Energy moves one way, and cold is not a thing

Say what actually happens at the boundary between a warm system and a cool one. Fast particles on the warm side collide with slower particles on the cool side. On average the fast ones lose energy and the slow ones gain it. That is the entire mechanism, and it has one direction and one currency.

So two common sentences describe nothing physical:

1. "The mug contains a lot of heat." The mug has internal energy. $Q$ names energy in transit, so it is a property of a process, not of an object.
2. "Cold from the ice moves into the drink." There is no cold to move. Energy leaves the drink and enters the ice, so the drink's internal energy falls and its temperature drops.

The habit costs more than tidiness. A student who believes in two fluids, one hot and one cold, has no way to write $\Delta U = Q + W$ correctly, because they are tracking two signed quantities where the physics has one.

Energy moves spontaneously from the higher-temperature system to the lower-temperature one. Not from the bigger one, not from the one holding more thermal energy in total.

Drop a $200^\circ$C nail into a swimming pool at $25^\circ$C. The pool holds vastly more thermal energy than the nail, by any accounting you like, and the nail still heats the pool. The reason is in the mechanism: the collisions happen between individual particles, and temperature is exactly the average energy of an individual particle. A nail particle arriving at the boundary with far more energy than a water particle is far more likely to give energy up than to take it.

This is the point of the previous topic paying off. Temperature answers a per-particle question, and per-particle is the scale on which the transfer is decided.

Two systems in thermal contact reach thermal equilibrium when their temperatures are equal. What happens then is that the NET transfer becomes zero:

$$T_1 = T_2 \quad \Longrightarrow \quad Q_{\text{net}} = 0,$$

while particles at the boundary keep colliding and keep exchanging energy in both directions at matching rates. Nothing switched off. A metal block sitting at room temperature is still handing energy to air molecules, still being struck by them, and still radiating; it is also absorbing radiation at the same rate. Its internal energy holds steady because two rates are equal, not because two rates are zero.

Insist on the word net and a whole class of questions becomes answerable. Why does an object at room temperature still emit infrared? Why does a thermometer left in a drink stop changing? Because equal temperature means equal exchange rates, and equal exchange rates mean nothing further changes.

The same energy flows by three mechanisms, and problems name which one is in play.

1. Conduction. Energy passes along by particle collisions without the material moving. This is the metal spoon in the soup, and its rate is the subject of topic 9.5.
2. Convection. The heated material itself moves, carrying its internal energy with it. Warm air rising is the standard case, and it needs a fluid.
3. Radiation. Electromagnetic waves carry the energy, so it needs no medium at all. This is how the Sun reaches you across vacuum, and it is why a thermos is silvered.

All three run hot to cold on net, and all three run in both directions at once. A thermos attacks all three: a vacuum gap removes conduction and convection, and the silvering reflects the radiation.