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The Sources of Thermal Radiation

All material objects with temperatures above absolute zero radiate electromagnetic waves. The energy distribution of this radiation depends upon the temperature and the nature of the material. The source of the energy for this radiation is the thermal aggitation in the material.

The literature on thermal radiation attributes it to the acceleration/deceleration of the charges in the molecules which occur as the result of collisions. The literature also mentions dipole oscillations as a possible source of thermal radiation.

In Appendix I the energy of the most frequent photon of the thermal radiation of H2 at 300° K is determined. In Appendix II it is shown that the acclerations due to collisions of the molecules in a gas account for only about one trillionth of the energy of the thermal radiation. That leaves dipole (and other multi-pole) oscillations as the major source of thermal oscillation. In gases at high temperature there is also ionization and the recapture of electrons as a source of thermal radiation.

In molecules made up of multiple atoms there are various modes of vibration. Those modes of vibration are excited by collisions and near collisions. The molecules are quantized systems and may shift to a lower quantum state by the emission of a photon. This means that the spectrum of emissions will give spikes at discrete frequencies. The spectrum at the spikes is spread over a small range of frequencies due to such things as the Doppler effect. This is seen in the graph of the radiation emissions of water vapor.

Molecules with only two atoms such as O2 and N2 have only one mode of vibration, the stretching of the bond between the two atoms. Triatom molecule such a H2O and CO2 have the stretching of the bonds, symmetrically and asymmetrically. They have a mode of vibration involving the flexing of the angle between the two end atoms in the molecule. The three atoms in these molecules do not lie in a straight line so there is a rotational motion as well. The effect of the various vibration modes show up in the emission spectrum of the molecule at difference ranges of frequencies. The emissions of the triatomic molecular gases are much more extensive than the emissions of diatomic gases.

The continuous part of the emission spectrum of water vapor, which is shown above, resembles in shape that of blackbody radiation.

Blackbody radiation is derived as a thermodynamic equilibrium of a photon ensemble. The continuous parts of the emission spectra of multipole molecules could be the dynamic equilibrium of a system that has an inflow of photons from the oscillations of the molecules and an outflow due to thermal radiation. This would produce a spectrum with some spikes and a continuous part resembling that of blackbody radiation.

Monatomic gases such as the noble gases of helium, neon, argon, krypton and radon have no vibration modes and therefore no emissions except those due to their ionization and de-ionization. The spectrum of monatomic gases is therefore involves only discrete frequencies such as shown below for helium.

Conclusion

There is no doubt that the source of the energy for thermal radiation is thermal energy. The question is what is the mechanism for for the transformation of thermal energy into radiation.The significant source of thermal radiation is the dipole oscillations of the molecules making up a material. These discrete frequencies create a photon gas that evolves a continuous spectrum of radiation by the same mechanism that generates the spectrum of This continuous component of the spectrum of a gas resembles the spectrum of blackbody radiation. The effect of acceleration/deceleration of electrical charges in collisions is quantitative insignificant. At high tempetures the radiation for the capture of electrons by ions is discernable.

This is a satisfactory resolution to the matter of the sources of thermal radiation and it is a bit different from the conventional view. The conventional view attributes thermal radiation to the acceleration/deceleration of electrical charges in the collisions taking place among the molecules of matter through the Larmor formula. Even if the Larmor formula is valid for matter the eff ect on thermal radiation is quantitatively insignificant. The major source of thermal radiation is from the oscillations of dipole (or multipole) molecules. At higher temperatures the ionization and de-ionization (electron capture) effects are also involved. But what is left out of the conventional view is the dynamics of the photon gas created. Not much is known about photon gas except that at equilibrium it assumes the energy distribution associated with Planck's blackbody formula. So when a gas like water vapor is held at a particular temperature the various modes of oscillation of the H2O molecule are excited by collisions. These oscillations can shift to a lower energy state through the emission of photons. This produces a spectrum of radiation involving discrete frequencies. But the interactions involved in the photon gas produces a continuous spectrum approximating the blackbody distribution. The actual thermal radiation from the water vapor is a sum of the two spectra; i.e., the peaked curve of blackbody radiation with spikes at discrete frequencies. These spikes are spread over small ranges of frequencies due to such things as the Doppler effect.


Appendix I: The Wavelength of Thermal Radiation from
H2 at Room Temperature

Wien's Displacement Law says that the most frequent wavelength λmax of radiation for a blackbody at absolute temperature (°K) of T is

λmax =b/T

where b is equal to 0.0029 mK. Thus for a temperature of 300° K the most frequent wavelength of thermal radiation is about 10-5 meters. The energy of a photon of this radiation is

photon energy = hc/λmax
= (6.626×10-34)(3×108)/(10-5)
= 2.0×10-21 joules

Appendix II: Determination of the Energy of a Photon Generated
by the Collision of A Charge

The Lamor formula is

R = (2/3)a²q²/c³

where a is acceleration, q is charge and c is the speed of light. This is the rate of energy generation.

The acceleration generated in a collision is the change in velocity divided by the time involved in the collision.

The charge diameter of a proton is approximately 1.68 fermi = 1.68×10-15 meters. This makes the quantum of time equal to 5.6×10-24 seconds.

The average velocity of an H2 molecule at room temperature (300deg; K) is about 2000 m/s. In a head-on collision with a container wall the direction is reversed. If this takes place in one quantum of time the magnitude of the acceleration is (4×103/5.6×10-24)=7.14×1026. This quantity squared is 5.1×1053.

The charge of the proton is 1.6×10-19 coulombs. This squared is 2.56×10-38. The value of R is the rate of energy generation; the quantity of energy generated in one quantum of time δ is then

Ecol = δR = (5.6×10-24)[(2/3)(5.1×1053)(2.56×10-38)/(2.7×1025)
Ecol = 6.74×10-33 joules

The energy of a photon generated at room temperature by a head-on collision of an H2 molecule with a container wall of 6.74×10-33 joules is a far cry from the energy of 2.0×10-21 joules which is the average photon energy of the thermal radiation from H2 at room temperature (300° K). The acceleration/deceleration photon energy is about a third of a trillion times smaller than the thermal radiation photon energy.

Thus if the transformation of thermal energy into thermal radiation is involved in thermal radiation it is quantitatively insignificant. However there are other reasons to believe the accelerated charge effect is even less significant than the above computation indicates. The spatial distribution of charge results in the charge being divided up into a myriad of small pieces having near infinitesimal total effect. Some physicists doubt the validity of the proposition that accelerated/decelerated charges generate electromagnetic waves. Richard Feynman, for one, believes the Larmor formula and the related Liénard-Weichert formula are not valid.


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