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On the Equation which Governs Cavity Radiation II (Revised 12-26-2014)
Abstract
In this work, the equation which properly governs cavity radiation is addressed once again, while presenting a generalized form. A contrast is made between the approach recently taken (P. M. Robitaille. On the equation which governs cavity radiation. Progr. Phys., 2014, v. 10, no. 2, 126–127) and a course of action adopted earlier by Max Planck. The two approaches give dramatically differing conclusions, highlighting that the derivation of a relationship can have far reaching consequences. In Planck's case, all cavities contain black radiation. In Robitaille's case, only cavities permitted to temporarily fall out of thermal equilibrium, or which have been subjected to the action of a perfect absorber, contain black radiation. Arbitrary cavities do not emit as black-bodies. A proper evaluation of this equation reveals that cavity radiation is absolutely dependent on the nature of the enclosure and its contents. Recent results demonstrating super-Planckian thermal emission from hyperbolic metamaterials in the near field and emission enhancements in the far field are briefly examined. Such findings highlight that cavity radiation is absolutely dependent on the nature of the cavity and its walls. As previously stated, the constants of Planck and Boltzmann can no longer be viewed as universal.
Supplementary resource (1)
... It can be applied to any thermal spectrum, whether on Earth in the laboratory, or within any astrophysical context, provided of course, that thermal equilibrium can be demonstrated. † However, if Kirchhoff's Law can be shown to be false, then Planck's equation, while still valid for laboratory blackbodies, loses all universal significance [8,10,[14][15][16][17][18][19]. ...
... Silver walls would prefer to increase their temperature when confronted with an influx of heat, such as that typically used to drive blackbodies in the laboratory (see [8] and references therein). They would not easily maintain their temperature while building a radiation field within a cavity using reflection (see [19] for a discussion). It has also not been established that cavities constructed from walls of low emissivity can contain Lambertian emission. ...
... As such, in order to drive the reflection term, one must try to inject heat into the walls of these cavities, while hoping that additional photons will be produced. But, if one attempts to pump heat into their walls using conduction, for instance, the temperature of the walls can simply increase [18,19]. Nothing dictates that new photons can become available for the buildup of the reflective term, while maintaining the cavity at the same temperature. ...
Affirming Kirchhoff’s Law of thermal emission, Max Planck conferred upon his own equation and its constants, h and k, universal significance. All arbitrary cavities were said to behave as blackbodies. They were thought to contain black, or normal radiation, which depended only upon temperature and frequency of observation, irrespective of the nature of the cavity walls. Today, laboratory blackbodies are specialized, heated devices whose interior walls are lined with highly absorptive surfaces, such as graphite, soot, or
other sophisticated materials. Such evidence repeatedly calls into question Kirchhoff’s Law, as nothing in the laboratory is independent of the nature of the walls. By focusing on Max Planck’s classic text, “The Theory of Heat Radiation’, it can be demonstrated that the German physicist was unable to properly justify Kirchhoff’s Law. At every turn, he was confronted with the fact that materials possess frequency dependent reflectivity and absorptivity, but he often chose to sidestep these realities. He used polarized light to
derive Kirchhoff’s Law, when it is well known that blackbody radiation is never polarized. Through the use of an element, dσ, at the bounding surface between two media, he reached the untenable position that arbitrary materials have the same reflective properties. His Eq. 40 (ρ =ρ′), constituted a dismissal of experimental reality. It is evident that if one neglects reflection, then all cavities must be black. Unable to ensure that
perfectly reflecting cavities can be filled with black radiation, Planck inserted a minute carbon particle, which he qualified as a “catalyst”. In fact, it was acting as a perfect absorber, fully able to provide, on its own, the radiation sought. In 1858, Balfour Stewart had outlined that the proper treatment of cavity radiation must include reflection. Yet, Max Planck did not cite the Scottish scientist. He also did not correctly address real materials, especially metals, from which reflectors would be constructed. These shortcomings led to universality, an incorrect conclusion. Arbitrary cavities do not contain black radiation. Kirchhoff’s formulation is invalid. As a direct consequence, the constants h and k do not have fundamental meaning and along with “Planck length”, “Planck time”, “Planck mass”, and “Planck temperature”, lose the privileged position they once held in physics.
... Not all cavities contain this type of radiation, even if Kirchhoff's law of thermal emission had dictated such an outcome [4,5]. There are demonstrable shortfalls in Kirchhoff's ideas [6][7][8][9][10][11][12][13][14][15] and arbitrary cavities are not black. Everything is very much dependent on the nature of the walls [6][7][8][9][10][11][12][13][14][15]. ...
... There are demonstrable shortfalls in Kirchhoff's ideas [6][7][8][9][10][11][12][13][14][15] and arbitrary cavities are not black. Everything is very much dependent on the nature of the walls [6][7][8][9][10][11][12][13][14][15]. ...
... Nonetheless, if can be shown that the interior of a cavity is lined with a nearly ideal absorber, or subjected to the action of a carbon particle [8][9][10], then it can support black body radiation [15]. It is also possible, under special circumstances, to drive the reflectivity of a cavity through a temporary violation of thermal equilibrium [15]. ...
In this work, the claim that optically thick gases can emit as
blackbodies is refuted. The
belief that such behavior exists results from an improper consideration of heat transfer
and reflection. When heat is injected into a gas, the energy is
primarily redistributed
into translational degrees of freedom and is not used to drive emission. The average
kinetic energy of the particles in the system simply increases and the temperature rises.
In this respect, it is well-know that the emissivity of a gas can drop with increasing
temperature. Once reflection and translation are properly considered, it is simple to
understand why gases can never emit as blackbodies.
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We study super-Planckian near-field heat exchanges for multilayer hyperbolic metamaterials using exact scattering-matrix (S-matrix) calculations. We investigate heat exchanges between two multilayer hyperbolic metamaterial structures. We show that the super-Planckian emission of such metamaterials can either come from the presence of surface phonon-polariton modes or from a continuum of hyperbolic modes depending on the choice of composite materials as well as the structural configuration. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4800233]
We develop the fluctuational electrodynamics of metamaterials with hyperbolic
dispersion and show the existence of broadband thermal emission beyond the
black body limit in the near field. This arises due to the thermal excitation
of unique bulk metamaterial modes, which do not occur in conventional media. We
consider a practical realization of the hyperbolic metamaterial and estimate
that the effect will be observable using the characteristic dispersion
(topological transitions) of the metamaterial states. Our work paves the way
for engineering the near-field thermal emission using metamaterials.
In this work, Kirchhoff's law (Kirchhoff G. Monatsberichte der Akademie der Wissenschaften zu Berlin, sessions of Dec. 1859, 1860, 783-787) is being revisited not only to mark its 150th anniversary but, most importantly, to highlight serious overreaching in its formulation. At the onset, Kirchhoff's law correctly outlines the equivalence between emission and absorption for an opaque object under thermal equilibrium. This same conclusion had been established earlier by Balfour Stewart (Stewart B. Trans. Royal Soc. Edinburgh, 1858, v.22(1), 1-20). However, Kirchhoff extends the treatment beyond his counterpart, stating that cavity radiation must always be black, or normal: depending only on the temperature and the frequency of observation. This universal aspect of Kirchhoff's law is without proper basis and constitutes a grave distortion of experimental reality. It is readily apparent that cavities made from arbitrary materials () are never black. Their approach to such behavior is being driven either by the blackness of the detector, or by black materials placed near the cavity. Ample evidence exists that radiation in arbitrary cavities is sensitive to the relative position of the detectors. In order to fully address these issues, cavity radiation and the generalization of Kirchhoff's law are discussed. An example is then taken from electromagnetics, at microwave frequencies, to link results in the resonant cavity with those inferred from the consequences of generalization.
Since the days of Kirchhoff, blackbody radiation has been considered to be a universal process, independent of the nature and shape of the emitter. Nonetheless, in promoting this concept, Kirchhoff did require, at the minimum, thermal equilibrium with an enclosure. Recently, the author stated (P.-M. Robitaille, IEEE Trans. Plasma Sci., 2003, v.31(6), 1263-1267; P.-M. Robitaille, Progr. in Phys., 2006, v.2, 22-23), that blackbody radiation is not universal and has called for a return to Stewart's law (P.-M. Robitaille, Progr. in Phys., 2008, v.3, 30-35). In this work, a historical analysis of thermal radiation is presented. It is demonstrated that soot, or lampblack, was the standard for blackbody experiments throughout the 1800s. Furthermore, graphite and carbon black continue to play a central role in the construction of blackbody cavities. The advent of universality is reviewed through the writings of Pierre Prevost, Pierre Louis Dulong, Alexis Therese Petit, Jean Baptiste Joseph Fourier, Simeon Denis Poisson, Frederick Herve de la Provostaye, Paul Quentin Desain, Balfour Stewart, Gustav Robert Kirchhoff, and Max Karl Ernst Ludwig Planck. These writings illustrate that blackbody radiation, as experimentally produced in cavities and as discussed theoretically, has remained dependent on thermal equilibrium with at least the smallest carbon particle. Finally, Planck's treatment of Kirchhoff's law is examined in detail and the shortcomings of his derivation are outlined. It is shown once again, that universality does not exist. Only Stewart's law of thermal emission, not Kirchhoff's, is fully valid.
It has been advanced, on experimental P.-M. Robitaille, IEEE Trans. Plasma Sci., 2003, v.31(6), 1263-1267) and theoretical (P.-M. Robitaille, Progr. Phys., 2006, v.2, 22-23) grounds, that blackbody radiation is not universal and remains closely linked to the emission of graphite and soot. In order to strengthen such claims, a conceptual analysis of the proofs for universality is presented. This treatment reveals that Gustav Robert Kirchhoff has not properly considered the combined effects of absorption, reflection, and the directional nature of emission in real materials. In one instance, this leads to an unintended movement away from thermal equilibrium within cavities. Using equilibrium arguments, it is demonstrated that the radiation within perfectly reflecting or arbitrary cavities does not necessarily correspond to that emitted by a blackbody.
In this work, the claim that optically thick gases can emit as
blackbodies is refuted. The
belief that such behavior exists results from an improper consideration of heat transfer
and reflection. When heat is injected into a gas, the energy is
primarily redistributed
into translational degrees of freedom and is not used to drive emission. The average
kinetic energy of the particles in the system simply increases and the temperature rises.
In this respect, it is well-know that the emissivity of a gas can drop with increasing
temperature. Once reflection and translation are properly considered, it is simple to
understand why gases can never emit as blackbodies.
A closed form expression for the local density of electromagnetic states (LDOS) due to a thermally emitting metamaterial bulk is derived from Maxwell's equations combined with fluctuational electrodynamics. The final form is the same as that for nonmagnetic materials, where the influence of the magnetic permeability is embedded in the Fresnel reflection coefficients. Spectral distributions of LDOS near metallic- and dielectric-based metamaterials are investigated. Results reveal that LDOS profiles are dominated by surface polaritons (SPs) in both TE and TM polarization states. A detailed discussion is provided on the necessary conditions for exciting TM- and TE-polarized SPs via a dispersion relation analysis that accounts for losses. Beyond the conventional conditions for excitation of SPs, the lossy dispersion relation analysis demonstrates mathematically that SPs exist when the imaginary parts of the permittivity or permeability, as well as n′n″, are close to zero, where n′ and n″ are the real and imaginary parts of the refractive index, respectively. An asymptotic expression for the extreme near field LDOS is derived, showing a Δ−3 power law relationship, as for nonmagnetic media, between LDOS and distance from the emitting bulk Δ. Results obtained from this study will assist in assessing material properties of arbitrarily electromagnetic materials in applications related to energy harvesting.
A new method is described for evaluating the quality of a blackbody radiator. All earlier calculations given in literature are executed under the simplifying assumption that the reflection of the inner walls of the blackbody is perfectly diffuse. In the present method the actual reflection of the inner surface can be taken into account. The calculation has been worked out for some different types of blackbodies especially the types which are used for the determination of the emissivity of metals. The method was developed for the design of a tubular blackbody required for the determination of the emissivity of tungsten (Physica 20 (1954) 696).
The Radiative Properties and Their Interrelationships Electromagnetic Wave-Surface Interactions Behavior of Ideal Materials Estimation of Radiative Properties Measurement of Thermal Radiation Properties Representative Data on Metallic and Nonmetallic Materials References
A simple derivation is given of the formula for the spectral emission of a thermally excited gas. The accompanying discussion provides a clear answer to the problem of how line emission and blackbody emission of any gas or vapor are interrelated.
The control of thermal radiation is of great current importance for applications such as energy conversions and radiative cooling. Here we show theoretically that the thermal emission of a finite-size blackbody emitter can be enhanced in a thermal extraction scheme, where one places the emitter in optical contact with an extraction device consisting of a transparent object, as long as both the emitter and the extraction device have an internal density of state higher than vacuum, and the extraction device has an area larger than the emitter and moreover has a geometry that enables light extraction. As an experimental demonstration of the thermal extraction scheme, we observe a four-fold enhancement of the far-field thermal emission of a carbon-black emitter having an emissivity of 0.85.
The understanding of far-field thermal radiation had directly led to the
discovery of quantum mechanics a century ago, and is of great current practical
importance for applications in energy conversions, radiative cooling, and
thermal control. It is commonly assumed that for any macroscopic thermal
emitter, its maximal emitted power within any given frequency range cannot
exceed that of a blackbody with the same surface area. In contrast to such
conventional wisdom, here we propose, and experimentally demonstrate, that the
emitted power from a finite size macroscopic blackbody to far field vacuum can
be significantly enhanced, within the constraint of the second law of
thermodynamics. To achieve such an enhancement, the thermal body needs to have
internal electromagnetic density of states (DOS) greater than that of vacuum,
and one needs to provide a thermal extraction mechanism to enable the
contributions of all internal modes to far field radiation.