’t all fast. Here’s a slow one in the warm water, and here’s a fast one in the ice, so what makes the water warmer is that its molecules have more kinetic energy on average. Energy passed along by collisions like these, from particles with more kinetic energy on average to particles with less, is what we call heat transfer, and you’ll also hear it called heat exchange, or the transfer of energy as heat.

So the reasoning the AP exam wants is that a higher temperature means a greater average kinetic energy, that when two things touch, their particles collide, and that those collisions move energy from the warmer one to the cooler one, on net. And it’s always energy that moves. Cold never flows anywhere, so when the snowflake cools the water around it, what really happens is that the water’s energy flows into the flake. So why does energy flow from the bath into the snowflake? Pick the best explanation.

Thermal equilibrium: the flow stops, the molecules don’t

The snowflake vanishes into the pool, which makes it hard to see how that story ends, so let’s build a cleaner version where we can watch all the way to the end. Here are two sealed samples of the same gas, a hot one on the left and a cold one on the right, with a perfectly insulating wall between them that doesn’t let any energy through. Now let’s swap that wall for a thin sheet of metal and slow everything way down.

A fast atom from the hot side slams into the wall, the metal atoms pass the jolt along, and a slow atom on the cold side bounces off the far face moving faster than it came in. Now and then a collision goes the other way, like this fast atom on the cold side giving energy back to the wall, but far more of them carry energy from hot to cold, so on net, that’s the way it flows.

Now you run it. Flip the wall to metal, and watch until the energy stops flowing one way. But look at the atoms, because they haven’t stopped at all. They’re still flying around and still hitting the wall, and energy still crosses it in both directions, it’s just that now, as much goes one way as the other, so there’s no net flow.

That’s worth saying twice, because so many people picture equilibrium as everything stopping. The atoms keep right on moving, and what has become the same is their average kinetic energy, which is exactly what it means for the two temperatures to be equal. Let’s try it with twice as many atoms on the hot side.

This time they meet at about three hundred thirty-three kelvin, closer to where the bigger sample started, and at the end both sides have the same average kinetic energy, even though the left side holds twice as much energy in total. So when two samples of different sizes reach the same temperature, which of these has to be true?

And this is the same idea the 2024 AP exam asked students to draw. A metal cube heated in boiling water goes into a calorimeter of cooler water, and the question shows the water molecules before, with arrow lengths standing for their speeds, and asks you to draw them after.

Which after drawing earns the point? And if a question asks you to explain a drawing like that, this is the sentence that earns the point. The metal’s particles had a greater average kinetic energy, so collisions transferred energy to the water molecules, and the water molecules’ average speed increased.

Back to Hell Valley

Now let’s go back to the pool, because it’s been hiding one last puzzle since the very beginning. Every second, this bath is losing energy to the freezing air above it, and yet it stays warm all winter long.

So is this pool in thermal equilibrium with the air above it? So let’s follow the energy through this whole scene one more time. A snowflake lands and takes in energy from the water as it melts, which is endothermic for the flake. Vapor rising off the pool condenses into those drops and hands energy to the air, which is exothermic. The warm surface keeps losing energy to the cold air, while hot water from underground keeps bringing more in.

And wherever warmer and cooler things touch, the energy crosses the same way, one molecular collision at a time, on net from the warmer side to the cooler one, while the hot spring water simply carries its energy in as it flows. So the next time you see a snow monkey soaking in a hot spring, you’ll know exactly where all of that energy is going.