Molecular Kinetic Energy

[Anon E. Mouse]

It is universally agreed that heating a gas increases mean molecular
velocity. My question is: "How does heating a gas molecule increase
its kinetic energy?

I am interested in listening to other peoples opinions but I also
appreciate citations when appropriate.

Thanks you for your consideration or contribution,

AAG

[[Mod. note -- It's not clear to me what "heating a gas molecule"
(emphasis on the "a", i.e., this is a *single* gas molecule) means,
at least as it refers to translational degrees of freedom. (Internal
degrees of freedom are a separate issue.) How do you increase the
variance of a sample of size one?

This reminds me of a reference which is peripherally related:
Wang et al,
"Experimental Demonstration of Violations of the Second Law of
Thermodynamics for Small Systems and Short Time Scales"
Phys. Rev. Lett. 89, 050601 (2002)
http://link.aps.org/abstract/PRL/v89/e050601
http://adsabs.harvard.edu/abs/2002PhRvL..89e0601W
-- jt]]

[holog]

On May 19, 12:30=A0pm, "Anon E. Mouse" <agall...@gmail.com> wrote:
> It is universally agreed that heating a gas increases mean molecular
> velocity. My question is: "How does heating a gas molecule increase
> its kinetic energy?
>
> I am interested in listening to other peoples opinions but I also
> appreciate citations when appropriate.
>
> Thanks you for your consideration or contribution,
>
> AAG

you answered your own question, by increasing velocity you increase
energy, the question should be - how much energy applied to an atom
would cause it to jump, or how much can it hold before it jumps.

holog

[Moderator's note: The original poster was talking about the kinetic
energy of a molecule, while the response about jumps seems to involve
internal degrees of freedome, e.g. exciting atoms via absorption of
radiation. -P.H.]

[Phillip Helbig---undress to reply]

In article
<4c5e5d13-2ad8-482b...@em1g2000vbb.googlegroups.com>,

"Anon E. Mouse" <agal...@gmail.com> writes:

> It is universally agreed that heating a gas increases mean molecular
> velocity. My question is: "How does heating a gas molecule increase
> its kinetic energy?

Heat is a statistical quantity which by definition applies to a sample
of particles. Thus, one cannot speak of heating ONE gas molecule. Heat
is a measure of the average kinetic energy, so the question "how" is
really moot: more kinetic energy and more heat are the same thing,
though the latter is only a useful concept for a group of particles.

[Giorgio Pastore]

I agree about the statistical nature of heat. However, in a well
definite way, one can speak of heating a single molecule.
Actually, it is what everybody does every time one is speaking about
heating of a perfect gas. The perfect gas can be thought as made by non
interacting molecules. Still it can be equilibrated or heated simply by
means of many interactions of each molecule with the container walls. Of
course statistics and averages are required, but only over many collisions.

Notice, that I am not claiming that the behavior of the single molecule
fully agrees with thermodynamics (for instance, the one-molecule system
is trivially non extensive). I am just writing that one can meaningfully
speak about "heating a singe molecule".

There is also another point in your answer that would require some
conceptual/linguistic correction: in the technical language of physics
heat is not the same as kinetic energy. The object directly related to
kinetic energy is temperature. Heat is just a special flux of energy.
Often, an incoming flux of heat, increasing the energy of a system,
increases its kinetic energy as well. But at a (first order) phase
transition energy is increased without any change of temperature (i.e.
of average kinetic energy).

Such a behavior (latent heath) is of course excluded in presence of just
one molecule. Its average kinetic energy can only increase if wall
temperature has been increased.

I think that the answer to the original question is implicit in all the
above comment: heating of a a single molecule goes on through
interaction with the surroundings. A simple mechanism is the sequance of
collisions with wall atoms. Another possible channel for energy changes
is the interaction with the unavoidable blackbody radiation field
present in the cavity (although I would expect this would be a less
efficient mechanism).

Giorgio

[David Staup]

"Anon E. Mouse" <agal...@gmail.com> wrote in message
news:4c5e5d13-2ad8-482b...@em1g2000vbb.googlegroups.com...

Heat is energy, when you add energy to a substance it expresses as an
increase in the average kinetic energy of the molecules unless the energy is
used to occomplish a phase change.

So the answer to your question is:

By definition

[Roland Franzius]

Am 19.05.2012 18:30, schrieb Anon E. Mouse:
> It is universally agreed that heating a gas increases mean molecular
> velocity. My question is: "How does heating a gas molecule increase
> its kinetic energy?

Thats very easy. A box with a single molecule is a thermodynamic system,
if considered as an instance of a large ensemble of equally prepared
systems. The ideal gas merely represents the whole ensemble of one
particel systems in a single box, a thought trick that works for many
purposes except quantum correlation statistics for systems of identical
particles.

The state of this "single molecule in a box" ensemble is a quantum
state, that may be more or less mixed or pure between the edges of pure
energy eigenstates in the configuration space of states in the
appropriate Hilbert space (Schr?dinger wave functions with vanishing
current across the boundaries of the box.


If the ensemble is in a pure state, eg in an free energy eigenstate with
sinus-eigenfunctions and nodes on all boundaries of a cube, this system
may be coupled to a more chaotic system, eg a radiation field of certain
temperature.

According to the laws of quantum thermodynamics, each different
one-particle system in the ensemble aquires or radiates at random some
energy by hopping into another pure state sinus eg.

So, after the exposure of all single particle systems, the distribution
of the molecule ensembles one particle energy over the physical possible
quantum energy spectrum is broader than in the pure state.

Variance of the free particle energy (or the factoring kinetic energy in
more complicated cases of inner potentials) is called temperature and,
provided the distribution is exponential the energy parameter, it is the
mean kinetic energy, too.

The mystery of quantum mixing and randomness lies in the fact, that even
one-particle systems can be in mixed states as contrasted to the
classical particle picture, where one particle cannot be in mor than one
places having a noisy velocity.

The other mystery is the fact, that <p^2> is, at the same time, the
kinetic energy for free particles in state (e^ikx), the repulsive
quantum concentration part of the energy|grad psi|^2 in in bound states
(e^-x^2) and in both cases the variance of the momentum and mean and
variance of energy in the case of exponential energy distributions.

Ok, but this was historical the universal key feature of thermodynamics
that made Plancks idea work.

An article from yesterday will give you some useful information on
infection by and amplification of quantum randomness:

http://www.sciencedaily.com/releases/2012/05/120516093015.htm


--

Roland Franzius

[Anon E. Mouse]

> According to the laws of quantum thermodynamics, each different
> one-particle system in the ensemble aquires or radiates at random some
> energy by hopping into another pure state sinus eg.

It is the proposed mechanism of this hopping and its radiative
conjugate that is of particular interest to me, that and finding the
proper terminology.

A difficulty I have with thermo-quantum-dynamics is that once you
redact all the 64 dollar words you are left with some 16 cent words
like hopping. I am sorry, but I don't think either the large words or
the simple will be of great help to me.

I do appreciate that the effect in question is almost certainly
quantized and my research confirms it is frequency dependent, but
describing the transfer of a quanta of momentum properly is for me
problematic.

I did reference the article you mentioned. My project involves
extracting useful resonances from otherwise chaotic signals. More of a
chaos theory application than a QM problem. None the less, your
comments have a constructive intent and may yet prove very helpful for
me. thank you.

AAG

[David Staup]

"Phillip Helbig---undress to reply" <hel...@astro.multiCLOTHESvax.de> wrote
in message news:jpa81h$g5v$5...@online.de...

moot maybe, but rather simple.... momentum transfer

[Anon E. Mouse]

>
> So the answer to your question is:
>
> By definition

One of my research interests involves coherent black-body radiation.
This is not a typical natural condition for black-body radiation.

[[Mod. note -- The usual meaning of "black-body radiation" in
physics is the thermal radiation emitted by a black body. This is
not coherent. Perhaps you meant to refer to coherent radiation with
a black-body spectrum?
-- jt]]

It is possible here to draw a parallel to natural light and laser
light. What I am attempting to do would then be analogous to the
functioning of a q switched laser. However in my work a narrowly
confined beam would be less useful than a broad beam or a spherical
field radiation.

For this project, it seems as though the coherence of the momenta of
the black-body quanta are of use and heat in the form of induced
temperature changes are a waste product.

Naturally, due to the unusual nature of the project finding a
reasonably standard terminology to use has been a challenge. The
comments of the contributors is much appreciated. I found Giorgio
Pastore's detailed commentary so far most helpful, but my thanks go to
all commentators.

I think that there is a correlation between the Pioneer anomaly and my
work, but there also there is some difficulty expressing the full
mechanism of the thrust, or transfer of kinetic energy.

If the pioneer anomaly is seen as a conservation of radiant energy
(heat) and kinetic energy (thrust) then their finding is that this
mechanism is highly efficient, which seems to match my own findings
which are far more preliminary. This is in contrast to Giorgio's
expectations, and my own as well. Still, it is the only solid data of
which I am aware.

Then there is the question of interpretation. I inter prate the
Pioneer anomaly to equate black body radiation and molecular thrust.
That is my interpretation and not necessarily theirs, nor a finding
that might find support in this forum. As it implies that heat in the
form of a flux of black body radiation can and does efficiently
accelerate molecules changing both their internal and external
kinetics. If this were purely electrodynamics it there would be less
debate. The difficulty seems to lay in the apparently direct transfer
of momenta. A property not necessarily ascribed to black body
radiation.

My thanks to all contributors,

AAG