Re: Charles' Law:
V/T = Constant, i.e., V and T are directly proportional; that is, assuming a constant pressure and amount of an 'ideal' gas.
It is easy to understand that the volume of a gas will increase proportionally following Charles' Law, when you heat it.
I am picturing a gas contained in an idealized friction-less, mass-less piston, with the initial volume of the gas sitting inside the piston under atmospheric pressure.
I am assuming that as you heat the gas, the molecules now have greater average kinetic energy (T), will hit the piston head with more momentum, and thereby push it up until the pressure is equalized inside and outside of the piston. (So, only in this sense does pressure 'remains' constant; if it shouldn't be involved at all, please correct me.)
What I cannot picture (either in the real world or in a laboratory set-up) is the reverse, although the math says it must be true. I.e. if the volume of the gas increases (this somehow happening under constant pressure), then the temperature must increase.
Is this solely a question of causality being in one direction only (an increase in temperature causing an increase in volume), or is there more to this question, possibly involving pressure, work, or the laws of thermodynamics?
Intuitively, gases (in nature) cool as they expand, but almost always the expansion is induced by lower pressure in the surroundings, and the expanding gas (I'm guessing) is probably doing work, allowing its kinetic energy (and temperature) to decrease.
I am trying to explain Charles' Law to a high-school chemistry student, but on this I am stuck although the math seems clear; any help will be much appreciated!
Many Thanks, V. Jaroslaw, Brooklyn NY