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Assuming that 1-dimensional self-assembly nanotubes can be represented as a 1-dimensional cavity-type black-body radiator of length L and radius r in thermal equilibrium at a temperature T, analytical expressions for the thermal radiative and thermodynamic functions of the emitted black-body radiation are obtained in the finite spectral range of the electromagnetic spectrum. The total energy density, the Stefan-Boltzmann law, the number density of the photons, the Helmholtz free energy density, the entropy density, the heat capacity at constant volume, and the pressure are expressed in terms of the polylogarithm functions. In the frequency range 0.05-0.19 PHz, the thermal radiative and thermodynamic functions of the 1-dimensional black-body radiation at different temperatures are calculated. To confirm our assumption, it is necessary to measure the total energy density in the direction L in the finite frequency range 0.05-0.19 PHz, using a single nanoparticle mass spectrometer or other optical devices., Comment: 17 pages, 4 Tables

A new optimized band-pass filter for wavelengths is proposed to increase the optical temporal coherence of thermal light. The choice of parameters for this filter is based on solving an optimization problem for finding the most intensely emitted frequency interval in the black-body radiation spectrum. The calculated frequency interval is also the narrowest band for the coherence filter for a given value of the total transmitted energy. As a result, the interval found can be used to achieve the highest possible coherent properties at a given level of total energy that has passed. The achieved coherence length values for such optimized band-pass filters are calculated. Analytical results are given for finding optimal intervals and calculating the coherence of optimized filters., Comment: 15 pages

The Sunyaev-Zel'dovich effect is a small spectral distortion of the spectrum of the cosmic microwave background (CMB) radiation. This slight distortion is described by the Bose-Einstein (mu-type) distribution with non-zero chemical potential. It is now interesting to investigate the effect of this distortion on the integral characteristics of the Bose-Einstein spectrum. The thermal radiative and thermodynamic functions of the Bose-Einstein distribution are such integral characteristics. These functions are as follows: a) the total radiation power per unit area; b) total energy density; c) number density of photons; d) grand potential density; e) Helmholtz free energy density; f) entropy density; g) heat capacity at constant volume; h) enthalpy density; and i) pressure. The exact analytical expressions are obtained for the temperature dependences of these functions. Using experimental data measured by the COBE FIRAS instrument, the thermal radiative and thermodynamic functions are calculated at the monopole temperature T = 2.72548 K and at z = 0. A comparative analysis of the results obtained with the results for the same functions of the CMB spectrum is carried out. The thermal radiative and thermodynamic functions of the Bose-Einstein distribution are calculated in the redshift range from 10(5) to 3x10(6). The expressions are obtained for new astrophysical parameters, such as the entropy density/Boltzmann constant and number density, created by the mu- distortion of the CMB spectrum.

The knowledge of thermal radiative and thermodynamic properties of uranium and plutonium carbides under extreme conditions is essential for designing a new metallic fuel materials for next generation of a nuclear reactor. The present work is devoted to the study of the thermal radiative and thermodynamic properties of liquid and solid uranium and plutonium carbides at their melting/freezing temperatures. The Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and normal total emissivity are calculated using experimental data for the frequency dependence of the normal spectral emissivity of liquid and solid uranium and plutonium carbides in the visible-near infrared range. It is shown that the thermal radiative and thermodynamic functions of uranium carbide have a slight difference during liquid-to-solid transition. Unlike UC, such a difference between these functions have not been established for plutonium carbide. The calculated values for the normal total emissivity of uranium and plutonium carbides at their melting temperatures is in good agreement with experimental data. The obtained results allow to calculate the thermal radiative and thermodynamic properties of liquid and solid uranium and plutonium carbides for any size of samples. Based on the model of Hagen-Rubens and the Wiedemann-Franz law, a new method to determine the thermal conductivity of metals and carbides at the melting points is proposed., Comment: 17 pages, 2 Tables

The general analytical expressions for the thermal radiative and thermodynamic properties of a real-body are obtained in a finite range of frequencies at different temperatures. The frequency dependence of the spectral emissivity is represented as a power series. The Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and total emissivity are expressed in terms of the polylogarithm functions. The general expressions for the thermal radiative and thermodynamic functions are applied for the study of thermal radiation of liquid and solid zirconium carbide. These functions are calculated using experimental data for the frequency dependence of the normal spectral emissivity in the visible-near infrared range at the melting (freezing) point. The gaps between the thermal radiative and thermodynamic functions of liquid and solid zirconium carbide are observed. The general analytical expressions obtained can easily be presented in wavenumber domain., Comment: 21 pages, 2 tables

Using polylogarithm functions the exact analytical expressions for the radiative and thermodynamic properties of blackbody radiation, such as the Wien displacement law, Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, and pressure in the finite range of frequencies are constructed. The obtained expressions allow us to tabulate these functions in various finite frequency bands at different temperatures for practical applications. As an example, the radiative and thermodynamic functions using experimental data for the monopole spectrum of the Cosmic Microwave Background (CMB) radiation measured by the COBE FIRAS instrument in the 60 - 600 GHz frequency interval at the temperature T = 2.725 K are calculated. The expressions obtained for the radiative and thermodynamic functions can be easily presented in wavelength and wavenumber domains., Comment: 20 pages, 2 tables

Using the three-component spectral model describing the FIRAS average continuum spectra, the analytical expressions for the temperature dependence of the thermodynamic and radiative functions of the galactic far-infrared radiation are obtained. The COBE FIRAS instrument data in the 0.15 - 2.88 THz frequency interval at the mean temperatures T = 17.72 K, T = 14 K, and T =6.73 K are used for calculating the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, total emissivity, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume and pressure for the warm, intermediate-temperature and very cold components of the Galactic continuum spectra. The generalized Stefan-Boltzmann laws for the warm, intermediate-temperature and very cold components are constructed. This result is important when we construct the cosmological models of radiative transfer in the inner Galaxy. Within the framework of the three- component spectral model, the total number of photons in our Galaxy and the total radiation power (total luminosity) emitted from the surface of the Galaxy are calculated. Other radiative and thermodynamic properties of the galactic far-infrared radiation (photon gas) for the Galaxy are presented. The expressions for astrophysical parameters, such as the entropy density/Boltzmann constant, and number density of the galactic far-infrared photons are obtained. We assume that the obtained analytical expressions for thermodynamic and radiative functions may be useful for describing the continuum spectra of the far-infrared radiation for outer galaxies., Comment: 23 pqges, 3 tables

Using the explicit form of the function to describe the average spectrum of the extragalactic far infrared background (FIRB) radiation measured by the COBE FIRAS instrument in the 0.15 - 2.4 THz frequency interval, the radiative and thermodynamic properties, such as the total emissivity, total radiation power per unit area, total energy density, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume, pressure, enthalpy density, and internal energy density are calculated. The calculated value of the total intensity received in the 0.15 - 2.4 THz frequency interval is 13.6 nW m^-2 sr^-1, and comprises about 19.4 % of the total intensity expected from the energy released by stellar nucleosynthesis over cosmic history. The radiative and thermodynamic functions of the extragalactic far infrared background (FIRB) radiation are calculated at redshift z = 1.5., Comment: 13 pages, 3 tables

Use formulas to describe the monopole and dipole spectra of the Cosmic Microwave Background (CMB) radiation, the exact expressions for the temperature dependences of the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume, pressure, enthalpy density, and internal energy density in the finite range of frequencies are obtained. Since the dependence of temperature upon the redshift z is known, the obtained expressions can be simply presented in z representation. Utilizing experimental data for the monopole and dipole spectra measured by the COBE FIRAS instrument in the 60 - 600 GHz frequency interval at the temperature T = 2.728 K, the values of the radiative and thermodynamic functions, as well as the radiation density constant a and the Stefan-Boltzmann constant are calculated. In the case of the dipole spectrum, the constants a and the Stefan-Boltzmann constant, and the radiative and thermodynamic properties of the CMB radiation are obtained using the mean amplitude Tamp = 3.369 m K. It is shown that the Doppler shift leads to a renormalization of the radiation density constant a, the Stefan-Boltzmann constant, and the corresponding constants for the thermodynamic functions. The radiative and thermodynamic properties of the Cosmic Microwave Background radiation for the monopole and dipole spectra at the redshift z = 1089 are calculated., Comment: 21 pages, 2 tables

The weighty evidences of specific transformations of the thermal motion in pure water in the physiological temperature interval (PTI) from (30 +(-) 3)o C to (42 +(-) 3)o C for warm-blooded organisms are presented. It is shown that near the right end of the PTI (42 +(-) 3)o C the crystal-like thermal motion in water transforms to argon-like one (i.e. the dynamic phase transition (DPT) occurs). It is show that the similar transformation takes also place in water-Mioglobin solutions. It is proposed that the DPT takes also place in the intracellular water, where it stimulates the denaturation of proteins. The restriction of the PTI on the left of (30 +(-) 3)o C is naturally explained by the clusterization of water molecules, which strongly increases when temperature drops. The middle, ((36 +(-) 1)o C), of the PTI for warm-blooded organisms is disposed at the minimum of the heat capacity at constant pressure, that forwards to the stability of heat-exchange for bio-cells., Comment: 13 pages, 6 figures

The Niagara River self-purification through the natural formation of froth at a site of the Niagara Whirlpool basin has been investigated. It is shown that the naturally formed froth on the water surface of the Niagara Whirlpool contains a greater concentration of nutrients, trace metals and phenol in comparison to subsurface water. The natural pollutants removal process is explained in detail. As a result, the Niagara River at the Niagara Whirlpool basin possesses its own natural capacity to self-purify through the natural formation of froth. We can conclude that the Niagara Whirlpool is a natural source of Niagara River self-purification. The necessity for the long-term research on the sites of Niagara River for developing the remediation strategies is pointed out., Comment: 11 pages, 1 table, 2 photos