Generalization of Kirchhoff’s Law: The inherent relations between quantum efficiency and emissivity

Planck’s law of thermal radiation depends on the temperature, \(T\), and the emissivity, \(\epsilon\), which is the coupling of heat to radiation depending on both phonon-electron nonradiative-interactions and electron-photon radiative-interactions. In contrast, absorptivity, \(\alpha\), only depends on the electron-photon radiative-interactions. At thermodynamic equilibrium, nonradiative-interactions are balanced, resulting in Kirchhoff’s law of thermal radiation, \(\epsilon =\alpha\). For non-equilibrium, Quantum efficiency (QE) describes the statistics of photon emission, which like emissivity depends on both radiative and nonradiative interactions. Past generalized Planck’s equation extends Kirchhoff’s law out of equilibrium by scaling the emissivity with the pump-dependent chemical-potential \(\mu\), obscuring the relations between the body properties. Here we theoretically and experimentally demonstrate a prime equation relating these properties in the form of \(\epsilon =\alpha \left(1-QE\right)\). At equilibrium, these relations are reduced to Kirchhoff’s law. Our work lays out the evolution of non-thermal emission with temperature, which is critical for the development of lighting and energy devices.

Novelty Surface Coatings for Far Infrared Spectrum Black Body Radiators

Black body radiation sources are commonly used devices in areas related to thermal imaging and radiometry. They are the closest physical approximation of theoretical black body emitter derived from the Planck’s law. Majority of such devices are costly with restricted information about their production technology, including their emitter surface. A few relatively easily accessible coatings with potential application in such devices have been chosen and their emissivity measured. The paper presents measurements that provides information necessary to determine whether there are coatings viable for black body emitter or reference surface.

Analysis of the prediction of the 2021 time-evolution of the Covid-19 Pandemic in Italy using a Planck’s distribution

In a previous paper we studied the time evolution of the Covid-19 pandemic in Italy during the first wave of 2020 using a number of distribution laws. We concluded that the best distribution law to predict the evolution of the pandemic, if basic conditions of the pandemic (such as distancing measures, use of masks, start of schools, intensive use of public transportation, beginning and end of holidays, vaccination campaign and no significant onset of new Covid variants) do not appreciably change, is a distribution of the type of Planck’s law with three parameters. In our 2020 study we did not use the number of daily positive cases in Italy but the ratio of daily positive cases per number of daily tests, ratio today sometimes referred to as: “positivity rate”. We showed that, if basic conditions do not change, the Planck’s distribution with three parameters provides very good predictions of the positivity rate about one month in advance. In particular, in a second paper, using the Planck’s distribution with three parameters, we predicted, about one month in advance, the spread of the pandemic in Italy during the Christmas 2020 holidays with an error of a few percent only. We then study the present (September 2021) evolution of the pandemic in Italy and we show that the Planck’s distribution, based on the data of July and August, predicts well the evolution of the pandemic. In particular, we show that the peak of the positivity rate was predicted to occur approximately around the middle of August and that the agreement of this Planck’s function (obtained fitting the data up to 10 July 2021) and the positivity rate observed after 5 weeks, on 12 September 2021 is very good. However, the end of the Italian holidays and the start of all the activities including schools, intensive use of public transportation and further changes in distancing measures may cause a discrepancy of the predicted trend of the positivity rate of the pandemic with respect to the real observed values.

Thermal radiation of extended particles with subwavelength transverse dimensions

The paper proposes a new method for calculating the integral and spectral radiation coeffi-cients of extended subwavelength particles (ESPs), which include micro and nanocylinders and parallelepipeds. Comparison of the results of calculations by the proposed method with the calculated and experimental data found in the literature is carried out. It is shown that with decrease in only the transverse dimensions of the ESP (from values much larger than λmax to values much smaller than max) from the radiation spectrum, which was originally de-scribed by Planck's law and contained modes with both polarization directed along the axis and with polarization directed perpendicular to the axis , modes with wavelengths exceeding λcutoff (λcutoff is the cutoff wavelength) and having polarization perpendicular to the longi-tudinal axis of the ESP will be gradually eliminated, while modes with wavelengths polarized along the ESP axis will always be present in the radiation spectrum of the ESP. When the transverse dimensions of the ESP become much less than λmax, then all modes with polariza-tion perpendicular to the axis will disappear from the emission spectrum of this ESP, and on-ly modes with longitudinal polarization will remain. This is a fundamental difference from the SPs considered earlier in [16, 17], where methods for calculating SPs as disks, spheres, cubes were proposed. All the proposed calculation methods use the formalism of the decom-position of radiation fluxes into spectral-spatial modes.

SUPREME THEORY OF EVERYTHING: Theoretical Formulation of The Spectral Density of Electromagnetic Radiation Emitted By A Nonblack Body

Hertzsprung-Russel Diagram (HRD) plots each star on a graph measuring the star’s brightness concerning its temperature (color) between 2000K and 50000 K. It registered about 90 percent of the stars in the universe, including the Sun, located in the main sequence branch of stars in HRD. HRD is an experimental diagram, and its theory could be supposed to be Planck's law. However, Planck's law itself is empirical and contradicts recorded astronomical experimental data. Modern astronomy can observe celestial bodies in space, with surface temperatures ranging from 0 Kelvin to millions of degrees. During this time either Planck's law or HRD didn't develop. In this paper, the spectral density of electromagnetic radiation of non-black bodies is described theoretically.

Advances in Material Wide Range Temperature Determination by Dual-Color Emissivity Free Methodology in Long-Mid-near Infrared Ranges and Non-stationary Aerospace Re-Entry Conditions

Dual color emissivity free methodology by thermography allows to obtain 2D (two-dimensional) temperature maps by using local grey body hypotheses and narrowband filters. By using a suitable pair of filters is possible to obtain the ratio between two thermal camera input signals that depend only on the temperature and not on the emissive properties of the investigated surface. The aim of this concise review paper is to summarize and discuss the developments and applications from long- to mid-near infrared ranges and in a wide range of temperature values of the dual-color thermographic technique that has been analysed through the use of an analytical model based on the integration of Planck’s law and attenuated with the transmission curves of sensors, optics, filters, and attenuators during the last years. Moreover, the applicability to the non-stationary temperature conditions and finalized to the materials mainly used in the aerospace plasma wind tunnel (PWT) re-entry are shown.

Ladislas Natanson and Alfred Landé versus Planck’s law, the Boltzmann-Planck-Natanson statistics and the Bose statistics

The article describes the context and content of the November 1925 correspondence – so far overlooked by historians of physics – between Władysław (Ladislas) Natanson and Alfred Landé on Planck’s law and Bose statistics, and the effects of this interaction. The article publishes for the first time the transcription of two original letters in German and their translations into English.

Thermal radiation ofsubwavelengthparticles

A method is proposed for calculating the dependences of the emissivity of subwavelength parti-cles (SP) from various materials in the form of disks, spheres, cubes and cylinders on their sizes (D) and temperature (T), for cases when external electromagnetic radiation practically does not affect their temperature. For all the listed types of particles, the cutoff wavelengths λcutoffdepending on the size of the SP and the particle shape coefficients ξare determined. With a decrease in the particle size, from the radiation spectrum, which was originally described by Planck's law, wavelengths exceeding λcutoffare gradually excluded. This leads to a decrease in the integral radiation, a decrease in the emissivity and a shift of the radiation spectrum to the blue region. A simple scheme is also proposed for determining ε -the emission coefficients of the midrange according to the calculated graph ε (U), where: U = (ξ × D × T) / B; B is the con-stant of the Wien displacement formula.

Radiative heat transfer at the nanoscale: experimental trends and challenges

Beyond the usual surface-to-surface Planck's law of thermal radiation, nanoscale radiative heat transfer is experiencing a revolution.

Are smaller microplastics missing?

The size distribution of marine microplastics (< 5 mm) provides a fundamental data source for understanding the dispersal, break down, and biotic impacts of the microplastics in the ocean. The observed size distribution generally shows, from large to small sizes, a gradual increase followed by a rapid decrease. This decrease has led to the hypothesis that the smallest fragments are selectively removed by sinking or biological uptake. Here we propose a new model of size distribution without any removal of material from the system. The model uses an analogy with black-body radiation and the resultant size distribution is analogous to Planck's law. In this model, the original large plastic piece is broken into smaller pieces once by the application of “energy” or work by waves or other processes, under two assumptions, one that fragmentation into smaller pieces requires larger energy and the other that the probability distribution of the “energy” follows the Boltzmann distribution. Our formula well reproduces observed size distributions over wide size ranges from micro- (< 5 mm) to mesoplastics ( > 5 mm). According to this model, the smallest fragments are fewer because large “energy” required to produce such small fragments occurs more rarely.