Thermodynamics Of Ideal Gas Research Articles

Non-commutative correction of ideal gas thermodynamics

In this study, we investigate the thermodynamics of a relativistic ideal gas within the context of κ-deformed space–time and Rainbow gravity background. To achieve this, we construct a modified partition function by considering a deformed Hamiltonian and incorporating corrections based on the time-invariant phase-space volume. We explore the implications of our model on the modified black body radiation spectrum and the modified Debye theory of specific heat in κ-deformed space–time and Rainbow gravity background.

Ideal Gas Thermodynamic Functions For NO From the Total Partition Sum and Its Moments

The total internal partition sum, Qint(T), and the translational partition sum, Qtrans(T), were computed for six isotopologues of NO: 14N16O, 15N16O, 14N18O, 14N17O, 15N18O, 15N17O. These were used to determine the total partition sum, Q(T), and its first and second moments, Q̃′T and Q̃″T. The total internal partition sum was computed using term values determined by Qu et al. [Mon. Not. R. Astron. Soc. 504, 5768–5777 (2021)] for 14N16O and those of Wong et al. [Mon. Not. R. Astron. Soc. 470, 882–897, (2017)] for the other isotopologues. These term values are the best available and hence provide the most accurate total internal partition sums and its first and second moments. The uncertainties in Qint(T), its moments, and the resulting thermodynamic functions were determined from the uncertainty in the term values and the uncertainty due to the convergence of the partition sum and its moments. From these quantities, the isobaric heat capacity, Helmholtz energy, entropy, enthalpy, Gibbs function, and the JANAF functions hef and gef, and their uncertainties, were computed on a 1 K grid from 1 to 9000 K. The data are compared with the literature values. The resulting thermodynamic quantities are the most accurate determined from direct summation of Q(T), Q̃′T, and Q̃″T.

Ideal gas thermodynamics with an invariant energy scale

A viable approach towards Quantum Gravity is the Doubly Special Relativity (DSR) framework in which an observer-independent finite energy upper bound (or a finite smallest length scale) appears quite naturally. In this work, we have studied the thermodynamic properties of an ideal gas in a specific DSR framework, known as the Magueijo-Smolin (MS) Model. We use the fact that DSR can be considered as nonlinear representation of Lorentz Group. Subsequently, various thermodynamic parameters of ideal gas have been derived in this modified framework to compare the corresponding deviations from the usual scenario due to the presence of the invariant energy (length) scale.

Thermodynamics of a charged relativistic ideal Boltzmann gas

This paper presents a toy model of a charged relativistic classical gas in flat spacetime of an arbitrary number of dimensions equipped with some ``pair production'' mechanism. Working with the microcanonical ensemble, the charge is taken to be conserved in contrast with the total number of ``particles'' plus ``antiparticles'' which varies with temperature $T$. Thermodynamics of the classical gas is detailed studied in the nonrelativistic ($Mc^{2}\gg kT$) as well as in the ultrarelativistic ($Mc^{2}\ll kT$) regimes. It is shown that, although we are dealing with classical distributions, at the ultrarelativistic regime the behavior of the gas is Planckian. We also compare the thermodynamics of the toy model with that of quantum gases.

Thermodynamic analysis of metal oxides, metal peroxides and metal hydrides

The standard entropy differences between metal oxides (metal peroxides) and metal elements Δ S were roughly expressed by the following equation, |Δ S | ∝ Rln|Δ V |, R: gas constant, Δ V : volume differences below 10 cm 3 /molO 2 , which is similar to the relation of metal hydrides. It was presumed that the entropy of oxygen in the metal oxides and the metal peroxides, together with the entropy of hydrogen in the metal hydrides can be controlled by the thermodynamics of ideal gas. Those volume differences were increased by increasing of the work function based on the small ion binding properties. However, the absolute values of the standard enthalpy differences |Δ H | had large values at Δ V of -22 to 8 cm 3 /molO 2 . The thermodynamic stabilities which are the absolute values of the standard enthalpy differences decreased in the order, metal oxides > metal peroxides > metal hydrides. • The relation between standard entropy and volume differences Δ S, Δ V was analyzed. • |Δ S | linearly increased with ln|Δ V | below 2⊡3⊡ • The slope was approximately gas constant R. • |Δ H | had large values at Δ V of -22 to 8cm 3 /molO 2 ,Δ H standard enthalpy differences. • |Δ H | decreased in the order, metal oxides > metal peroxides > metal hydrides.

ULYSSES: An Efficient and Easy to Use Semiempirical Library for C+.

We introduce ULYSSES, a user-friendly and robust C++ library for semiempirical quantum chemical calculations. In its current version, ULYSSES is equipped with a large set of different semiempirical models, most of which are based on the Neglect of Diatomic Differential Overlap (NDDO) approximation. Empirical corrections for dispersion and hydrogen bonding are available for most methods, so that higher quality is achieved in the calculation of energies of nonbonded complexes. The library is furthermore equipped with geometry optimization, as well as modules for calculating molecular properties of general interest. Ideal gas thermodynamics is available and allows single structure as well as conformer (multistructure) averaged properties to be calculated. We offer the possibility to use several vibrational partition functions according to the nature of interactions being studied: for covalent systems, the traditional harmonic oscillator approximation is available; for nonbonded complexes, we systematically extended the partition function proposed by Grimme for all thermodynamic functions. The library is also capable of running Born-Oppenheimer molecular dynamics.

Quantum gravity modifications of magnetized ideal gas thermodynamics

In this article, we study minimal length effects on the statistical thermodynamic properties of a magnetized ideal gas. We reformulate the Lagrangian density of the 3-D spatial dimensional static electromagnetic field by employing Kempf Algebra to get the modified magnetostatic potential energy. We derive the modified thermodynamic properties of a magnetized ideal gas such as the mean energy, Helmholtz free energy and entropy. Also, we derive the magnetization, susceptibility, and permeability in the presence of a minimal length. It is found that quantum gravity affects all thermodynamic properties. In addition, we derive the respective upper bounds on the deformation parameter and minimal length.

On the thermodynamics of relativistic ideal gases in the presence of a maximal length

We investigate the thermostatistics of relativistic ideal gases within the recently proposed deformed Heisenberg algebra (Perivolaropoulos, 2017), which includes a maximal length. By using the semiclassical method, the generalized canonical partition function is established and the modified thermodynamic functions are then calculated. It is explicitly shown that the maximal length, unlike the minimal length, modifies the equation of state of relativistic ideal gases. Furthermore, the ultrarelativistic and nonrelativistic regimes are discussed. In contrast to the minimal length corrections, the maximal length corrections do not depend on the considered regime. Such a result confirms that the effects of the maximal length and those of the minimal length are fundamentally different.

An efficient way to examine thermodynamics of relativistic ideal Fermi and Bose gases

The determination of thermodynamic properties such as entropy, energy, pressure, free energy and etc. is very important for all fields of thermodynamic physics. Also giving reliable analytical formulas for evaluating thermodynamic properties of relativistic ideal gases is essential. One of the way of solving thermodynamic properties of ideal Fermi and Bose Gases is determining the expression of pressure integral. In this study we have presented a new computational method for the evaluation of the pressure term of the relativistic ideal Fermi and Bose gases. The purposed method shows that obtained analytically series expansions works for any values of parameters at high temperatures.

Reproducing GaN HEMT Kink Effect by Simulating Field-Enhanced Barrier Defect Ionization

The kink effect, long observed in GaN high electron mobility transistors (HEMTs), is investigated with the Fermi kinetics transport hot electron simulation method. Fermi kinetics assigns piecewise Fermi-Dirac electron distributions to the conduction band valleys determined by the GaN electronic band structure and computes their behavior according to the thermodynamics of ideal Fermi gases. Charge fluxes are determined from moments of the Boltzmann equation, including nonparabolic electron densities of states and group velocities, as well as phonon and ionized impurity scattering. The model has been further generalized to include field-enhanced tunneling ionization of deep traps. Comparing simulations with measured data suggests that the kink effect could be caused by field-enhanced ionization of deep AlGaN barrier traps beneath the gate and close to the GaN/AlGaN interface. Further simulations indicate hot electrons may play key roles in both the trap emission and capture processes.

Mayer’s convergence and thermodynamics of ideal Bose gas

The equation of state for a collection of ideal bosons in both the low-density and high-density regions is found using the method of cluster expansion with a new generating function. The importance of the radius of convergence in the cluster expansion and its connection to the Bose–Einstein condensation phenomenon are studied. The radius of convergence of the partition function is calculated and the values of critical density, fugacity and other thermodynamic properties at condensation are obtained using Mayer’s convergence method.

A finite temperature study of ideal quantum gases in the presence of one dimensional quasi-periodic potential

We study the thermodynamics of ideal Bose gas as well as the transport properties of non interacting bosons and fermions in a one dimensional quasi-periodic potential, namely Aubry–André (AA) model at finite temperature. For bosons in finite size systems, the effect of quasi-periodic potential on the crossover phenomena corresponding to Bose–Einstein condensation (BEC), superfluidity and localization phenomena at finite temperatures are investigated. From the ground state number fluctuation we calculate the crossover temperature of BEC which exhibits a non monotonic behavior with the strength of AA potential and vanishes at the self-dual critical point following power law. Appropriate rescaling of the crossover temperatures reveals universal behavior which is studied for different quasi-periodicity of the AA model. Finally, we study the temperature and flux dependence of the persistent current of fermions in presence of a quasi-periodic potential to identify the localization at the Fermi energy from the decay of the current.

Quantum gravity modifications of the relativistic ideal gas thermodynamics

In the frame work of the generalized uncertainty principle, we study the theoretical modifications induced by the quantum gravity on the thermodynamics of the relativistic ideal gas. The merit of this work is that we have applied two different research methods while the results of both methods point to a complete consistency between them. These approaches emerge from different viewpoints of the incorporation of the underlying theory. Here, we call them as the modified Hamiltonian method and the modified density of states method. In the first method, we have an active viewpoint and suppose that the Hamiltonian is modified via the momentum transformation induced by the theory. However, in the second method, we adopted rather a passive interpretation and consider a transformation of the coordinates as a result of the theory. In order to have a time invariant volume element of phase space, this method leads to a redefinition of the density of states. We show that these approaches expectedly lead to the same partition functions and hence are equivalent. Since, there are two models of the generalized uncertainty principle, with quadratic and linear momentum terms, we show these equivalencies are established for both models. We obtain the modifications of the thermodynamics of the relativistic ideal gas induced by the quadratic model and estimate the consequences for the limiting case the nonrelativistic domains. All the results are in agreement with the previous issues. Also the results for the extreme relativistic and asymptotic ultrarelativistic domains are obtained which shows novel properties. In addition, we indicate that the black body energy spectrum will be changed, due to the quantum gravity corrections, but this effect can be seen at high temperature limits.

Analysis and Mathematical Description of the Ideal Thermotropic Cycle of Internal Combustion Engines

A mathematical model of an ideal thermotropic cycle is proposed, which extends the idea of real working processes in the internal combustion engine (ICE). The thermotropic cycle the same for diesel, gasoline and gas ICE, and also provides significantly better correspondense to the real cycles than classical cycles. Heat supply to the cycle is carried out in the form of a combined process "compression-expansion". The combined process consists of two incomplete thermotropic processes and with a high degree of approximation reproduces the laws of real combustion processes in the ICE, from compression to expansion. The mathematical model of the basic thermotropic process is based on the laws of molecular kinetic theory and thermodynamics of ideal gases. The main thermotropic process is based on three fundamental equations of thermodynamics: differential equations of the first law of thermodynamics and the law of heat exchange of the external source of the working medium, as well as the equation of state (Clapeyron). The heat of the process in the thermotropic process, in contrast to the polytropic, is an independent value and takes into account fuel consumption. The equation of the main thermotropic process has additivity, which allows us to consider its parameters as the sum of the adiabatic and thermal components of the process occurring in the gas mixture. An important feature of the thermotropic process is also the variable heat capacity of the process. The gas laws of classical thermodynamics are special cases of a new process. The advantage of the new cycle model is mathematical simplicity. The initial system of equations made it possible to perform precise integration and express the equations of processes and cycles in elementary functions. Precise integration ensured high accuracy of estimation of influencing factors contained in the model and absolute convergence of thermal and material balances of the cycle. A number of elements of the theory of thermotropic processes and cycles can be used to replace isochoric-isobaric-polytropic combustion models in undergraduate and specialist studies. This is facilitated by the absence of the need for complex computer programs that significantly complicate the development of educational material. In General, models with more complex laws of heat supply can be useful for undergraduates and graduate students to pre-evaluate the effectiveness of the proposed project activities to improve the internal combustion engine.

A Mach-sensitive splitting approach for Euler-like systems

Herein, a Mach-sensitive fractional step approach is proposed for Euler-like systems. The key idea is to introduce a time-dependent splitting which dynamically decouples convection from acoustic phenomenon following the fluctuations of the flow Mach number. By doing so, one seeks to maintain the accuracy of the computed solution for all Mach number regimes. Indeed, when the Mach number takes high values, a time-explicit resolution of the overall Euler-like system is entirely performed in one of the present splitting step. On the contrary, in the low-Mach number case, convection is totally separated from the acoustic waves production. Then, by performing an appropriate correction on the acoustic step of the splitting, the numerical diffusion can be significantly reduced. A study made on both convective and acoustic subsystems of the present approach has revealed some key properties as hyperbolicity and positivity of the density and internal energy in the case of an ideal gas thermodynamics. The one-dimensional results made on a wide range of Mach numbers using an ideal and a stiffened gas thermodynamics show that the present approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.

A particle method for two-phase flows with compressible air pocket

When using particle methods to simulate water–air flows with compressible air pockets, a major challenge is to deal with the large differences in physical properties (e.g., density and viscosity) between water and air. In addition, the accurate modeling of air compressibility is essential. To this end, a new two-phase strategy is proposed to simulate incompressible and compressible fluids simultaneously without iterations between the solvers for incompressible and compressible flows. Water is modeled by the recently developed 2-phase Consistent Particle Method for incompressible flows. For air modeling, a new compressible solver is proposed based on the ideal gas law and thermodynamics. The formulation avoids the problem of determining the actual sound speed that is dependent on the temperature and is therefore not necessarily constant. In addition, the compressible air solver is seamlessly integrated with the incompressible solver 2-phase Consistent Particle Method because they both use the same predictor–corrector scheme to solve the governing equations. The performance of the proposed method is demonstrated by three benchmark problems as well as an experimental study of sloshing impact with entrapped air pockets in an oscillating tank. Copyright © 2016 John Wiley & Sons, Ltd.

Thermodynamics of the low-density excluded-volume hadron gas

We consider the thermodynamics of excluded-volume particles at finite temperature and chemical potential in the low-density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas thermodynamics at the same temperature, pressure, and number of particles. We show that considering the change of the free enthalpy due to the excluded volume, and using the Maxwell identities, one can derive relevant thermodynamic functions and parameters of multicomponent gases. The derivation is quite general, because particles may have different sizes and shapes which can also depend on their momenta. Besides its simplicity and generality, our approach has the advantage of eliminating the transcendental equations occurring in earlier studies. A representative example of the excluded-volume thermodynamics is the single-component gas of hard spheres. For this case, using a virial expansion, the validity limits of the low-density approximation are also discussed.

Weyl, Dirac and Maxwell Quantum Cellular Automata

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the elementary automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets, and some account on the position space description in terms of a discrete path-integral approach. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton distorted dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.

Standard Model thermodynamics across the electroweak crossover

Even though the Standard Model with a Higgs mass mH = 125GeV possesses no bulk phase transition, its thermodynamics still experiences a “soft point” at temperatures around T = 160GeV, with a deviation from ideal gas thermodynamics. Such a deviation may have an effect on precision computations of weakly interacting dark matter relic abundances if their mass is in the few TeV range, or on leptogenesis scenarios operating in this temperature range. By making use of results from lattice simulations based on a dimensionally reduced effective field theory, we estimate the relevant thermodynamic functions across the crossover. The results are tabulated in a numerical form permitting for their insertion as a background equation of state into cosmological particle production/decoupling codes. We find that Higgs dynamics induces a non-trivial “structure” visible e.g. in the heat capacity, but that in general the largest radiative corrections originate from QCD effects, reducing the energy density by a couple of percent from the free value even at T > 160GeV.

Thermodynamics of Ideal Bose Gas Under Generic Power Law Potential in $d$-dimensions

Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.