Nathanael said:
So you're saying there's a difference between "temperature" and "heat"?
I never knew this. All the times I said "heat" in my previous posts, what I was actually talking about is "temperature."
So, "heat" can be considered as "the flow of temperature"? Or am I misunderstanding?
"Heat" is not motion.
Example: Consider an ice-cold comet falling sunward from beyond Pluto's orbit. Even though the comet is moving rather quickly, it's still ice cold. It's the random motions of the atoms and molecules in the comet that determine it's temperature. You have to subtract the average motion of the comet as a whole to see those random motions.
Internal energy and temperature are attributable to random atomic motion. At least in an ideal gas. What about a non-ideal gas, or a solid such as that comet? Heat, temperature, and internal energy are distinct concepts, and there's a hidden elephant in the room called "work". And another called "entropy".
A number of factors come into play in determining the internal energy of some object. One is that random motion. Adding heat to the object and the atoms and molecules that comprise it increases those random motions. It can also induce phase changes such as making the solid melt into liquid, the liquid boil off into a gas. Those phase changes also are a part of the overall internal energy. If one ignores those details, you can think of internal energy as being a measure of those random motions.
Temperature is also related to those random motions. In general, understanding entropy is crucial to understanding the connection between internal energy and temperature. It's much simpler with an ideal gas. In an ideal monatomic gas such as helium, the relationship is ##\frac 3 2 kT^2 = K.E. = \frac 1 2 m\bar v^2## where ##\bar v## is the mean random velocity of the atoms that comprise the gas.
Heat and work are related to change in internal energy by the first law of thermodynamics. The change in internal energy is equal to the heat added to the system less the work done by the system. There's a big problem with looking at "heat" as a property of a system. Suppose a system starts at one temperature/energy/volume state and ends at another. The amount of heat flow and the amount of work done depend on the path between those start and end states. One path might involve more work and less heat transfer than another.
This is a very important concept. It is how heat engines operate. Suppose instead of taking a system from point A to point B we take it from point A to point B by one path and then from point B back to point A by another path. That's a heat engine. Even though the engine has come right back to where it started from, that work and heat are path-dependent means the engine can be used to produce a net amount of work on the external environment. A heat engine converts heat into work. Heat engines can also convert work into heat transfer.
