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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

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I think it is a mistake to think about Charles' law in the context of an increase in volume at constant pressure "causing" an increase in temperature. Or of an increase in temperature at constant pressure "causing" an increase in volume. Or of an increase in volume at constant pressure "causing" an increase in temperature. And, of course, the reverse of each as well.

It is probably better, at least in my opinion, to look at Charles' law in the context that it says gradually adding heat to, or extracting heat from, a gas in such a way that the internal and external pressures are always in equilibrium, causes an increase or decrease in both volume and temperature such that the ratio of volume to temperature is constant.

In my experience teaching fundamentals in thermodynamics, I found it is probably more important to make students aware of the difference between a constant pressure process where the pressure does not change in going from one equilibrium state to another, and any unspecified path between two equilibrium states where the initial and final pressure happen to be the same. Charles' law applies to the former. The ideal gas equation of state applies to any process where the initial and final pressures are the same, whether or not it is a constant pressure process. It's a distinction that many new learners fail to realize.

Hope this helps.

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  • $\begingroup$ I think the key to this common disorientation in students is not to put the right emphasis to heat. Plus 1. $\endgroup$
    – Alchimista
    Commented Oct 1, 2019 at 12:35
  • $\begingroup$ @Alchimista That has been my experience too. It's not the physical properties (temperature, pressure, volume, etc.) that determine each other. It is the heat and work transfers that drive property changes. Thanks. $\endgroup$
    – Bob D
    Commented Oct 1, 2019 at 22:36

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