From molecular vibrational KE to temperature

[A. Monte]

I'm thinking of absorption of infrared radiation by gas molecules. This interaction results in an increase in vibrational KE. For the kinetic definition of temperature only translational energy is considered. Nevertheless as gases absorb infrared their temperature goes up. What are the important mechanisms in transferring vibrational KE to translational KE in gases.
Thanks!

 

[antonima]

Hi Monte,

I think that a part of the answer lies in molecular collisions. As you said yourself, infrared absorptions result in vibrational energy. It seems that when molecules collide they can then impart this vibrational energy to push off of one another, raising the translational energy of both molecules.

 

[kmarinas86]

I'm thinking of absorption of infrared radiation by gas molecules. This interaction results in an increase in vibrational KE. For the kinetic definition of temperature only translational energy is considered. Nevertheless as gases absorb infrared their temperature goes up. What are the important mechanisms in transferring vibrational KE to translational KE in gases.
Thanks!

You can think of vibration as an oscillation between different translational modes.

To transfer vibration to translation KE in gases, the gases must be able to travel longer distances between collisions.

This can be done by expanding the gas via adiabatic expansion. This cools the gas and converts vibratory energy into translational energy (translating outwardly).

In a way, vibratory energy can be thought of as being due to acceleration around an imaginary mobile pivot that progresses at a speed of translation. Also note that, if you simply shrunk a convective cell to the nano-level, it will look like a vibration. That's not to say all vibration is simply a bunch of tiny convective cells (or not). You might realize that what counts as vibratory vs. translation, or static vs. moving, is arbitrary because it depends on the scale in which you consider the gas moving or stationary. A jar of "still" air has particles moving at the speed of sound in air. Whether you consider gas itself to be still or in persistent translating motion will probably depend on the time scale of your analysis. If you are considering nanosecond intervals, then you might be looking at individual gas molecules as having mainly translating motions between collisions. At human time-scales however, there will be so many collisions, we will probably consider the particles of "still" air to be vibrating rather than translating.

A macroscopic rotating convective cell can be thought of as a mish-mash of different zones having different translational modes. Eddies can actually form a bigger wave, through constructive interference, so sometimes some zones of these smaller vibrations can go in sync, and in parallel, causing large scale translations, dampened over an extended period of time.

A laser is a device that can convert vibratory motion to linear motion in a most obvious way.

 

[A. Monte]

Thanks antonima and kmarinas86!

I had thought about this in terms of energy being transferred from smaller to larger spatial scales (from eddy to mean flow or constructive interference) but am still not very clear why there is a net transfer from smaller to larger scales. Would it be because translational movement has more degrees of freedom than vibrational movement?

kmarinas86: I think I understand your argument about the distinction between translation and vibration being arbitrary, still, in terms of temperature as a measured quantity, is translation (or continuous displacements above a certain spatial scale) not the relevant parameter? This distinction seems, for example, to be important in explaining the difference in specific heat between gases, where gases with more complex molecular structure (and hence more vibrational modes) have higher specific heat because a larger fraction of the gained/lost energy is stored/removed from vibrations?

Nice video too, and narrated by The Shatner, always a plus!

 

[kmarinas86]

Thanks antonima and kmarinas86!

I had thought about this in terms of energy being transferred from smaller to larger spatial scales (from eddy to mean flow or constructive interference) but am still not very clear why there is a net transfer from smaller to larger scales. Would it be because translational movement has more degrees of freedom than vibrational movement?

When we say the "atomic scale", "human scale", "planetary scale", or "galactic scale", we are really talking about systems whose motions are defined in terms of their boundary or extent of motion in the sense of:
[1] The distance between collisions, or
[2] The "radius" of curvature traced by the path of the matter.

The net transfer of energy from smaller to larger scales is therefore all about increasing the distance mass can travel before interacting with other matter, and, less often in our world, increasing the radius about which some mass moves around some other mass.

We inadvertently do this by means of releasing chemical, nuclear, and other energies that are derived from the substance of matter. We also do this by doing expansion work in thermodynamic engines.

I say "inadvertently" because we normally do not think of moving energy from smaller to larger scales when we do so. Instead we tend to think of substances as "energy sources", without reference to any particular scales at which energy may interact. Nonetheless, energy transfer from small scales to large scales is a very real thing indeed.

kmarinas86: I think I understand your argument about the distinction between translation and vibration being arbitrary, still, in terms of temperature as a measured quantity, is translation (or continuous displacements above a certain spatial scale) not the relevant parameter?

It would be helpful to keep in mind that heat transfer by conduction is limited in scale. It occurs as a result of random collisions between the electric fields of particles. This occurs only at the atomic and molecular scales.

However, other forms of heat transfer, such as that from radiation, are not limited to atomic and molecular scales.

So continuous displacements above a certain spatial scale may be important, but which spatial scale matters here may depend on the degree of thermal contact that is suitable to conductive heat transfer, relative to the the amount of heat that is produced as a result of "black body" or "gray body" radiative emissions.

If, from the center of mass frame of a two-body system, you have two "black bodies" of consideration:
[1] A lighter, fast-moving cold body.
[2] A heavier, slow-moving hot body (of the same shape).

Let's say the motions of the two share the same line. So we have motion only along, say, the x-axis.

In the center of mass frame, the momenta of the two bodies must be equal and opposite, and the velocity ratio of the objects must be inverse to the mass ratio of the objects.

For calculation of kinetic energy, the velocity squares, but the mass does not.

From there, you can easily see that the lighter, fast-moving cold body has more "gross" kinetic energy than the heavier, slow-moving hot body.

You will easily see that if the cold body and hot body are not in contact in such a way as to transfer energy by an inelastic collision with each other, more energy will flow from the hot body to the cold body (in the form of radiative heat).

However, using simple logical reasoning, you can see that in an inelastic collision between the two, the lighter, fast-moving body will transfer energy to the heavier, slow-moving hot body. While both objects get "hotter to the touch", the energy gained by the heavier, slow-moving hot body mass exceeds what it gives off to the lighter, fast moving cold body. Here, the cold body does work on the hot body in excess of the converse.

If the cold body and the hot body are both the size of say, grapefruits, then we would assume that it was not heat which was transferred from the former to the latter, but simply mechanical work.

However, if the cold body and the hot body are both microscopic, what we conclude is that the faster moving body is actually hotter than the slower moving body and that the collision of the former with the latter involves a conduction of heat from the former to the latter.

In other words, if you have objects labeled A and B, what object is "hotter" than the other will depend on the "gross kinetic energy" it has when evaluated on a particular scale.

In a simple situations, a hotter particle (with the same number of degrees of freedom) has more gross kinetic energy at all scales (think wavelengths). The blackbody radiation intensity diagram for different temperatures shows intensity, which correlates with energy possessed at different wavelengths or "scales of matter", per degree of freedom, clearly depicting a case where hotter objects are deemed to have more intensity at all scales than colder ones.

However, when such is not the case, the result may be energetic oscillations between different scales of matter.

This distinction seems, for example, to be important in explaining the difference in specific heat between gases, where gases with more complex molecular structure (and hence more vibrational modes) have higher specific heat because a larger fraction of the gained/lost energy is stored/removed from vibrations?

Right.

 

[antonima]

However, using simple logical reasoning, you can see that in an inelastic collision between the two, the lighter, fast-moving body will transfer energy to the heavier, slow-moving hot body. While both objects get "hotter to the touch", the energy gained by the heavier, slow-moving hot body mass exceeds what it gives off to the lighter, fast moving cold body. Here, the cold body does work on the hot body in excess of the converse.

If the cold body and the hot body are both the size of say, grapefruits, then we would assume that it was not heat which was transferred from the former to the latter, but simply mechanical work.

However, if the cold body and the hot body are both microscopic, what we conclude is that the faster moving body is actually hotter than the slower moving body and that the collision of the former with the latter involves a conduction of heat from the former to the latter.

I like what you did there


IRT I like this problem because it of how simply it can be addressed by conservation laws. An incoming photon of light cannot raise the momentum of a gas molecule by a considerable amount because a photon carries only very little momentum. There will always be excess energy in the photon which will be held by the molecule's various vibrational conformations. This energy can be re-radiated (momentum allowing) or it can react with another molecule's vibrational energy levels in such a way that overall momentum is conserved.

 

[antonima]

IRT I like this problem because it of how simply it can be addressed by conservation laws. An incoming photon of light cannot raise the momentum of a gas molecule by a considerable amount because a photon carries only very little momentum. There will always be excess energy in the photon which will be held by the molecule's various vibrational conformations. This energy can be re-radiated (momentum allowing) or it can react with another molecule's vibrational energy levels in such a way that overall momentum is conserved.

This isn't as clear as I would like it to be. Instead:
a single gas molecule cannot gain considerable momentum, and so velocity, from absorbing a photon. However, a macro scale gas most certainly gains translational energy by absorbing photons. Thus, two or more particles have to be involved when translational energy is produced.