In a previous thread, it was stated that a gas is only in a state of internal thermodynamic equilibrium when there is no heat flow between any two subsystems. I question whether any system comprising of a gas could actually reach such a state, in theory or in practice, since I may arbitrarily divide any thermodynamic system into any number of subsystems. A gas is composed of a number of discrete particles in motion, and if I draw small enough bounding boxes, some subsystems will come up with little internal energy and some with lots. Therefore it seems to me that no gas can possibly be in an actual state of internal thermodynamic equilibrium; alternatively, whether a gas is in a state of internal thermodynamic equilibrium depends on how I arbitrarily divide the system into subsystems.
I hesitated a bit, because some people will not like this answer. But you did specifically say “in theory or in practice”, so I hope you might accept this:
The first key word is “eventually”. If I say that it is in equilibrium now, you will draw “small enough bounding boxes”, so that some are different than others. So I’ll say to wait a while, and each those boxes will indeed be in equilibrium. So you’ll draw boxes that are even smaller to prove me wrong. And the cycle will continue. “Eventually” those boxes will be smaller than a Planck length, and I will have shown the system to be in total equilibrium. Which bring us to the next key word, which is always going to come up in questions of this sort: “infinite”.
Max_S, I am not a physicist or a thermodynamicist, but I have done a fair number of calcs and measurements involving gases in my career. There is very old paper which you will find very interesting: MICRO- AND MACRO-THERMODYNAMICS, MYRON TRIBUS, American Scientist, Vol. 54, No. 2 (JUNE 1966), pp. 201-210 https://www.jstor.org/stable/27836395?seq=1
The author argues that classical thermodynamics is a construct and statistical methods are more rigorous (and less circular).
For example he points out, the circular nature of other things in physics :
“ The laws of Euclidean geometry are demonstrable in Euclidean space. Euclidean space is defined as a space in which Euclidean geometry is valid.
Newtonian mechanics is valid in a Newtonian frame of reference. A Newtonian frame of reference is one in which Newton’s laws are valid.
The case of thermodynamics is no different. The laws of thermodynamics define the conditions of equilibrium. The laws are valid at equilibrium. “ (Bolding mine)
So using classical thermodynamics, everywhere the gas has equal internal energy at equilibrium and that is the definition of equilibrium.
Not sure if that helps you, but the author does point to information theory for a better understanding of equilibrium - maybe that’s what you are seeking ?
Not smaller, just different. I imagine a video of a bunch of marbles rolling around a very slippery box. The marbles are as evenly distributed as possible, at every second in the video. But still, between any two individual frames of the video, I can draw bounding boxes such that more marbles leave one region than enter. This is because a marble leaving or entering a region is an atomic operation - there is no fundamental force of physics which ensures that when a marble (or particle) moves over an arbitrary invisible line that another marble (or particle) moves back. The lack of such a force is consistent with the first law of motion as I see it.
It is my understanding, that thermodynamics is, by definition, statistical, requiring large numbers of particles to make sense.
So, drawing smaller volumes would eventually fail to include enough particles for statistical analysis, and would fall out of “bounds” for thermodynamics.
Drawing weird shaped regions which depend on knowing the position and velocities of the set of particles also seems out of bounds for thermodynamics, in not being properly statistical. It would be like saying “superhero flicks are clearly the best kind of movie, just look at the poll results of this random sample (that happens to include only the teenage boys of the nation, oh and by the way, I was very careful too only include teenage boys and exclude everyone else)”.
For clarification, Avogadro’s number is quite huge, so even a millionth of a mole of particles is a very large number.
There is the old example of having all the molecules of gas spontaneously move to one side of the room. This is possible in a human sized room at atmospheric pressure, but does not really happen, even in many lifetimes of the universe. But if there were a very hard vacuum, with only one particle (or a few particles) in the room, it would happen frequently, many times a day.
This does not disprove thermodynamics- it just doesn’t really apply to systems of a few particles. I think.
I’m not sure if it makes the assumption, but surely it cannot be denied that convection takes place within thermodynamic systems at equilibrium; it is assumed that the heat baths forming the boundaries of an isolated system exactly compensate any heat flow.
Oh, looks like your question is much simpler than I thought.
Yes absolutely, you can draw those bounding boxes. It’s not a static equilibrium but a dynamic one. For example, N2 + 3H2 <—> 2NH3 gets to a dynamic equilibrium where the forward reaction is balanced by the reverse reaction. Reactions don’t stop they just equal each (forward and backward) other.
So for your case, if there is a region with less particles, then that’s the concentration gradient that will drive diffusion. For any gas, gravity pulls the molecules down but that in turn creates a concentration gradient resulting in diffusion which drives the molecules up. This is basically a part of Einstein’s theory on Brownian motion.
Yes, but not instantly which is what I meant when I said the movement of one marble across the invisible boundary is atomic (independent in the instant sense). Over time, on average, absolutely. The reason I’m avoiding statistical mechanics (including Brownian motion) is because I am trying to avoid the assumption of random motion. The reason for that being the previous thread, in which it was argued that the second law of thermodynamics is never violated, even in theory.
Probably not. I was reading Boltzmann’s Wikipage recently and was surprised to learn that, up until the late 1890s/early 1900’s, most physicists did not believe atoms and molecules were real objects. Chemists, on the other hand, did.
At the end of the day the gasses are always seeking equilibrium and the lowest energy state they can be in.
Given time they will find it to within the Heisenberg Uncertainty Principle. After that all bets are off.
I suppose, technically, nothing ever really stops (i.e. there is no absolute zero) so there will always be a little motion and therefore, in theory, at least a slight imbalance that forever gets closer to zero.
Your “classical” theory with the infinitely divisible medium and the smaller and smaller boxes is OK, because you also wait an infinite amount of time to achieve an equilibrium condition.
You can look at a typical classical solution by eg explicitly solving the heat equation; you will observe an exponential decay of normal modes.
So it sounds to me like your OP question is actually suffering from a bit of the X-Y problem. You want to assume pre-Boltzman (ie. now known to be incomplete / inaccurate) physics so as to test an assertion made in even earlier even more incomplete / inaccurate physics?
Not sensible IMO.
IMO …
Physics is, at a large enough grain, 100% statistical. It always has been and always will be, regardless of physicists’ incomplete knowledge in any given era including our own. A consequence of that statistical nature is that at a fine enough grain the statistics fail. Always. A single coin flip may have 50/50 odds, but it does not come out 50/50 when you make the measurement.
So before you (anyone) can make any statement of the format “X is true” or “X is false” you need to specify at what scale, across what time interval you’re interested in the answer. Which essentially amounts to “at what degree of truthness?”.
Said another way, all theory can be regarded as a description of Nature’s asymptotic behavior as it approaches a limit. How big (or small) a magnifying glass you want to apply to that convergence is a situational question.
“Theory X is always and everywhere True” is a statement about a Platonic Form. That is, a statement about a philosophical ideal that Nature does not in fact contain. At least insofar as we can tell to date.
Heat and thermodynamics are only statistical conceptions for a continuum, which break down at small scales. This isn’t anything exciting about thermodynamics, it’s just an example of the failure of continuum models.
For what it’s worth, I am asking about the older, classical thermodynamics. Not as a prelude to understanding modern physics, just to understand that theory for what it is. The previous thread was based on the question of whether the second law is always and everywhere true, and at least in the classical sense it seems to be assumed so.
Let’s get our definitions correct, because sometimes we maybe thinking different things :
Specific Internal Energy (Classical Thermodynamics) Expressed in J/kg or J/mol. It is the internal energy per unit mass (kg) or quantity (mol).
Intensive Properties (Classical Thermodynamics) : “ An intensive property is a [physical quantity] whose value does not depend on the amount of the substance for which it is measured. For example, the [temperature] of a system in thermal equilibrium is the same as the temperature of any part of it.” Intensive and extensive properties - Wikipedia
Now Specific Internal Energy is an Intensive property per Classical Thermodynamics. Same cite as Number 2.
Therefore, per Classical Thermodynamics, Specific Internal Energy (an intensive property) is the same everywhere in the gas at equilibrium, no matter how you draw your boundary.
This is where you confused me because this is not Classical Thermodynamics. A gas in Classical Thermodynamics is a continuum and not discrete particles in motion. In my opinion, you are mixing Classical TD and Statistical Mechanics in the question but want the answer purely from the Classical TD
I believe you are mistaken. Temperature is said to be intensive at equilibrium, but specific internal energy is extensive and proportional to size. It is also measured in joules, not joules per kg which is effectively a measure of acceleration.
