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dolimitless
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[*] posted on 8-10-2009 at 17:21
Why are atoms in constant motion?


Why are all atoms in constant motion? It is just a fundamental phenomena of our world? Can someone explain the theory behind this?

Why does decreasing/increasing the "temperature" affect the speed (kinetic energy) of atoms? Again, can someone explain the fundamental theory behind this?
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[*] posted on 8-10-2009 at 17:41


Quote:

Why does decreasing/increasing the "temperature" affect the speed (kinetic energy) of atoms?


For the 2nd question:

Speed is changed by transfering energy to or from the atoms, eg, by heat transfer. Temperature is just a measurement of that speed.




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[*] posted on 9-10-2009 at 07:30


Since no one else is offering I will take a stab at the 1st question.

At 0 deg K (absolute zero) the molecules are not in motion. As energy is added it has to be taken up in some form. This can be vibratory, rotational, or translational motion, or other forms. If taken up as translational motion this will be called kinetic energy and is quantified as (mv^2)/2.

To the fundamental why? Why not? Or, why anything?




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entropy51
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[*] posted on 9-10-2009 at 07:57


Like Magpie, I hesitate to try this because I know we have some good physical chemists here who could answer much better than I can. But so far none of them have answered the question. I looked at the statistical thermodynamics textbooks, and there's no anser to be found. Yeah, the Boltzmann distribution, blah, blah. Atoms of gas must lose energy when they collide with the walls of their container, right? So why don't they lose their energy, stop moving, and slow down? I'm frustrated that I don't know the answer, but encouraged that no one else seems to know it either.:P

Some things are just fundamental, such as the fact that atoms contain electrons. I don't think anyone knows why, it's just the way the universe is. Developing a theory around the concept of electrons allowed the development of chemical theories which are consistent with observation. Thus we have come to accept the concept of electrons as constituents of atoms, although the concept had to be modified to accomodate some other observations and these modifications are quantum theory.

Atoms have motion, as evidenced by the diffusion of Br2 vapor across a room when you open a bottle in the corner. Soon the entire room smells of bromine.

The motion of atoms was postulated to explain the concepts of temperature and pressure in the kinetic theory. Pressure is a manifestation of atoms colliding with the walls of their container. This postulate allowed the successful explanation of many physical phenomena, and it fits the observed facts.

Hopefully one of you can do better than that, but it's my story and I'm sticking with it until you do.

[Edited on 10-10-2009 by entropy51]
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[*] posted on 9-10-2009 at 09:15


The reason is generally because of degrees of freedom on a massive (statistical) scale.

Gasses are made of molecules,which are free to move. That motion corresponds to energy. Solids are rigid, but springy, and that springiness can contain energy. What we call 'temperature' is the background energy stored in these media. Many systems, from nuclear spins to ionized atoms, contain energy of various sorts, and when a lot of those elements are brought together and allowed to interact, the integral over all the elements in all their states represents their thermal properties. This is the essence of statistical mechanics and thermodynamics.

Gasses are composed of molecules which are free to move in three dimensions (translational degrees of freedom), with additional degrees of freedom at higher temperatures: rotational at room temperature; vibrational at higher temperatures, dissociative higher still (as in a flame), then ionizing (as in plasma). Each stage has a certain minimum activation energy before its states are occupied, which means that there are more states available at higher energies, which means the specific heat always rises as temperature rises.

In a solid, atoms fit together in a somewhat "springy" network. Imagine a lattice of ball bearings held together with springs, then imagine tugging on one. You'll see waves propagate from that atom, throughout the lattice. These waves are called phonons, and have a maximum frequency (and therefore, in quantum terms, energy) corresponding to the time constant of the mass-spring system. These waves are constantly reflecting back and forth, and other sources and sinks of energy are constantly transferring energy back and forth: this is how your hot plate heats the air, or how your freezer keeps things cold.

BTW, depending on exactly how you want to interpret quantum mechanics, nothing is standing still at absolute zero. If it had a constant position (delta x = 0), its momentum would be infinite (delta x * delta p >= hbar/2), which isn't possible. Also, if its position dropped to zero, matter would collapse, which also isn't observed: matter keeps almost the same dimensions near 0K as at room temperature (the thermal expansion coefficient is small). "Zero point energy" is the minimum amount of energy that a system can have, and this is actually the state of the system at absolute zero.

And to cover the subject completely, the minumum energy state is the lowest energy state found in the system's solution in the Schroedinger equation. For instance, atomic states are ranked with n = 1, 2, ..., with n = 1 having the lowest energy state (for the lone hydrogen atom, that's -13.6eV). The position and momentum of the electron in that state are well defined (by which I mean, instantaneous measured values may be measured anywhere, but their average values are finite and nonzero, and equal to the values found), and there is no other possible state for it to decay into.

Tim

[Edited on 10-9-2009 by 12AX7]




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[*] posted on 9-10-2009 at 13:06


See any good textbooks on statistical mechanics, quantum mechanics, and thermodynamics, for the full mathematical explanation; search on Google and in gigapedia.org. It is the basis of "Brownian motion", which also applies to much larger molecules and particles (including ones visible microscopically), besides single atoms. The Brownian translational motion of molecules is responsible for gas pressure, and, increasing in quantum steps with temperature as per the Boltzmann equation, explains why compounds undergo melting and vaporization with increasing temperature.

[Edited on 9-10-09 by JohnWW]
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[*] posted on 9-10-2009 at 13:39


Looking up Boltzmann distribution would also provide some insight.

Having said that, zero point energy is a rather abstract and absurd thing, given the fact that is defined as the energy of an atom/molecule at 0K in the gas phase. WTF? Gas phase at 0K?

[Edited on 9-10-2009 by vulture]




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[*] posted on 9-10-2009 at 14:12


Vulture--is zero point energy defined as the system in the gas phase?? This is the first time I'm hearing this.

Part of the answer to this question stems from the solution of the Schroedinger equation for the harmonic oscillator problem in quantum mechanics; at least, that's a good introduction to it. What you arrive at is a potential well, with different rungs representing different energy states. It looks very much like a ladder...well, a fancy ladder, perhaps created by an artist ;)

Refer to this picture:


I don't want to confuse things too much--but this is actually a diagram of a morse potential curve; but at low energy (which I am discussing) it approximates the harmonic potential well pretty closely) It shows the first few bound eigenstates for a harmonic oscillator system, but this is the potential well I'm referring to.

Theoretically, at 0 K, there should be no translational, rotational, or vibrational energy--this "should" be the only state where motion stops. On the potential well, this is represented as the n = 0 state where rotational and vibrational motion are also equal to 0. However, as you see, the lowest eigenstate (n=1) is NOT at the very bottom of the well. The difference between the n = 0 state and the bottom of the well is the "Zero Point Energy" that has been brought up a few times in this thread. However, one cannot go *below* the n=0 state, so there is always some energy remaining in the system (the atom/molecule)!

Also, if all motion stopped, wouldn't that violate the Heisenberg Uncertainty Principle? delta p * delta x >= hbar/2. With zero motion, p, the momentum operator, would be 0 and the preceding equation would no longer hold true.

However, in discussions with a friend of mine who is enthralled with nuclear chemistry... Research into "low energy nuclear reactions" has been continuing in sort of a quiet manner, but one fascinating bit is the "D-S Cathode" by a Japanese group. It is basically a solid Palladium tube with Palladium black inside. Using only deuterium oxide, they have measured Helium and Tritium leaving the system, in addition to energy gains. However, one opposing explanation is that the atoms have actually gone into a sort of n = -1 state where the electrons have actually collapsed onto the nucleus!

So to digress a bit: either they've achieved low energy nuclear reactions or they've somehow managed to extract zero point energy. Either way, pretty exciting, no?

Again, there are a few physical chemical ways to approach this question, whether through quantum mechanics, statistical kinetics, or thermodynamics. In each case, though, the results are in strong agreement. So WHY are atoms in constant motion? Laws of the universe, brutha; I don't write them, I just follow them :D




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[*] posted on 9-10-2009 at 15:53


I took the simple route to the answer - and that if they stopped, they'd fall over. Almost everything moves. Gas especially, let's keep the gas moving. :P



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[*] posted on 9-10-2009 at 15:54


Both in quantum mechanics and chemical thermodynamics the ZPE is derived from ideal systems in the gas phase, with no interaction between the particles.

There's a type of enthalpy in chemical thermodynamics which is also defined as 0K in the gas phase, but I can't remember which one.





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[*] posted on 9-10-2009 at 18:30


Quote: Originally posted by vulture  
Both in quantum mechanics and chemical thermodynamics the ZPE is derived from ideal systems in the gas phase, with no interaction between the particles. There's a type of enthalpy in chemical thermodynamics which is also defined as 0K in the gas phase, but I can't remember which one.

Entropy is regarded as being 0 at absolute zero, 0ºK, which is unattainable although it can be closely approximated to within millionths of a degree, and at which only zero-point energy (ZPE) would exist. By the Gibbs equation, at 0ºK, enthalpy and Gibbs free energy are equal. Above that, by the Debye model, the specific heat and entropy are proportional to T³, while enthalpy and chemical potential are proportional to T^4. For further info, see http://en.wikipedia.org/wiki/Absolute_zero .
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[*] posted on 9-10-2009 at 18:36


I'm sure glad I didn't throw out my cheesy explanation about super bouncy balls and average velocity being the speed of sound and the lighter balls going faster than the heavier balls, but having the same energy, all while emitting and catching photons.
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[*] posted on 10-10-2009 at 06:20


The far more simple (and thus wrong) explanation that I have been taught up to now is that heat is the same thing as the amount of movement the atoms have. So, at 0 Kelvin, they have no movement.
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[*] posted on 10-10-2009 at 06:28


For those interested in various one-dimensional quantum systems (wells, oscillators, etc), here's an interactive Java applet that lets you play around with the various system parameters and see the wave functions and various energy levels in function of them:

http://www.falstad.com/qm1d/

Also fantastic is the hydrogen atom applet (same page): look at electron orbitals in function of quantum numbers n and l.
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[*] posted on 10-10-2009 at 09:43


and as the Law of Conservation of Energy states, energy is neither created nor destroyed, simply changed from one form to another. eg. Kinetic, Potential, Internal etc

[Edited on 10-10-2009 by devongrrl]
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[*] posted on 10-10-2009 at 10:11


Although I don't think any of us answered the question in a satisfying way, our answers are much better than the answers dolimitless provoked on the Physics Forum

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[*] posted on 10-10-2009 at 12:17


Quote: Originally posted by entropy51  
Although I don't think any of us answered the question in a satisfying way, our answers are much better than the answers dolimitless provoked on the Physics Forum



Pretty much... Some rather vague and 'dumb' answers there...

I would simply say that as long as atoms (or molecules) posses some kinetic energy, they will be in motion: translational, vibrational or rotational.

Temperature being an indirect measure of the average speed of a large number of atoms (or molecules), at absolute zero all motion stops. But these atoms (or molecules) still contain energy: the ground state energy of the hydrogen atom for instance but in more complex atoms also the binding energy of their nuclei.
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[*] posted on 12-10-2009 at 08:15


The real question isn't "why" but, "if those little buggers are going to keep moving no matter what, how can I tether each one of them to a teensy little generator wired up to run my car"?
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[*] posted on 12-10-2009 at 09:11


Quote: Originally posted by jgourlay  
The real question isn't "why" but, "if those little buggers are going to keep moving no matter what, how can I tether each one of them to a teensy little generator wired up to run my car"?


Ya, but I dare you to make a smaller generator that moves slower than those little buggers. Hard to get around when your generator is itself made of them. :D

Tim




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[*] posted on 12-10-2009 at 11:19


And when you start extracting energy (heat or mechanical work) from larger numbers of atoms/molecules (macroscopic systems), the temperature drops and you need to pump some more heat into the (macroscopic) system. That's the working principle of heat engines like steam engines, the internal combustion engine or Stirling engines. See also the http://en.wikipedia.org/wiki/Carnot_cycle Carnot cycle for instance.

It was atomic theory that eventually made us understand what heat was and how to convert it to mechanical work...


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[*] posted on 13-10-2009 at 22:11


From a historical perspective, atoms are in constant motion because of the success of Newtonian law: experimentally, you can drop a ball that starts at rest, and 'drop' a ball that is already moving, and the change in their velocities after a given amount of time (due to acceleration from gravity) would be the same. Naturally, without this 'force', we could not explain why objects move. In addition, this seemingly constant force, acts the same on objects whether they are moving, or whether they are not.

Newton postulated that this indicated that unless a force compels an object to slow down (or speed up), well, the object has no reason to do so - so it doesn't and it retains its' current 'state' (whatsoever that may be), until a force acts upon it to do otherwise. This is Newton's first law, the law of inertia - stated (presumably following Newton's great admiration for Euclid) as what we would probably now consider an axiom (similar perhaps, to how Euclidean geometry is a geometry following certain definitions/axioms). In addition, Newton also realized that the assumption that anything is at rest depends on the frame of reference - though he obviously had no need to create relativistic reference frames due to the lack of experimental necessity to do so, it can be clearly seen in the Principia that he certainly realized that his treatment was from a certain perspective.

In addition, since the great success of the Principia was in the quantitative prediction of the motion of celestial bodies - it doesn't take much effort (look up at night!) to realize that if the Earth revolves around the Sun, and the moon around the Earth, and other celestial objects around other objects (all while rotating, to say nothing of the motions of the constituents of those objects) - there is little reason to assume that there exists something 'not in constant motion'. Then by induction, what Newton realized might be aptly stated (as a koan no less) as such:

Why do I assume that anything is at rest?

From this, much of modern physics followed - and naturally, few people, given the mathematical success of Newtonian law, found it necessary to assume otherwise. And of course, as theory developed, you also get more advanced explanations, but I think the above question (or answer perhaps) really is at the heart of the matter.

I guess that doesn't *actually* answer the question why, since after all, whether or not atoms are in constant motion depends on your acceptance of the Newtonian axioms (and the applicability of such axioms to atoms). But hopefully, it at least makes clear why, based on experiment and observation, such a notion was postulated.

----

As far as your question about temperature: let us first define our question, so that we may analyze it: kinetic energy is a convenient way of representing some measurable quantity, called energy, in this case, energy specifically related to movement. At the time of the postulation of the theory relating temperature to atomic movement, atoms were considered to be the fundamental constituents of the universe. If we think about them classically (that is, following Newtonian law) an atom is like a little planet - and we are just very, very big in comparison. Thus, the kinetic energy we are asking about, is really the total movement of a collection of objects.

Temperature is not initially postulated - rather, temperature is a type of measure, a measure related to the thermometer. When we measure temperature by way of a thermometer, what we are doing is measuring the change in pressure of the fluid inside the thermometer - when something is heated, the pressure of the fluid against the 'air' in the thermometer increases - 'then', this air decreases in volume and concurrently, the volume of the fluid in the thermometer increases, and the thermometer reading increases. Thus, temperature increases,

So, when something is heated, it expands because of the change in pressure. When we think about the thermometer as a closed system, with the fluid inside being the object (or rather, the collection of objects) which causes the change that allows us to measure temperature, we think of a fluid made up of tiny atoms, each with some tiny amount kinetic energy. We must think of what we do to the thermometer that causes us to observe the measurable change of the fluid level (and thus, the reading of the change in temperature). If heating the thermometer causes a change in pressure, and P = F/A (pressure is force divided by area), if P increases while area stays the same - then the force must increase. If pressure decreases while area stays the same, then force must decrease. Since area does appear to stay the same, we must assume that the change in temperature, being related to pressure, is subsequently related to force - if there was no force applied there would be no change in the temperature reading. Thus, if everything related to temperature is made of atoms, then when we heat the thermometer, we must generate a force....

Kinetic energy is 1/2mv^2 (KE is one half mass times velocity squared, by definition) - this is related to F=ma (force is mass times acceleration, by definition), now, acceleration is the derivative of velocity, so that when acceleration changes, the rate at which velocity changes at a given moment in time - also changes. We know that pressure (and thus force) in a thermometer increases when it is heated.

If force increased, and F = ma, and we presume that the mass of an atom does not change, then that means that acceleration must increase, if force increases. Finally, if acceleration increases, the rate at which velocity changes also increases - if acceleration increases, then velocity also increases.

Since KE = 1/2mv^2, that means that kinetic energy also increases if velocity increases. Similarly, if pressure drops, force drops, which means acceleration drops, which means kinetic energy decreases.

Finally, this approach works for one object, and it also works (with some extra additions) on a collection of objects: the collective is analyzed from a statistical perspective, but the reasoning is the same: if the (average) velocity of a collection of things increases, and the kinetic energy of that collection is related to that (average) velocity: so that when (average) velocity increases, so will kinetic energy (and vice versa). Since velocity relates to force, and force to pressure - and pressure the basis for temperature measurements (at least back then): that is how kinetic energy is related to temperature. Once we have formulated a framework for temperature, we can alternatively state temperature by a mathematical definition (although, I personally prefer the measurable definition, 'equivalent' though some may claim them to be).

As aside to the last comment - I don't think anyone can really say anything about '0*K' because, we would never know when we reached it, since after all - how can you measure a lack of the thing you are trying to measure? Forget *getting* to 0*K, someone let me know when they can convince me that they have 'measured' such a thing! I suppose you could induct a zero-point energy, but that is hardly convincing, being the 'final' inductive step you can do for a while, until the next - so you assume it's the last. Very convincing!! ^_^

[Edited on 14-10-2009 by PainKilla]
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