Hot side, cold side
What heat really is, and why it only flows one way on its own.
What you are looking at
The dots on one side are orange and move fast. The dots on the other side are blue and move slowly. As time passes, the colors blend and the speeds even out.
The idea
Heat is not a thing that flows like water. Heat is how hard the tiny bits of a material are shaking. A hot spoon has bits that shake a lot. A cold spoon has bits that barely shake.
When fast bits bump into slow bits, the fast ones lose a little speed and the slow ones gain a little. Do that over and over and the shaking spreads from the hot end to the cold end. Put a metal spoon in hot soup and the handle warms up for this reason.
It never runs the other way by itself. A cold spoon does not heat up the soup. That is because, again, there are far more ways to share the shaking out evenly than to keep it all in one place.
Where else you see it
- A hot cup warming your hands.
- A metal bar warming along its length when you heat one end.
- A cooling cup of coffee reaching room temperature.
Go deeper: the proper names and the math
The rate of heat flow is proportional to how steeply the temperature changes: Fourier's law, q = −k ∇T. Combined with conservation of energy, this gives the heat equation, ∂T/∂t = α ∂²T/∂x².
The animation uses a solution for a bar with insulated ends, written as a sum of cosine waves. Each wave fades at a rate proportional to the square of its frequency, so the sharp edge between hot and cold smooths out first, and the long, gentle shapes last the longest. In the end the temperature is uniform at the average value.