Related papers: A hydrodynamic approach to the classical ideal gas
The constraints imposed by the relativistic compressibility hypothesis on the square of the speed of sound in a medium are obtained. This result allows to obtain purely hydrodynamic conditions for the physical reality of a perfect energy…
he necessary and sufficient conditions for a unit time-like vector field to be the unit velocity of a classical ideal gas are obtained. In a recent paper [Coll, Ferrando and S\'aez, Phys. Rev D {\bf 99} (2019)] we have offered a purely…
Every evolution of a fluid is uniquely described by an energy tensor. But the converse is not true: an energy tensor may describe the evolution of different fluids. The problem of determining them is called here the {\em inverse problem}.…
A criterion is presented and discussed to detect when a divergence-free perfect fluid energy tensor in the space-time describes an evolution in local thermal equilibrium. This criterion is applied to the class II Szafron-Szekeres perfect…
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…
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…
Thermodynamics of power means applies to an ideal quantum gas which may be nonextensive. Transition to an ideal classical gas occurs when the empirical temperature exponents of the internal energy and absolute temperature coalesce. Limiting…
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 necessary and sufficient conditions for a perfect energy tensor to describe the energy evolutions of a monoatomic relativistic Synge gas are obtained. Then, a Rainich-like theory for the Einstein-Synge solutions can be constructed.…
Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between…
Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and…
The spatially homogeneous perfect fluid solutions by Kompanneets-Chernov-Kantowski-Sachs are interpreted as a thermodynamic perfect fluid in isentropic evolution, namely, the isentropic limit of their non-homogeneous generalizations, the…
We consider an ideal gas of massive hadrons in thermal and chemical equilibrium. The gas expands longitudinally in an adiabatic way. This evolution for a baryonless gas reduces to a hydrodynamic expansion. Cooling process is parametrized by…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…
The necessary and sufficient conditions are obtained for a unit time-like vector field $u$ to be the unit velocity of a divergence-free perfect fluid energy tensor. This plainly kinematic description of a conservative perfect fluid requires…
Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…
This article concerns the mathematical justification of an averaged system of partial differential equations governing the evolution of a two-phase mixture of compressible ideal fluids, with viscosity and without conductivity, in space…
We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston…
We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard…