How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?

We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3=Constant, where P isthe pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work （Yarman et al. 2010 Int. J. Phys. Sci. 5 1524）. We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.

The duality of internal energy of ideal gas

This contribution starts with the discussion on the classification of energy, and then the behaviors of various thermodynamic processes are analyzed, accompanying with the comparison of the adiabatic compression process of an ideal gas and an elastic rod. All these analyses show that the internal energy of ideal gases exhibits the duality of thermal energy–mechanical energy, that is,the internal energy acts as the thermal energy during the isochoric process, while the internal energy acts as the mechanical energy during the isentropic process. Such behavior of the internal energy is quite different from other types of energy during the energy conversion process because the internal energy of ideal gases exhibits the duality of thermal energy–mechanical energy. Because of this duality, the internal energy of ideal gas is proposed to be refered to as thermodynamic energy rather than thermal energy as indicated in some literature, although it consists of kinetics of the microscopic random motion of particles and can be expressed as the function of temperature only.

Short-time Asymptotics of the Heat Kernel on Bounded Domain with Piecewise Smooth Boundary Conditions and Its Applications to an Ideal Gas

The asymptotic expansion of the heat kernel Θ(t)=sum from ∞ to j=1 exp(-tλ_j) where {λ_j}_(j=1)~∞ are the eigen-values of the negative Laplacian -Δ_n=-sum from n to k=1((?))~2 in R^n(n=2 or 3) is studied for short-time t for a generalbounded domain Ω with a smooth boundary (?)Ω.In this paper,we consider the case of a finite number of theDirichlet conditions φ=0 on Γ_i (i=1,...,J) and the Neumann conditions (?)=0 on Γ_i (i=J+1,...,k) andthe Robin conditions ((?)+γ_i)φ=0 on Γ_i (i=k+1,...,m) where γ_i are piecewise smooth positive impedancefunctions,such that (?)Ω consists of a finite number of piecewise smooth components Γ_i(i=1,...,m) where(?)Ω=(?)Γ_i.We construct the required asymptotics in the form of a power series over t.The senior coefficients inthis series are specified as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a“special ideal gas”,i.e.,the set of non-interacting particles set up in abox with Dirichlet,Neumann and Robin boundary conditions for the appropriate wave function.Calculationof the thermodynamic quantities for the ideal gas such as the internal energy,pressure and specific heat revealsthat these quantities alone are incapable of distinguishing between two different shapes of the domain.Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function;nevertheless,its formal theoretical motivation is of some interest.

Investigation into the improved axial compressibility of a spinning non-ideal gas

Using theoretical analysis and mumerical calculation method,the axial adiabatic compression of a spinning non-ideal gas in a cylinder with a smooth surface is investigated.We show that the axial pressure of a spinning gas will gradually become lower than that of a stationary gas during continuous compression,even though the initial axial pressure of the spining gas is larger than that of the stationary gas at the same initial temperature and average density.This phenomenon indicates that the axial compressibility of gas is improved in a rotating system.In addition,the effect of different forms of virial coefficient B(T)on pressure and temperature changes in spinning and stationary gases are investigated.Research on the axial compressibility of spinning non ideal gas can provide useful references for fields that require high compression of gases,such as laser fusion,laboratory astrophysics,and Z-pinch experiments.

A Theoretical Study on Energy of a Gaseous System Vis-a-Vis Mass and Temperature

To study various properties of a gas has been a subject of rational curiosity in pneumatic sciences. A gaseous system, in general, is studied by using four measurable parameters namely, the pressure, volume, number of moles and temperature. In the present work, an attempt is made to study the variation of energy of an ideal gas with the two measurable parameters, the mass and temperature of the gas. Using the well known ideal gas equation, PV = nRT where symbols have their usual meanings and some simple mathematical operations widely used in physics, chemistry and mathematics in a transparent manner, an equation of state relating the three variables, the energy, mass and temperature of an ideal gas is obtained. It is found that energy of an ideal gas is equal to the product of mass and temperature of the gas. This gives a direct relationship between the energy, mass and temperature of the gas. Out of the three variables, the energy, mass and temperature of an ideal gas, if one of the parameters is held constant, the other two variables can be measured. At a constant temperature, when the power or energy is stabilized, the increase in the mass of the gas may affect the new works and an engine can therefore be prevented from overheating.

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.

Thermodynamics of Criticality: Percolation Loci, Mesophases and a Critical Dividing Line in Binary-Liquid and Liquid-Gas Equilibria

High-temperature and pressure boundaries of the liquid and gas states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatures or pressures to “ideal gas” states. Using computational methodology described previously we present results for the thermodynamic states at which clusters of excluded volume (VE) and pockets of available volume (VA), for a spherical molecule diameter σ, percolate the whole volume (V = VE + VA) of the ideal gas. The molecular-reduced temperature (T)/pressure(p) ratios ( ) for the percolation transitions are = 1.495 ± 0.015 and = 1.100 ± 0.015. Further MD computations of percolation loci, for the Widom-Rowlinson (W-R) model of a partially miscible binary liquid (A-B), show the connection between the ideal gas percolation transitions and the 1st-order phase-separation transition. A phase diagram for the penetrable cohesive sphere (PCS) model of a one-component liquid-gas is then obtained by analytic transcription of the W-R model thermodynamic properties. The PCS percolation loci extend from a critical coexistence of gas plus liquid to the low-density limit ideal gas. Extended percolation loci for argon, determined from literature equation-of-state measurements exhibit similar phenomena. When percolation loci define phase bounds, the liquid phase spans the whole density range, whereas the gas phase is confined by its percolation boundary within an area of low T and p on the density surface. This is contrary to a general perception and opens a debate on the definitions of gaseous and liquid states.

Influence of quantum degeneracy on the performance of a gas Stirling engine cycle

Based on the state equation of an ideal quantum gas, the regenerative loss of a Stirling engine cycle working with an ideal quantum gas is calculated. Thermal efficiency of the cycle is derived. Furthermore, under the condition of quantum degeneracy, several special thermal efficiencies are discussed. Ratios of thermal efficiencies versus the temperature ratio and volume ratio of the cycle are made. It is found that the thermal efficiency of the cycle not only depends on high and low temperatures but also on maximum and minimum volumes. In a classical gas state the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal quantum gas state the thermal efficiency of the cycle is smaller than that of the Carnot cycle. This will be significant for deeper understanding of the gas Stirling engine cycle.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.

INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.

Speed of Sound and Ideal-Gas Heat Capacity at Constant Pressure for HFC-125

The gaseous speed of sound, the ideal gas heat capacity at constant pressure, and the second Virial coefficient were determined for pentafluoroethane (HFC 125). A total of 49 data points of speed of sound for gaseous HFC 125 were measured for temperatures from 273 to 313 K and pressures from 32 to 479 kPa with a cylindrical, variable path acoustic interferometer. The ideal gas heat capacity at constant pressure and the second acoustic Virial coefficient were determined over the temperature range from the speed of sound measurements and were correlated as functions of temperature. An analytical expression for the second Virial coefficient derived using the square well intermolecular potential model was compared with the data.

A Study of the Critical Nozzle for Flow Rate Measurement of High-Pressure Hydrogen Gas

The mass flow rate measurement using a critical nozzle shows the validity of the inviscid theory, indicating that the discharge coefficient increases and approaches unity as the Reynolds number increases under the ideal gas law However, when the critical nozzle measures the mass flow rate of a real gas such as hydrogen at a pressure of hundreds bar, the discharge coefficient exceeds unity, and the real gas effects should be taken into account. The present study aims at investigating the flow features of the critical nozzle using high-pressured hydrogen gas. The axisymmetric, compressible Navier-Stokes computation is employed to simulate the critical nozzle flow, and a fully implicit finite volume method is used to discretize the governing equation system. The real gas effects are simulated to consider the intermolecular forces, which account for the possibility of liquefying hydrogen gas. The computational results are compared with past experimental data. It has been found that the coefficient of discharge for real gas can be corrected properly below unity adopting the real gas assumption.

quantum gases power law potential grand potential condensation hierarchy

The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U =∑~d_（i=1）ci｜xi/ai｜~（ni） are studied carefully. Detailed calculation of Kim et al.（J. Phys. Condens. Matter 11（1999） 10269） yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume CV are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.

Transverse momentum spectra in high-energy nucleus-nucleus, proton-nucleus and proton-proton collisions

The transverse momentum distributions of final-state particles produced in nucleus-nucleus （AA）, proton-nucleus （pA）, and proton-proton （pp） collisions at high energies are investigated using a multisource ideal gas model. Our calculated results show that the contribution of hard emission can be neglected in the study of transverse momentum spectra of charged pions and kaons produced in Cu-Cu collisions at √SNN=22.5 GeV. And if we consider the contribution of hard emission, the transverse momentum spectra of p and ^-p produced in Cu-Cu collisions at √SNN=22.5 GeV, K^0 produced in Pb-Pb collisions at 158 A GeV, J/φ particles produced in p-Pb collisions at 400 GeV and π^＋, K^＋, p produced in proton-proton collisions at √s=200 GeV, can be described by the model, especially in the tail part of spectra.

Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions：Further Results

The asymptotic expansions of the trace of the heat kernel Θ(t) = Σ_(v =1)~∞exp(-tλ_v) for small positive t, where {λ_v} are the eigenvalues of the negative Laplacian-△_n = -Σ_(i = 1)~n(partial deriv/(partial deriv)x^i)~2 in R^n (n = 2 or 3), are studied for ageneral annular bounded domain Ω with a smooth inner boundary (partial deriv)Ω_1 and a smoothouter boundary (partial deriv)Ω_2, where a finite number of piecewise smooth Robin boundaryconditions (partial deriv/(partial deriv)n_j + γ_j)φ = 0 on the components Γ_j(j = 1, …, k) of(partial deriv)Ω_1 and on the components Γ_j(j = k + 1, …, m) of (partial deriv)Ω_2 areconsidered such that (partial deriv)Ω_1 = ∪_(j = 1)~kΓ_j and (partial deriv)Ω_2 = ∪_(j = k +1)~mΓ_j and where the coefficients γ_j(j = 1, …, m) are piecewise smooth positive functions. Someapplications of Θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given.Further results are also obtained.

Transverse mass distributions of protons produced in heavy-ion collisions at high energies

The transverse mass distributions of protons produced in Au-Au collisions at 8 A GeV and Pb-Pb collisions at 158 A GeV are calculated by using the Monte Carlo method in the framework of the multisource ideal gas model.It is found that our calculated results are in agreement with the experimental data in nucleusnucleus collisions at high energies.

On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws

This paper is concerned with a new version of the Osher-Solomon Riemann solver and is based on a numerical integration of the path-dependent dissipation matrix.The resulting scheme is much simpler than the original one and is applicable to general hyperbolic conservation laws,while retaining the attractive features of the original solver:the method is entropy-satisfying,differentiable and complete in the sense that it attributes a different numerical viscosity to each characteristic field,in particular to the intermediate ones,since the full eigenstructure of the underlying hyperbolic system is used.To illustrate the potential of the proposed scheme we show applications to the following hyperbolic conservation laws:Euler equations of compressible gasdynamics with ideal gas and real gas equation of state,classical and relativistic MHD equations as well as the equations of nonlinear elasticity.To the knowledge of the authors,apart from the Euler equations with ideal gas,an Osher-type scheme has never been devised before for any of these complicated PDE systems.Since our new general Riemann solver can be directly used as a building block of high order finite volume and discontinuous Galerkin schemes we also show the extension to higher order of accuracy and multiple space dimensions in the new framework of PNPM schemes on unstructured meshes recently proposed in[9].

Critical temperature and condensed fraction of Bose-Einstein condensation in an external potential

Based on Bose-Einstein condensation at minimized momentum state, we get the expressions for the critical temperature and condensed fraction of Bose-Einstein condensation （BEC） in an external potential in the three-dimensional （3D） case. For the 1D and 2D cases, we present not only the critical temperature and corresponding particles but also the condition of BEC occurrence.