scholarly journals Ultrarelativistic Gas with Zero Chemical Potential

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 249
Author(s):  
Daniel Mata-Pacheco ◽  
Gonzalo Parga ◽  
Fernando Angulo-Brown
Keyword(s):  
Chemical Potential ◽  
Ideal Gas ◽  
Cavity Radiation ◽  
Classical Gas ◽  
Photon Gas ◽  
Spin Degeneracy ◽  
Classical Particles

In this work, we propose a set of conditions such that an ultrarelativistic classical gas can present a photon-like behavior. This is achieved by assigning a zero chemical potential to the ultrarelativistic ideal gas. The resulting behavior is similar to that of a Wien photon gas. It is found to be possible only for gases made of very lightweight particles such as neutrinos, as long as we treat them as classical particles, and it depends on the spin degeneracy factor. This procedure allows establishing an analogy between an evaporating gas and the cavity radiation.

scholarly journals A Study of K/Ti-co-doped NaAlH4 on Thermodynamic Tailoring, Surplus Hydrogen Amount and Metal Hydride Molar Volume

2021 ◽  
Author(s):  
Roland Hermann Pawelke
Keyword(s):  
Hydrogen Storage ◽  
Molar Volume ◽  
Metal Hydride ◽  
Chemical Potential ◽  
Reaction Pathway ◽  
Ideal Gas ◽  
Point Of View ◽  
Phase Point ◽  
Desorption Enthalpy ◽  
Co Doped

A remarkable finding of metal hydride hydrogen storage is that substituting 4 mol % sodium by potassium in 4 mol % Ti-doped NaAlH<sub>4</sub> raises the reversible hydrogen storage capacity from 3.3 % w/w H to 4.7 % w/w H. This increase by 42% is concomitant with a slightly lower desorption enthalpy: intriguingly enough, it is substantially more hydrogen capacity at slightly less desorption enthalpy. The general solution to that puzzle has been already derived from a gas phase point of view, taking advantage of the equilibrium nature of the matter, which thus comes in terms of an ideal gas chemical potential. However, it is also interesting to investigate for the flipside effect in the sorbent phase, affecting molar volume. This paper elucidates by the example of K/Ti-co-doped NaAlH<sub>4</sub> the relation of doping modifications to surplus hydrogen amount and hydride molar volume, defining the term “reaction pathway” in this context, yielding the according figures.<br>

scholarly journals The influence of elastic deformations in high-strength structural materials on the hydrogen transport

2021 ◽  
Vol 225 ◽  
pp. 01010
Author(s):  
Polina Grigoreva ◽  
Elena Vilchevskaya ◽  
Vladimir Polyanskiy
Keyword(s):  
Chemical Potential ◽  
Potential Gradient ◽  
Elastic Solid ◽  
High Strength ◽  
Ideal Gas ◽  
Linear Elastic ◽  
Coupled Diffusion ◽  
Elastic Boundary ◽  
Linear Effects ◽  
Solid System

In this work, the diffusion equation for the gas-solid system is revised to describe the non-uniform distribution of hydrogen in steels. The first attempt to build a theoretical and general model and to describe the diffusion process as driven by a chemical potential gradient is made. A linear elastic solid body and ideal gas, diffusing into it, are considered. At this stage, we neglect any traps and non-linear effects. The coupled diffusion-elastic boundary problem is solved for the case of the cylinder under the tensile loads. The obtained results correspond to the experimental ones. Based on them, the assumptions about the correctness of the model and its further improvement are suggested.

scholarly journals Towards Thermodynamics with Generalized Uncertainty Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ahmed Farag Ali ◽  
Mohamed Moussa
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Ideal Gas ◽  
Considerable Change ◽  
Heisenberg Uncertainty Principle ◽  
Ideal Gases ◽  
Quantum Gravity Effect ◽  
Photon Gas ◽  
Heisenberg Uncertainty

Various frameworks of quantum gravity predict a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. In this paper we investigate the modification in thermodynamic properties of ideal gases and photon gas. The partition function is calculated and using it we calculated a considerable growth in the thermodynamical functions for these considered systems. The growth may happen due to an additional repulsive force between constitutes of gases which may be due to the existence of GUP, hence predicting a considerable increase in the entropy of the system. Besides, by applying GUP on an ideal gas in a trapped potential, it is found that GUP assumes a minimum measurable value of thermal wavelength of particles which agrees with discrete nature of the space that has been derived in previous studies from the GUP.

scholarly journals Particle number fluctuations in a non-ideal pion gas

2018 ◽  
Vol 182 ◽  
pp. 02066
Author(s):  
Evgeni E. Kolomeitsev ◽  
Maxim E. Borisov ◽  
Dmitry N. Voskresensky
Keyword(s):  
Critical Point ◽  
Particle Number ◽  
Chemical Potential ◽  
Pion Mass ◽  
Thermodynamic Characteristics ◽  
Ideal Gas ◽  
Fixed Number ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Bose Einstein

We consider a non-ideal hot pion gas with the dynamically fixed number of particles in the model with the λφ4 interaction. The effective Lagrangian for the description of such a system is obtained by dropping the terms responsible for the change of the total particle number. Within the self-consistent Hartree approximation, we compute the effective pion mass, thermodynamic characteristics of the system and identify a critical point of the induced Bose-Einstein condensation when the pion chemical potential reaches the value of the effective pion mass. The normalized variance, skewness, and kurtosis of the particle number distributions are calculated. We demonstrate that all these characteristics remain finite at the critical point of the Bose-Einstein condensation. This is due to the non-perturbative account of the interaction and is in contrast to the ideal-gas case.

Density expansion of the correlation function of a hard sphere gas

1979 ◽  
Vol 57 (3) ◽  
pp. 466-476 ◽  
Author(s):  
D. G. Blair ◽  
N. K. Pope ◽  
S. Ranganathan
Keyword(s):  
Correlation Function ◽  
Fourier Transforms ◽  
Hard Spheres ◽  
Kinetic Equations ◽  
Ideal Gas ◽  
Zero Density ◽  
Classical Gas ◽  
Density Expansions ◽  
The Moment ◽  
Derivatives Of

Using the grand canonical ensemble, the classical Van Hove correlation function G(r, t) is expanded in a power series in density. The zero density limit is the ideal gas result. We have derived, for a classical gas of hard spheres, exact expressions for [Formula: see text], the zero density derivative of the correlation function, and its Fourier transforms. These involve only two particle dynamics. The first two terms in the density expansions provide representation of the correlation functions for appropriate ranges of density and correlation function arguments. We also show that the same result can be obtained from generalized kinetic equations. To this order in density, the moment relations and the time derivatives of I(q, t) at t = 0+ are satisfied. Numerical results are compared with those of Mazenko, Wei, and Yip and with those of the Boltzmann equation and they show the expected behavior.

scholarly journals Entropic thermodynamics of nonlinear photonic chain networks

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Fan O. Wu ◽  
Pawel S. Jung ◽  
Midya Parto ◽  
Mercedeh Khajavikhan ◽  
Demetrios N. Christodoulides
Keyword(s):  
Thermal Conduction ◽  
Large Scale ◽  
Chemical Potential ◽  
Complex Dynamics ◽  
Tight Binding ◽  
Thermodynamic Approach ◽  
Specific System ◽  
Isentropic Expansion ◽  
Photon Gas ◽  
Nonlinear Behaviors

AbstractThe convoluted nonlinear behaviors of heavily multimode photonic structures have been recently the focus of considerable attention. The sheer complexity associated with such multimode systems, allows them to display a host of phenomena that are otherwise impossible in few-mode settings. At the same time, however, it introduces a set of fundamental challenges in terms of comprehending and harnessing their response. Here, we develop an optical thermodynamic approach capable of describing the thermalization dynamics in large scale nonlinear photonic tight-binding networks. For this specific system, an optical Sackur-Tetrode equation is obtained that explicitly provides the optical temperature and chemical potential of the photon gas. Processes like isentropic expansion/compression, Joule expansion, as well as aspects associated with beam cleaning/cooling and thermal conduction effects in such chain networks are discussed. Our results can be used to describe in an effortless manner the exceedingly complex dynamics of highly multimoded nonlinear bosonic systems.

Particle Entropies and Entropy Quanta. I. The Ideal Gas

2000 ◽  
Vol 214 (2) ◽  
Author(s):  
Helmuth W. Zimmermann
Keyword(s):  
Chemical Potential ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Translational Energy ◽  
Quantum Numbers ◽  
De Broglie Wavelength ◽  
Bose Einstein ◽  
Particle Statistics ◽  
The Ideal

We consider an ideal gas of monatomic independent particles, which is enclosed in a cubic box. At temperature T the particles are in thermal equilibrium. All relevant properties of the gas can be deduced from the particle statistics on the assumption that each particle of the ensemble has the particle entropy σ = ε/T = ka. ε is the translational energy of the particle. The non-dimensional number a measures the particle entropy σ in multiples of the Boltzmann constant k, which acts as an atomic entropy unit. a obeies an eigenvalue equation and satisfies boundary conditions. Eigenvalues and eigenfunctions are determined by the translational quantum numbers. Using particle entropies it is easy to calculate the Bose-Einstein and the Boltzmann distribution; and in combination with the density function we immediately get the internal energy E and the Helmholtz free energy F, the total entropy S, the chemical potential μ, the equation of state of the ideal gas at ordinary temperatures and at low temperatures near absolute zero, inclusively Bose-Einstein condensation. Entropy quanta are used to introduce the temperature into the equations of statistical thermodynamics and to calculate the thermal and the actual de Broglie wavelength at temperature T.

scholarly journals Nitrogen Dissolution in Liquid Ga and Fe: Comprehensive Ab Initio Analysis, Relevance for Crystallization of GaN

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1306
Author(s):  
Jacek Piechota ◽  
Stanislaw Krukowski ◽  
Petro Sadovyi ◽  
Bohdan Sadovyi ◽  
Sylwester Porowski ◽  
...  
Keyword(s):  
Experimental Data ◽  
Molecular Dynamics ◽  
Ab Initio Calculations ◽  
Ab Initio ◽  
Chemical Potential ◽  
Nitrogen Solubility ◽  
Molecular Nitrogen ◽  
Ideal Gas ◽  
The Difference ◽  
Good Agreement

The dissolution of molecular nitrogen in Ga and Fe was investigated by ab initio calculations and some complementary experiments. It was found that the N bonding inside these solvents is fundamentally different. For Ga, it is between Ga4s and Ga4p and N2p states whereas for Fe this is by N2p to Fe4s, Fe4p and Fe3d states. Accordingly, the energy of dissolution of N2 for arbitrarily chosen starting atomic configurations was 0.535 eV/mol and −0.299 eV/mol for Ga and Fe, respectively. For configurations optimized with molecular dynamics, the difference between the corresponding energy values, 1.107 eV/mol and 0.003 eV/mol, was similarly large. Full thermodynamic analysis of chemical potential was made employing entropy-derived terms in a Debye picture. The entropy-dependent terms were obtained via a normal conditions path to avoid singularity of ideal gas entropy at zero K. Nitrogen solubility as a function of temperature and N2 pressure was evaluated, being much higher for Fe than for Ga. For T=1800 K and p=104 bar, the N concentration in Ga was 3×10−3 at. fr. whereas for Fe, it was 9×10−2 at. fr. in very good agreement with experimental data. It indicates that liquid Fe could be a prospective solvent for GaN crystallization from metallic solutions.

From Ideal Gas to Photon Gas

1999 ◽  
pp. 401-449
Keyword(s):  
Ideal Gas ◽  
Photon Gas
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