Equating motion with energy

[matterdoc]

Why random motion of molecules, assumed for kinetic theory of gas, is currently accepted as real displacements and thus pave for equating energy with motion?

Nainan

[Strange]

Because atoms and molecules really move?

[studiot]

 

equating energy with motion?

 

Only certain types of energy are associated with motion of molecules, and in this case also pressure, which is not a form of energy.

 

Some other forms of energy are also associated with motion of other entities.

[Enthalpy]

The random motion of molecules is a daily observational evidence. We see it on any accelerometer or pressure sensor for instance.

The kinetic model of gas doesn't have to be accepted any more. It was a theory a century ago.

Find a more recent book maybe? Or one that gives more recent evidence instead of the historical deductions?

[matterdoc]

Thanks.

Nainan

[Bignose]

The kinetic model of gas doesn't have to be accepted any more. It was a theory a century ago.

Whoa whoa whoa, here. Just because it is a century old doesn't mean it isn't still awfully useful. Within its domain, its predictions are very good. And its domain has been extended significantly with improved interaction models.

 

I actually think that more than enough evidence can be given showing how good its predictions are that the kinetic model of gas indeed does need to be accepted today. Unless you can provide a more accurate model, I don't think one can abandon the kinetic model of gases at all.

[studiot]

 

Bignose

 

And its domain has been extended significantly with improved interaction models.

 

 

 

These extensions go way beyond the original kinetic theory of solids, liquids and gases to extend to 'gas like' entities such as the 'electron gas' in solids, particles in disperse systems and much much more.

Edited August 11, 2014 by studiot

[matterdoc]

Dear Enthalpy,

I don’t think there are accelerometers that can be attached to moving molecules in gas or pressure sensors that can measure impact pressure of individual molecules in gas. If random motion of molecules are already measured and found real, why is it still maintained with the list of assumptions on which gas-laws are based? Most people, while using this assumption for their purposes, usually forget to mention its assumed nature and thereby giving impression that random motion is real.

As Bignose suggested, within its domain, gas-laws give accurate prediction. However, these predictions are still based on the assumption of random motion of molecules. Unless definite mechanism can be explained for cause and random motion of molecules, the assumption cannot become real fact. It is not correct to carry an assumption that works for certain phenomenon as real fact for other phenomena that gives apparently similar results as original phenomenon.

Nainan

[studiot]

 

However, these predictions are still based on the assumption of random motion of molecules. Unless definite mechanism can be explained for cause and random motion of molecules, the assumption cannot become real fact. It is not correct to carry an assumption that works for certain phenomenon as real fact for other phenomena that gives apparently similar results as original phenomenon.

Nainan

 

 

I don't understand the question here.

 

What do you have against the kinetic theory and why does direct observation of Brownian motion not substantiate it?

[swansont]

And to add to that, why is random motion something that needs a mechanism?

[Enthalpy]

Dear Enthalpy,

I don’t think there are accelerometers that can be attached to moving molecules in gas or pressure sensors that can measure impact pressure of individual molecules in gas. If random motion of molecules are already measured and found real, why is it still maintained with the list of assumptions on which gas-laws are based? Most people, while using this assumption for their purposes, usually forget to mention its assumed nature and thereby giving impression that random motion is real.

As Bignose suggested, within its domain, gas-laws give accurate prediction. However, these predictions are still based on the assumption of random motion of molecules. Unless definite mechanism can be explained for cause and random motion of molecules, the assumption cannot become real fact. It is not correct to carry an assumption that works for certain phenomenon as real fact for other phenomena that gives apparently similar results as original phenomenon.

Nainan

 

Accelerometers can't be attached to single molecules, but the µm-sized accelerometers and pressure sensors we build are sensitive to individual molecule shocks. At moderate gas pressure we (I did 30 years ago) observe the global noise created by the many molecules, at low pressure we observe individual shocks through the signal given by the sensor.

 

That's why I say "not an assumption any more, but observation".

 

And that's why I write it's a model, not a theory as for a century ago.

 

I wrote "find a newer book" because those textbooks that describe evidence gathered a century ago give the wrong impression that no other proofs exist. Meanwhile we have far stronger observations. Books would better give these instead of the old indirect historic evidence: that would be more useful to readers.

Whoa whoa whoa, here. Just because it is a century old doesn't mean it isn't still awfully useful.

 

I did not write "useless", because I used it for my sensors. You did misinterpret.

Edited August 14, 2014 by Enthalpy

[studiot]

@enthalpy.

 

It is interesting to learn of the existence of pressure sensors sensitive enough to record the impact of a single molecule.

 

If it is not considered off topic a link to them would be appreciated.

[Bignose]

I did not write "useless", because I used it for my sensors. You did misinterpret.

Nor did I write "useless". You DID write "The kinetic model of gas doesn't have to be accepted any more." Whatever word choice I make it should be very clear that I very much disagree with this.

However, these predictions are still based on the assumption of random motion of molecules.

That isn't really what the kinetic theory of gases states. It starts with billiard balls running into each other. Mathematically, you can describe the entire ensemble completely deterministically, but considering the many quintillions of atoms that makes up a typical amount of gas, usually the average quantities are solved for. That's where the randomness comes in, from the fact that most typically an average is used and statistically there are error bars around an average. But I do think it is important to note that the basis of the kinetic theory of gases does not directly have any randomness in it.

Edited August 14, 2014 by Bignose

[studiot]

 

You DID write "The kinetic model of gas doesn't have to be accepted any more

 

@Bignose,

 

I do believe this is a matter of first language (I don't think English is Enthalpy's) and I think Enthalpy meant accepted in the sense of "taken on trust for granted or without direct proof" not in the more obvious sense.

 

I have made this sort of mistake before in discussions with Enthalpy; some of his statements have a deeper meaning behind them that is not obvious on first glance.

 

There is, however, no question that your summary of the Kinetic Theory is corrrect in declaring that the mechanics of motion of the particles is entirely deterministic in principle within the laws invoked in the Kinetic Theory.

 

If we however, consider from the point of view of a particular area or point being bombarded by these particles, the variable recording the time of bombardment takes on the mantle of a random variable, does it not?

[swansont]

I was pretty sure the existence of atoms was fairly well established (since Einstein's 1905 Brownian motion paper), so the kinetic theory of gases is on very solid ground, as it were. It has limitations, as all theories do, but that doesn't make it wrong or mean it is to be rejected.

 

Is there some competing theory out there that I'm not aware of? Has the ideal gas law stopped working in situations where it's valid?

[studiot]

The history in Wiki shows that the ideas behind the Kinetic Theory predate experimental proof by several centuries.

 

Maybe Enthalpy's timing is a bit off, but I take his point and have already commented on Brownian motion, which can be observed directly.

 

I would, however, support Bignose's assertion that the motion is in principle classically deterministic, not random, as claimed in the Wiki article.

 

http://en.wikipedia.org/wiki/Kinetic_theoryI

 

I would also like to add that I consider that the Kinetic Theory, in its various guises and developments, is one of the most important and satisfying theories in classical Physics.

Edited August 14, 2014 by studiot

[Bignose]

If we however, consider from the point of view of a particular area or point being bombarded by these particles, the variable recording the time of bombardment takes on the mantle of a random variable, does it not?

That's what I meant when I commented that we normally deal with the averages of quantities and that there are errors bars around any average quantity.

 

The actual theory is deeper, of course, but if we are hung up on whether kinetic theory is still valid or not, I am hesitant to discuss anything deeper at this time.

[matterdoc]

Thanks to all for illuminating comments.

@studiot

 

I have nothing against kinetic theory. It works admirably in its area. My doubt is only about one of its assumption being changed to a fact without having a definite mechanism or causes for action.

 

Explanation on Brownian motion is also based on the same assumption. Here again no mention of a logical mechanism of action. Having the same assumption, working in different areas does not make it a fact.

 

@swansot

 

Every physical action should have a prior cause. Nature follows strict cause and effect relation.

 

@Bignose

 

All references on kinetic theory of gas give ‘continuous, rapid, random motion of gas particles in linear direction’ as one of the assumptions used.

 

Nainan

[swansont]

 

Every physical action should have a prior cause. Nature follows strict cause and effect relation.

 

 

And yet we have things like radioactive decay. IOW, not so much.

[Sensei]

I have nothing against kinetic theory. It works admirably in its area. My doubt is only about one of its assumption being changed to a fact without having a definite mechanism or causes for action.

 

Explanation on Brownian motion is also based on the same assumption. Here again no mention of a logical mechanism of action. Having the same assumption, working in different areas does not make it a fact.

 

Mechanism for Brownian motion is conservation of energy and momentum..

 

Every physical action should have a prior cause. Nature follows strict cause and effect relation.

 

Every single day gases in atmosphere are heated by photons, accelerated, then giving their kinetic energy to surrounding them gas particles, then to solids and liquids on the ground. And energy is spread across all particles.

 

If Sun photons would stop arriving to Earth, all gas would freeze, and you would no longer have Brownian motion.

 

[studiot]

 

matterdoc

Explanation on Brownian motion is also based on the same assumption. Here again no mention of a logical mechanism of action. Having the same assumption, working in different areas does not make it a fact.

 

I offered no explanation of brownian motion. I did, however offer direct observation more than once since you were seeking experimental evidence.

 

Have you ever seen Brownian motion, it is a simple experiment to implement?

[Strange]

 

Explanation on Brownian motion is also based on the same assumption. Here again no mention of a logical mechanism of action. Having the same assumption, working in different areas does not make it a fact.

 

Didn't some guy called Einstein describe this in terms of the thermal movement of atoms?

 

Are you (in your usual vague and evasive way) trying to say that atoms don't exist?

[Bignose]

@Bignose

All references on kinetic theory of gas give ‘continuous, rapid, random motion of gas particles in linear direction’ as one of the assumptions used.

All? Sure about that?

 

Cercignani, Illner, and Pulvirenti's The Mathematical Theory of Dilute Gases only starts with: "In order to discuss the behavior of a system of N (identical) hard spheres it is very convenient to introduce the so-called phase space, i.e., a 6N-dimensional space where the Cartesian coordinates are the 3N components of the N position vectors of the space centers and the 3N components of the N velocities."

 

Absolutely nothing about randomness at its basic assumption here.

 

Chapman and Cowling's The Mathematical Theory of Non-Uniform Gases, Third edition starts with defining variables for a particle's velocity and position. Then deriving terms based on different kinds of averages over distributions of velocities and positions, like mean speed and density. Nothing about randomness at all.

 

Again, as I wrote above, it is possible to solve the Liouville equation that exactly solves how the entire ensemble evolves in time. But, as with the beginning of the Cercignani et al. text, if you have N particles, you have 6N dimensions required to describe that ensemble. If N is 1000, then your Liouville equation has 6000 dimensions in it! And 1000 particles is almost never enough to describe anything useful.

 

The randomness in the equations comes in because we ensemble average over the distribution of all the particles. We want to reduce that 6N dimensions down to 6, in order to make the possibility of solution at least somewhat tenable. That averaging does introduce some statistical randomness.

 

But, that randomness at this point is only introduced to reduce the dimensionality of the problem. NOT as inherent in the model itself. This may be a subtle point, but an important point nonetheless. The fundamental model of kinetic theory of gases -- billiard balls that undergo perfectly elastic collisions -- do not need randomness built into it. The randomness it displays comes from perfectly deterministic beginnings.

 

This is best evidenced by discrete element modeling simulations. Simulations where 1000s of spheres are modeled completely deterministically and allowed to evolve over time. These DEM simulations demonstrate gas-like behavior without having to introduce any random motion whatsoever.

Edited August 16, 2014 by Bignose

[studiot]

I have been trying to offer rational discussion of the Kinetic Theory with you, but you seem to prefer disputing minor points with others.

 

A really good description and history, both mathematical and physical is to be found in the chapter devoted to the Kinetic Theory of (IMHO) the best Physical Chemistry textbook ever written.

 

Physical Chemistry by W Moore. ( I like the 4th edition although I also have later).

 

Moore does not mention random in his definition of the motion of molecules.

 

 

The simplest kinetic-theory model of a gas assumes that the volume occupied by the molecules may be neglected compared to the volume. It is further assumed that the molecules behave like rigid spheres, with no forces of attraction or repulsion between them except during the actual collisions.

 

He does, however note that it is a model and he goes on to develop much more sophisticated kinetic model, including what it would be like if the motion were random.

 

The fact that it is a model is important for two reasons developed in my sketches below.

 

Firstly because if we consider fig1 which is a hollow tube carying particles.

There is a flux of particles in one end and out the other.

 

If we wish to model this we may find that exact calculations are too onerous and may be replaced with another function or mechanism that has the same flux at each end, but is mathematically much simpler to evaluate.

 

This process is much used in numerical maths as I will return to in fig2.

 

For a zero flux the assumption of a random motion mechanism has has the same end fluxes and is much much simpler to calculate since it is an averaging calculation.

 

It is so good that if we replace the tube with a bar and the gaseous flux with an electron flux we can explain the operation of a PN junction (and thus the transistors in this computer), using the drift and diffusion equations for the model.

 

 

Not only that but the principle is appropriate when we do finite element analysis (FEA) as in fig2a.

 

The values of the desired (or measured) function are exact at mesh points A, B etc, so we look to replace the difficult or impossible to solve actual function with an approximating simple one that has the same values at the mesh points.

Then we shrink to mesh to a fineness where the difference throughout the region is immaterial.

 

So the randomness is not a prerequisite it is just that a gas behaves as if its molecular motion was random when a large enough number of particles are involved.

 

 

 

 

 

[matterdoc]

Dear Studiot,

 

Please note that I have no argument against ‘Kinetic theory of gas’. My doubt (expressed in my first post) is how come an assumption used in it has transformed itself into a real fact without a proper mechanism that relates them and lead towards equating energy with motion (by many). I think it is only fair that a logical mechanism of action is required before equating them. In other words, I am interested to know how does energy move a matter-particle.

Thanks,

Nainan