32 minutes ago, dcarch said:A rise in the temperature of matter makes the particles vibrate faster. Thermal energy is what we call energy that comes from the temperature of matter. The hotter the substance, the more its molecules vibrate, and therefore the higher its thermal energy. "
What you're missing is that potential energy (like the heat of vaporization stored in steam) is not thermal energy. When you cook potatoes in a steamer, the steam condenses on the potatoes and transfers the heat of vaporization to them. This is a separate energy transfer, in addition to the energy the fast-moving steam imparts by banging into the cooler potatoes because it's at a higher temp.
Heat transfer via condensation is going to excite collisions in the food when you're cooking, but liberating heat of vaporization does not necessarily involve collision at all. If you put a blob of steam into outer space, it would lose the heat via radiation instead. It isn't useful to think of condensation as being some sort of collision effect, any more than burning is usefully understood as collision. You need to know how much EM potential energy is stored, and no matter how much calculus you throw at it, you can't derive that from treating the molecules as a vast collection of ping-pong balls operating under Newton's laws. This is not explained by classical statistical mechanics. There's more to thermodynamics than just hot things banging into cold things.
Here's a wiki article on latent heat.
QuoteLatent heat is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process.
Constant temperature => nonthermal energy transfer. Not collision.
