Wien's Law Research Articles

A wien displacement law for impact radiation

A flash of radiation is produced when a hypervelocity projectile strikes a target. By the term hypervelocity, we mean a collision in which the sound speeds characterizing the materials in the target and the projectile are less than the impact velocity. When the temperature and pressure ahead of the shock are low, it can be shown that the temperature, T o, behind the shock varies quadratically with impact velocity, v. If the shocked material and the radiation it emits are in thermodynamic equilibrium, the initial intensity of the radiation varies according to T 4 o, so that we obtain, finally, I ∼ v 8. Because I is the total radiated power per unit area of the source, integrated over all wavelengths, it can be accurately measured only by a detector with a very wide spectral response. If a detector having a limited spectral response is used instead, one observes I ∼ v z, where the value of z depends on the detector. Although such a detector will not, in general, be able to confirm the v 8 rule, it may be able to confirm that the wavelength of maximum emission satisfies λ max ∼ 1/v 2, a result which can be derived from the Wien displacement law under the same assumptions used to obtain the velocity dependence of the source intensity. To confirm the Wien law, the response time of the detector must be less than 1 ns for a shock release temperature of 100 kK and less than 1 μ s for shock release temperature of 10 kK. Between these limits, the required response time decreases as the release temperature increases.

Reprocessing in Luminous Disks

We develop and investigate a procedure that accounts for disk reprocessing of photons that originate in the disk itself. Surface temperatures and simple, black body spectral energy distributions (SEDs) of protostellar disks are calculated. In disks that flare with radius, reprocessing of stellar photons results in temperature profiles considerably shallower than r(sup -3/4). Including the disk as a radiation source (as in the case of actively secreting disks) along with the stellar source further flattens the temperature profile. Disks that flare strongly near the star and then smoothly curve over and become shadowed at some distance (decreasing curvature disks) exhibit nearly power-law temperature profiles which result in power-law infrared SEDs with slopes in agreement with typical observations of young stellar objects. Disk models in which the photospheric thickness is controlled by the local opacity and in which the temperature decreases with radius naturally show this shape. Uniformly flaring models do not match observations as well; progressively stronger reprocessing at larger radii leads to SEDs that flatten toward the infrared or even have a second peak at the wavelength corresponding (through the Wien law) to the temperature of the outer edge of the disk. In FU Orionis outbursting systems, the dominant source of energy is the disk itself. The details of the reprocessing depend sensitively on the assumed disk shape and emitted temperature profile. The thermal instability outburst models of Bell Lin reproduce trends in the observed SEDs of Fuors with T varies as r(sup -3/4) in the inner disk (r approx. less than 0.25au corresponding to lambda approx. less than 10 microns) and T varies as r(sup -1/2) in the outer disk. Surface irradiation during outburst and quiescence is compared in the region of planet formation (1 - 10 au). The contrast between the two phases is diminished by the importance of the reprocessing of photons from the relatively high mass flux outer disk (dot-M = 10(exp -5) solar mass/yr) which is present during both outburst and quiescence.

General interpolation equations for the calibration of radiation thermometers

Many interpolation equations used in the calibration of radiation thermometers are semi-empirical in nature, providing little information on the characteristics of the thermometer. In this paper a systematic approach is taken in the derivation of two general interpolation equations, the first based on Wien's law and the second on Planck's law. Because these equations are based on physical principles they can be used with increased accuracy and confidence over semi-empirical equations, and their limitations are easily understood. The two general equations provide a framework for the development of specific equations for radiation thermometers and for the understanding of the relationships of interpolation equations to the effective wavelength formulation currently employed in radiation thermometry.

The extension of the split window technique to passive microwave surface temperature assessment

The theoretical study of both land and sea surface temperature remote sensing is treated through investigating the extension to the microwave region (1-100GHz) of the split window technique, usually used in the thermal infrared region for sea surface temperature measurements. The study of land surface temperature shows that, in both regions (infrared and microwave), the influence (of atmospheric water vapor content and surface emissivity) is critical. The theory is based on the Radiative Transfer Equation, which assumed solutions can be given in both spectral regions, with respect to Wien's and Rayleigh-Jean's laws, respectively. The surface temperature determination is studied in connection with the surface emissivity in both infrared and microwave regions determined with an iterative process. Infrared data is provided by the sensor Advanced Very High Resolution Radiometer (AVHRR) and microwave data by Special Sensor Microwave/Imager (SSM/I), through the WETNET program, directed by NASA/HQS.

The temperature and the infrared luminescence of the uvenil fracture surface of glassy polymer

The fracture of solids is accompanied by such physical and chemical phenomena as emissions of electrons, ions, photons and molecular particles. The understanding of the mechanisms of all these processes is impossible without the knowledge of the uvenil fracture surface (UFS) temperature. In this research the temperature of UFS of glassy polymer polymethylmethacrylate (PMMA) was measured in time range 10–60 μs after the specimen rupture. The emissional infrared (IR) spectroscopy was chosen as an investigation method, that allows to obtain the Planck spectrum of the heat irradiation of the object, and by position of the maximum ( λ max) on the spectral curve with the application of Wien law ( λ max T=2896 μ m · K) to determine the radiating zone temperature of the progressing crack and of the UFS. It was shown that the IR emission spectrum contains two main components: the Planck (or “heat”) component and the characteristic (or luminescent) one. The UFS warming-up of the PMMA does not exceed 200°C. The temperature field in the vicinity of the top of the running crack and UFS of PMMA was calculated with the help of Rosenthal-Weichert-Schonert theoretical model. The kinetics of UFS cooling of PMMA, which is in a good agreement with the experimental one in long time (tens of μs) has been obtained. In the range of short time (smaller than 10 μs) the experimental data are absent while the calculation given the value of maximum warming-up in the same time range (on the top of the running crack) ∼ 250°C.

Thermodynamics, dynamics and relaxation in glass‐forming liquids ‐ the conformon concept

AbstractAny interpretation of the dynamics in liquids requires understanding of fluctuating collective motions in the stationary limit. To this end, “eigen‐states” are defined, named conformons. Conformons are to be considered as a new type of bosons. Their properties characterize the typical features of the dynamics in disordered systems. Eigen‐energy and “eigen‐entropy” are adjusted to each other to minimize the free energy of each mode (saturation). The whole conformon ensemble exhibits a photon statistics with a broad universal mode spectrum. Analogues of Stefan‐Boltzmann's law and of Wien's displacements law are formulated.A crucial point of our treatment is that conformons should, in principle, only become excited above a system‐typical temperature To (Vogel‐Fulcher temperature). Equilibrium properties of supercooled liquids are necessarily related to To. Cp/Cv, of the conformon ensemble should, for example, show a typical ΔT3‐dependence (ΔT=T‐To). Experimental data give evidence in support of this behaviour. As a consequence of the excluded volume supercooled liquids already solidify about 30 to 40 degrees above To at least at the quasi‐static glass temperature Tg.Relaxation in the glass transition regime of glass formers can fully be described if relaxation modes are connected to each conformon. The description covers a set of experiments so different like mechanical and dielectric relaxation or quasi‐elastic light‐ and neutron scattering.

Real Planck distribution for a complex Q-boson gas

We discuss the energy-density distribution for a gas of q-bosons with complex deformation parameter by exploiting a new q-complex oscillator algebra in which both the number operator and the energy eigenvalues are real. The corresponding Planck distribution generalizes the results obtained for a real q-boson gas, including Wien's and Stephan's laws, and the role of an effective Planck constant depending on the parameter modulus.

An accurate equation to determine the temperature for optimum efficiency of blackbody radiation

The accurate equations to determine the temperatures optimizing the efficiencies of blackbody radiation η(λ, T) and η(λ 1, λ 2, T) have been derived. The relation between Wien's law λ m T = 2897.8 μm · K and the equation first derived in this paper λT m = 3669.7 μm · K is discussed.

Intertheory relations from unified theories

The concept of unified theory is defined in logical and abstract semantic terms, and employed in the analysis of relations between empirical scientific theories. The conceptual framework of the approach applies to binary relations such as the reduction or replacement of one theory by another, and to multiple intertheory relations. Historically, unified theories tend to arise within the contexts of scientific conflicts which they may show susceptible of solution even in the most controversial cases of the logical incompatibility or conceptual incommensurability of competing theories. These conclusions are exemplified by the Planck-Einstein quantum theory of thermal radiation. The analysis shows in which sense it can, and in which it cannot, be said that this theory unifies Wien's law and the Rayleigh-Jeans law of black-body radiation.

The Pulsed Spectrum of the Transient Source A0535+26 in the Hard X-Ray Range

A long observation of the recurrent transient X-ray pulsar A0535+26 was performed when the source was near the maximum of its high intensity level outburst occurred on October 1980. We find a light curve quite different from those observed in previous outbursts. The time averaged pulsed spectrum is well fitted both by a blackbody (kT = 9.0 ± 0.1 keV) and a Wien law (kT = 9.1 ± 0.1 keV). Spectral variability with pulse phase has also been observed.

Hard X-ray emission from the recurrent transient A0535+26 during its 1980 high-intensity outburst

The transient X-ray pulsar A0535+26 was observed on October 4, 1980 during a high level intensity outburst with a balloon borne hard X-ray detector. High statistical quality source spectra were determined up to 100 keV. Both blackbody and Wien laws fit well the data. Pulse phase spectroscopy shows variation of temperature index between 7.5 and 8.5 keV in the off source spectra and between 7.4 and 10.5 keV in the off pulse spectra. The time averaged luminosity above 30 keV is ∼ 8×10 36 erg/s.

Temperature measurement of microcrystals heated by electron bombardment: W tips from 2800K to 3650K

For controlled heating of metal microcrystals up to the melting point, the end of the field emitter tips are bombarded by an electron beam (8 keV, 400 mu A, 200 mu m beam diameter). To measure local temperatures on small areas down to 2 mu m diameter a special one-wavelength micropyrometer was built. Using an optical microscope, an image of the glowing tip was projected on to a screen outside the vacuum chamber. The screen has a movable hole behind which a one-wavelength filter and a photomultiplier are placed to measure local radiant intensities. The relative temperatures are obtained from Wien's law, and are absolutely calibrated by a thermocouple spot-welded on the emitter shank. Local relative temperatures and temperature gradients for a tungsten emitter are measured in the range between 2800K and 3650K, with an error and a stability better than 10K. For absolute temperatures the error is 50K when no evaporation occurs.

Einstein's part in the development of quantum concepts

Einstein's papers on quantum theory over the period 1905-1925 are reviewed. These papers played a fundamental role in the development of quantum concepts. This review traces the relationship between these papers, on the one hand, and Wien's and Planck's theoretical work on thermal radiation and Einstein's own work on statistical thermodynamics, on the other. Einstein's 1905 development of the concept of light quanta from Wien's radiation law, the application of this concept to elementary interactions of radiation with matter, Einstein's 1906–1907 analysis of the Planck radiation law, and Einstein's development of the foundations of a quantum theory of specific heat are all discussed. Particular attention is paid to Einstein's 1909 development of the concept of a particle-wave duality for radiation from a study of the energy and momentum fluctuations in a radiation field. Einstein's 1916 papers on the quantum theory of radiation are analyzed, and it is emphasized that Einstein was the first to suggest a probabilistic interpretation of the particle-wave duality, in addition to introducing coefficients to characterize the probabilities for optical transitions and offering his well-known derivation of the Planck radiation law. There is a special discussion of Einstein's expression, in his 1925 paper on the quantum theory of monatomic ideal gases, of high regard for de Broglie's concept of a particle-wave duality for material particles.

Stimulated Emission and Bose-Einstein Statistics

Einstein's derivation of Planck's blackbody formula using the A and B coefficients for spontaneous and stimulated transition probabilities is reviewed. Application of the Einstein-Fowler equation for statistical fluctuations, 〈(ΔE)2〉 = kT2(δE/δT), shows that two terms contribute to the fluctuations, one from the particle nature of the system and one from its wave nature. When expressed in terms of the average number of quanta n̄, occupying g phase cells, the fluctuations become 〈(Δn)2〉 = n̄ + (n̄2/g). This is exactly the first order variance 〈(Δn)2〉 of a system of n̄ particles distributed among g phase cells in Bose-Einstein statistics. If stimulated emission is omitted in the Einstein derivation, the Wien formula results, and the fluctuations become equal to the single term n̄, which is characteristic of classical statistics. Since the Planck law, which depends on both stimulated emission and stimulated absorption, gives fluctuation in accord with the Bose-Einstein statistics, whereas Wien's law, which depends on stimulated absorption alone, gives fluctuations in accord with classical statistics, it is concluded that the stimulated emission process is the mechanism responsible for the appearance of the Bose-Einstein statistics in blackbody radiation.

On the possible generalizations of Planck’s law

It is suggested that a third universal constant 1 be added to quantum field theory, in addition to h and c. It is proposed that the h-c-1 theory might explain mass spectra and give coupling constants. Using the h-c-1 form of Wien's law and thermodynamic postulates, an h-c-1 form of Planck's law is derived. (T.F.H.)

Planck's Radiation Formula: a Correction

SINCE passing the proofs of my letter which appeared in Nature of April 20* I have found, as a result of a conversation with Dr. G. J. Whitrow, that the conditions prescribed for the radiation formula admit of a more general solution than that of Planck. Any function of I¾ = I½In-3/4 which satisfies the equation meets those conditions. It may be that dimensional or other considerations will be found to impose somewhat severe limits on the form of the function, and it would be possible to invoke the (purely macroscopic and continuous) Wien's law to limit n to the value 1/2, but at the present stage the possibilities appear to be too numerous to justify the statement that Planck's law has been deduced on macroscopic grounds. This statement must therefore be withdrawn.

The freezing-point of rhodium

The International Temperature Scale, which has been in force since 1927 (Bureau International des Poids et Mesures 1927, 1934), is based on certain values assigned to the boiling- and freezing-points of pure substances and on specified means of interpolation between, or extrapolation beyond, these points. The highest basic point of the scale is the freezing-point of gold, defined as 1063-0° C, while for extrapolation from this temperature use is made of the Wien law of radiation with a certain value of the constant c2. Though any temperature above 1063° C is thus completely defined without reference to further fixed points, determinations of such points are of considerable value. In particular, they serve to indicate the degree of reproducibility of the scale and, when well authenticated, to provide secondary standards for its realization in cases where this is more convenient than a primary calibration. A good example of the use of secondary fixed points is the establishment by the National Bureau of Standards, U.S.A., of a scale of colour temperature (Wensel, Judd and Roeser 1934), based on the freezing-points of platinum (1773° C), rhodium (1966° C) and iridium (2454° C).

The freezing point of palladium

The International Temperature Scale, which has been in force since 1927, is based on certain values assigned to the boiling and freezing points of pure substances and on specified means of interpolation between, or extrapolation beyond, these points. The highest basic point of the scale is the freezing point of gold, defined as 1063·0º C, while for extrapolation from this temperature use is made of the Wien law of radiation with a certain value of the constant c 2 . Though any temperature above 1063º C is thus completely defined without reference to further fixed points, determinations of such points are of considerable value. In particular, they serve to indicate the degree of reproducibility of the scale by the various users of it, and, when well authenticated, to provide secondary standards for its realization. Probably the most important of the fixed points referred to are the freezing points of palladium, platinum, rhodium, and iridium. The first-mentioned point has been the subject of considerable investigation in the past and a value of 1555º C has been assigned to it in the list of secondary points given in the appendix to the specification of the International Temperature Scale.

RECENT REVISIONS OF HIGH TEMPERATURES*

AbstractThis paper points out that, to convert temperature values recorded in the literature to the present International Temperature Scale, a correction must be applied which is calculated from the constants that define the particular scale upon which the recorded values are expressed. Applying the same corrections to all previous scales leads, in many cases, to values which depart from the present scale more than the values actually recorded.Examples are given showing the proper method of converting temperature values based on Wien's Law to the International Scale.

The freezing point of platinum

The International Temperature Scale, which has been in force since 1927, is based on certain values assigned to the boiling and freezing points of pure substances and on specified means of interpolation between, or extrapolation beyond, these points. The highest basic point of the scale is the freezing point of gold, defined as 1063·0° C, while for extrapolation from this temperature use is made of the Wien law of radiation, with a certain value of the constant C 2 . Though any temperature above 1063° C is thus completely defined without reference to further fixed points, determinations of such points are of considerable value. In particular, they serve to indicate the degree of reproducibility of the scale by the various users of it, and, when well authenticated, to provide secondary standards for its realization. Of such fixed points the most important has been the freezing point of palladium (1555° C), but the latest developments in furnace technique and refractory materials should now enable the freezing point of platinum to be used with equal, if not greater, advantage. The qualities of platinum which render it especially valuable in this connection are as follows: its freedom from oxidation; its high standard of purity, for which a convenient electrical test is available; its high freezing point (about 1775° C) which approaches the important zone of temperature covered by the electric fighting industry These qualities also make the platinum point especially suitable as the basis for a standard of fight, as has been proposed by a number of experimenters. It is with the two objects indicated above that the National Physical Laboratory has undertaken an investigation concerning the freezing point of platinum the precise scope of which may be defined as follows:— (1) To determine the value of the freezing point in terms of the International Temperature Scale.