A molecule can have kinetic energy, just like anything else can. When that kinetic energy comes from uncoordinated movement (the molecules are all moving chaotically, not together) then we call it heat. That’s simply the word we’ve chosen to describe that thing.
Now, why is this chaotic motion the ‘natural’ result of energy being released? Why do friction, chemistry, and radiation all create this chaotic heat? What happens to the uniform motion of a thrown ball that turns into chaotic microscopic motion (heat) when it lands?
This has to do with statistics. When we allow the moving ball to bounce off of molecules, the ball in more likely to give some of its energy to them than they are to give energy back, and this is because a single moving ball has a lot more energy than a single molecule. The ball will slow down until it has energy similar to a single molecule – not enough energy to notice.
A much smaller ‘ball’, like pollen, will visibly jiggle too. It’s small enough that the energy of a single molecule is significant, but large enough that we can see it.
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