Planck's Radiation Law Research Articles

In situ high P-T Raman spectroscopy and laser heating of carbon dioxide.

In situ high P-T Raman spectra of solid CO(2) up to 67 GPa and 1,660 K have been measured, using a micro-optical spectroscopy system coupled with a Nd:YLF laser heating system in diamond anvil cells. A metallic foil was employed to efficiently absorb the incoming Nd:YLF laser and heat the sample. The average sample temperature was accurately determined by detailed balance from the anti-Stokes/Stokes ratio, and was compared to the temperature of the absorber determined by fitting the thermal radiation spectrum to the Planck radiation law. The transformation temperature threshold and the transformation dynamics from the molecular phases III and II to the polymeric phase V, previously investigated only by means of temperature quench experiments, was determined at different pressures. The P-T range of the transformation, between 640 and 1,100 K in the 33-65 GPa pressure interval, was assessed to be a kinetic barrier rather than a phase boundary. These findings lead to a new interpretation of the high P-T phase diagram of carbon dioxide. Furthermore, our approach opens a new way to perform quantitative in situ Raman measurements under extremely high pressures and temperatures, providing unique information about phase relations and structural and thermodynamic properties of materials under these conditions.

Current induced light emission from a multiwall carbon nanotube

We investigated the optical emission from a freestanding individual multiwall carbon nanotube through which a current is passing. Since the emission spectra are well represented by Planck's black body radiation law, the optical emission from the nanotubes is assigned to thermal radiation. The average temperature for the sublimation of the nanotubes is estimated to be ∼2540 K from the fitting. Another emission component in the visible region has also been found. The optical and the thermal radiations using Joule heating of the nanotube can be used as a novel nanoscale-processing tool.

Effect of correlations in fitting spectral irradiance data

The uncertainty of a primary spectral irradiance scale based on filter radiometers (FRs) is studied by analysing the propagation of uncertainties and covariances through a spectral interpolation process, when a modified Planck's radiation law is fitted to the measurement data. The advantage of performing the uncertainty analysis in optimizing the selection of the FR wavelengths is demonstrated. We also estimate the effect that correlations in the FR signals have on the uncertainty of the fitted spectral irradiance values. In the case of correlated input data, the results of the uncertainty propagation are found to be within two practical limits: uncertainty values in the FR data and the values obtained by uncertainty propagation with uncorrelated FR signals.

Thermal Equilibrium Between Radiation and Matter

In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation.

The Planck Radiation Law: Exercises Using the Cosmic Background Radiation Data

Max Planck's blackbody radiation law is an early encounter that physical chemistry students have with quantum mechanics. To enhance students' interest, three simple exercises are presented based on the cosmic microwave background radiation data (CBR), the relic from the big bang primeval explosion. The CBR data free from atmospheric effects were obtained in 1989 from the Cosmic Background Explorer (COBE) satellite, which confirmed that all of space is filled with isotropic microwave radiation characterized by a single temperature corresponding to the Planck distribution law. From the radiation distribution data students are asked to find the characteristic temperature, verify Wien's displacement law, and calculate the Stefan-Boltzmann constant. The COBE satellite radiation distribution data (including weighting factors) are given.

The Kelvin and Temperature Measurements.

The International Temperature Scale of 1990 (ITS-90) is defined from 0.65 K upwards to the highest temperature measurable by spectral radiation thermometry, the radiation thermometry being based on the Planck radiation law. When it was developed, the ITS-90 represented thermodynamic temperatures as closely as possible. Part I of this paper describes the realization of contact thermometry up to 1234.93 K, the temperature range in which the ITS-90 is defined in terms of calibration of thermometers at 15 fixed points and vapor pressure/temperature relations which are phase equilibrium states of pure substances. The realization is accomplished by using fixed-point devices, containing samples of the highest available purity, and suitable temperature-controlled environments. All components are constructed to achieve the defining equilibrium states of the samples for the calibration of thermometers. The high quality of the temperature realization and measurements is well documented. Various research efforts are described, including research to improve the uncertainty in thermodynamic temperatures by measuring the velocity of sound in gas up to 800 K, research in applying noise thermometry techniques, and research on thermocouples. Thermometer calibration services and high-purity samples and devices suitable for “on-site” thermometer calibration that are available to the thermometry community are described. Part II of the paper describes the realization of temperature above 1234.93 K for which the ITS-90 is defined in terms of the calibration of spectroradiometers using reference blackbody sources that are at the temperature of the equilibrium liquid-solid phase transition of pure silver, gold, or copper. The realization of temperature from absolute spectral or total radiometry over the temperature range from about 60 K to 3000 K is also described. The dissemination of the temperature scale using radiation thermometry from NIST to the customer is achieved by calibration of blackbody sources, tungsten-strip lamps, and pyrometers. As an example of the research efforts in absolute radiometry, which impacts the NIST spectral irradiance and radiance scales, results with filter radiometers and a high-temperature blackbody are summarized.

The use of self-consistent calibrations to recover absorption bands in the black-body spectrum

High-temperature black bodies used as primary standards of spectral irradiance have to meet several requirements. One important demand is that the spectral irradiance of the black body is uniquely determined by Planck's radiation law, where the (radiometric) temperature of the black body is the only parameter that determines its relative spectral distribution. By combining determinations of the radiometric temperature of a black body over a wide temperature range with the corresponding spectral measurements, black-body spectra for different temperatures can be compared. This allows the use of self-consistency checks to ascertain whether (i) the temperature determinations are coherent over a wide temperature range; and (ii) the different spectral distributions show any deviation from Planck's law. Using this method of self-consistent calibrations, new absorption bands in the spectrum of a black body were discovered at very high temperatures. The level of absorption increases with temperature and depends on the operating conditions and imperfections of the black-body system. Possible origins of this effect are discussed and modifications proposed to avoid such absorption bands.

Experimental investigation on the establishment of a spectral-radiance scale based on a copper-freezing-point black-body radiator

The spectral radiance of a black body can be calculated from Planck's radiation law when the black-body temperature is known. Therefore, the spectral radiance of a black-body radiator of accurately known temperature may be used as a reference for the establishment of a spectral radiance scale. In this paper we investigate the feasibility of using a copper-freezing-point (1357.77 K) black-body radiator to directly calibrate gas-filled tungsten strip-filament lamps operating at a radiance temperature of 2300 K (at 650 nm). A silicon photodetector with a variable-gain amplifier, as well as optical apertures of different sizes, were used to measure the large radiance ratios observed. The comparison was performed at eight wavelengths between 400 nm and 900 nm using interference filters. The major problem encountered was out-of-passband infrared (IR) leakage of the interference filters, particularly those below 550 nm. We discuss the use of sharp-cut glass filters to correct the IR leakage of the filters.

Particle Entropies and Entropy QuantaII. The Photon Gas

We consider a photon gas, which is enclosed in a cavity and is in thermal equilibrium at temperature T. Each photon has a particle entropy σ = ka and a particle energy ε = hv = cp. The particle entropy σ is measured by the dimensionless number a in multiples of the Boltzmann constant k, which serves as an atomic entropy unit. The particle energy ε is related to the frequency Þgn and the momentum p of the relativistic photons, c velocity of light. Particle entropy and particle energy are connected by the temperature, ε = σT. Applying statistical thermodynamics we obtain the thermodynamics of the photon gas, written in particle entropies a. We also get the Planck distribution, and the Planck, Stefan-Boltzmann, and Wien radiation law. - The total entropy S of the photon gas is composed of two parts S

Suggestions for revised definitions of noise quantities, including quantum effects

Recent advances in millimeter- and submillimeter-wavelength receivers and the development of low-noise optical amplifiers focus attention on inconsistencies and ambiguities in the standard definitions of noise quantities and the procedures for measuring them. The difficulty is caused by the zero-point (quantum) noise hf/2 W/Hz, which is present even at absolute zero temperature, and also by the nonlinear dependence at low temperature of the thermal noise power of a resistor on its physical temperature, as given by the Planck law. Until recently, these effects were insignificant in all but the most exotic experiments, and the familiar Rayleigh-Jeans noise formula P=kT W/Hz could safely be used in most situations, Now, particularly in low-noise millimeter-wave and photonic devices, the quantum noise is prominent and the nonlinearity of the Planck law can no longer be neglected. The IEEE Standard Dictionary of Electrical and Electronics Terms gives several definitions of the noise temperature of a resistor or a port, which include: 1) the physical temperature of the resistor and 2) its available noise power density divided by Boltzmann's constant-definitions which are incompatible because of the nature of the Planck radiation law. In addition, there is no indication of whether the zero-point noise should be included as part of the noise temperature. Revised definitions of the common noise quantities are suggested, which resolve the shortcomings of the present definitions. The revised definitions have only a small effect on most RF and microwave measurements, but they provide a common consistent noise terminology from dc to light frequencies.

Some bounds upon the nonextensivity parameter using the approximate generalized distribution functions

In this study, the approximate generalized quantal distribution functions and their applications which appeared in the literature so far, have been summarized. Making use of the generalized Planck radiation law, which has been obtained by us [Physica A 240 (1997) 657], some alternative bounds for the nonextensivity parameter q have been estimated. It has been shown that these results are similar to those obtained by Tsallis et al. [Phys. Rev. E 52 (1995) 1447] and by Plastino et al. [Phys. Lett. A 207 (1995) 42].

Generalized distribution functions and an alternative approach to generalized Planck radiation law

In this study, recently introduced generalized distribution functions are summarized and by using one of these distribution functions, namely generalized Planck distribution, an alternative approach to the generalized Planck law for the blackbody radiation has been tackled. The expression obtained is compared with the expression given by C. Tsallis et al. [Phys. Rev. E 52 (1995) 1447], and it is found that this approximate scheme provides bounds to the exact result, depending on the values of q-index.

Newtonian Gravity, Quantum Discontinuity and the Determination of Theory by Evidence

A closer examination of scientific practice has cast doubt recently on the thesis that observation necessarily fails to determine theory. In some cases scientists derive fundamental hypotheses from phenomena and general background knowledge by means of demonstrative induction. This note argues that it is wrong to interpret such an argument as providing inductive support for the conclusion, e.g. by eliminating rival hypotheses. The examination of the deduction of the inverse square law of gravitation due to J. Bertrand, and R. Fowler's deduction of the quantization of the linear harmonic oscillator's energy spectrum from Planck's radiation law illustrates this point. It is suggested that demonstrative induction is a computational step in fitting a theoretical model and a set of phenomena, with little direct confirmational impact. The thesis of underdetermination, whatever one may think of it, is not threatened by demonstrative induction.

Generalized Distribution Functions and an Alternative Generalization of the Planck Radiation Law

In this study, recently introduced generalized distribution functions are summarized and by using one of these distribution functions (namely generalized Planck distribution), the generalization of the Planck law for the blackbody radiation has been tackled. The obtained expression is compared with that given by C. Tsallis et al. [{\it Phys.Rev.} {\bf E52,} (1995) 1447], and it is found that they are very similar.

Measurement of surface temperature and emissivity by a multitemperature method for Fourier-transform infrared spectrometers

Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single measurement at a known sample temperature, for example, at ambient temperature. The temperature of the sample surface can be measured rather easily at ambient temperature. The spectrum at ambient temperature is used to eliminate background effects from spectra as measured at other surface temperatures. The temperatures of the sample are found in a single calculation from the measured spectra independently of the response function of the instrument and the emissivity of the sample. The spectral emissivity of a sample can be measured if the instrument is calibrated against a blackbody source. Temperatures of blackbody sources are estimated with an uncertainty of 0.2-2 K. The method is demonstrated for measuring the spectral emissivity of a brass specimen and an oxidized nickel specimen.

IR, visible and UV components in the spectral distribution of blackbody radiation

The spectral distribution of blackbody radiation is given by the Planck radiation law, and the Stefan-Boltzmann and Wien displacement laws give the total power and the maximum of the spectral distribution respectively. However, the contributions of each of the IR, visible and UV components to the total radiation is not found in literature, although qualitative inferences can be made from the graphs of spectral irradiance given by the Planck radiation law. This article presents the percentage mix of IR, visible and UV components to the total radiant power of a blackbody as a function of temperature. At low temperature the radiant power is nearly 100% IR and the contributions of UV and visible components are nearly zero. As the temperature increases, the percentage of the IR component decreases, and the UV and visible components increase. The percentage of the visible component has a maximum value of 47.5% at 7100 K. At very high temperatures UV contributes the largest fraction to the radiant power with smaller, non-zero fractions of IR and visible radiation. At certain temperatures two of the three components contribute equally to the radiant power. The analysis has important application in medical and biophysics for UV protection from high temperature systems.

Measurement of the surface temperature distribution in the float zone of LiNbO 3

The thermal radiation emitted from a LiNbO 3 rod in a CO 2 laser-heated float-zone system has been measured by a two-dimensional thermal imaging radiometer with the spectral bandpass selected to be 3–5, 10.6 and 8–12 μm. When the float zone is formed, the interference of the monochromatic CO 2 laser with the thermal emission at the wavelengths of 10.6 and 8–12 μm can be minimized because the deformable gas-melt interface is optically smooth. The present results show that the emission of thermal radiation at the wavelengths of 10.6 and 8–12 μm is a surface phenomena, while that of 3–5 μm is a volumetric phenomena. The emission of thermal radiation in the 3–5 μm spectrum is used to determine the shape of the float-zone interface by using the method developed by Chen and Hu [J. Crystal Growth 149 (1995) 87]. Because the temperature at the gas-melt-solid interface is the melting point of the material, the emissivities for the wavelengths of 10.6 and 8–12 μm for the melting temperature can be obtained from the Planck radiation law, and they are around 0.92 and 0.98, respectively. Since the emissivity at these wavelengths is insensitive to the variation of the temperature, the surface temperature can be obtained from the thermal radiation distribution.

Planck's Radiation Law: A Many Body Theory Perspective

An exposition of Planck's Law of Radiation is presented within the context of modern quantum many body theory. In particular the generality of the Planck radiation law is demonstrated to be Valid to all orders of perturbation theory for an interacting system, regardless of the underlying statistics for the particles comprising the matter field and the precise nature of the interaction mechanism. This exposition justifies the use of Planck's law with minor modifications via the refractive index, in the optical properties of semiconductors and insulators. We conclude by clarifying when Planck's law is likely to fail.

Maxwell electromagnetic theory, Planck's radiation law, and Bose—Einstein statistics

We give an example in which it is possible to understand quantum statistics using classical concepts. This is done by studying the interaction of chargedmatter oscillators with the thermal and zeropoint electromagnetic fields characteristic of quantum electrodynamics and classical stochastic electrodynamics. Planck's formula for the spectral distribution and the elements of energy hw are interpreted without resorting to discontinuities. We also show the aspects in which our model calculation complement other derivations of blackbody radiation spectrum without quantum assumptions.

Generalization of the Planck radiation law and application to the cosmic microwave background radiation

Within the framework of the recently introduced nonextensive statistical mechanics, we generalize the Planck law for the blackbody radiation. The generalized thermal spectrum contains an additional parameter q, for which q=1 in the Planck limit. For the cosmic microwave background radiation, we find a 95% confidence limit of \ensuremath{\Vert}q-1\ensuremath{\Vert}3.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ from the data of Mather et al. [Astrophys. J. 420, 439 (1994)] that were obtained with the Cosmic Background Explorer satellite, under the assumption that the internal reference of the apparatus has a Planck spectrum.