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Despite its importance in geological sciences, our understanding of interactions between gas and condensed phases (comprising solids and liquids) remains clouded by the fact that, often, only indirect evidence remains for their occurrence.…
The equation of state for an ideal gas is simple, which is $P=nk_{\rm B}T$. In the case of imperfect gases where mutual interactions among the constituents are important, pressure $P$ can be expressed as the series expansion of density $n$…
The virial expansion of a gas is a correction to the ideal gas law that is usually discussed in advanced courses in statistical mechanics. In this note we outline this derivation in a manner suitable for advanced undergraduate and…
Ideal gas is the most fundamental and simple system in thermodynamics, which has extensive applications in energy research and engineering. By reviewing the physical concept of ideal gas, it is found that the current understanding of ideal…
Previously, we established a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules of an ideal gas (T. Yarman et al. arXiv:0805.4494). In such a gas, the motion of each molecule can…
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications,…
We derive the one-dimensional optimal system for a system of three partial differential equations which describe the two-dimensional rotating ideal gas with polytropic parameter $\gamma >2.$ The Lie symmetries and the one-dimensional…
The Reduced Relativistic Gas (RRG) is a simplified version of the ideal relativistic gas, which assumes that all particles have the same momentum magnitude. Although this is a very idealized situation, the resulting model preserves the…
The principle of Random Galilean Transformation (RGT) Invariance is applied to the random motion of particles in a turbulent gas to construct a kinetic equation for the transport of the particle phase space probability…
We obtain the specific heat in the third constraint scenario for a canonical ensemble of a nonextensive extreme relativistic ideal gas in a closed form. The canonical ensemble of N particles in D dimensions is well-defined for the choice of…
Recently proposed new method "Ethanol as Internal Standard" for determination of volatile compounds in alcohol products by gas chromatography (GC) is investigated from different sides including method testing on prepared standard solutions…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
The equations of state for an ideal generalized gas, like an ideal quantum gas, are expressed in terms of power laws of the temperature. The reduction of an ideal generalized gas to an ideal classical case occurs when the characteristic…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
A basic quantity in the characterization of relativistic particles is the proton-to-electron (p/e) energy density ratio. We derive a simple approximate expression suitable to estimate this quantity, U_p/U_e = (m_p/m_e)^(3-q)/2, valid when a…
The ideal gas laws are derived from the democritian concept of corpuscles moving in vacuum plus a principle of simplicity, namely that these laws are independent of the laws of motion aside from the law of energy conservation. A single…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of…
Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly apply…
The question of how classical thermodynamic laws emerge from the underlying quantum substrate lies at the foundations of physics. Here, we examine the validity of the ideal gas law (IGL) for a single quantum particle confined within a…