Extended thermodynamics of fluids and virial equations of state
type: Item
instance of: scholarly article
title: Extended thermodynamics of fluids and virial equations of state
zbMATH Open document ID: 0584.76002
DOI: 10.1007/BF00250680
author: B. George
published in: Archive for Rational Mechanics and Analysis
publication date: 1985-01-01T00:00:00Z
review text: Starting out with slight modified supply-free balance equations of extended thermodynamics for thirteen field-densities (mass, momentum, momentum flux and energy flux) the constitutive equations for the fluxes and productions in these balance equations are presupposed as functions of these thirteen fields. Using material axioms which the constitutive equations have to satisfy (entropy principle, hyperbolicity, material frame-indifference) restrictions of the possible constitutive functions are obtained: Objective constitutive quantities (tensors under Euclidean transformation) are isotropic functions of the objective parts of the thirteen density-fields representing ten thermodynamic variables. The objective parts of the fluxes, of the productions, of the entropy density, and of the entropy flux are approximated up to second - or third - order terms in the thermodynamic variables. In first order a usual Gibbs equation, and the entropy flux density as heat flux density over temperature is achieved by the axiom that both flux densities are continuous on ideal partitions. Exploiting hyperbolicity inequalities are derivable which includes the usual stability conditions. The linearized balance equations are the usual ones (mass, momentum, internal energy) and additional six further balances for the non-convective parts of the antisymmetric momentum flux and the energy flux. By using an iterative procedure the momentum- and the energy-flux can be eleminated so obtaining 5-field balance equations and constitutive equations with vanishing bulk viscosity. The thermal equation of state for an ideal gas is derived as \(p=T^{1+(n/2)}f(\rho T^{-(n/2)})\), if its caloric equation of state is presupposed as \(\epsilon =(n/2)(p/\rho)+c\). (p=pressure, T=absolute temperature, n=degree of freedom of a gas molecule, f=arbitrary function, \(\rho=\)mass density, \(\epsilon=\)internal energy density, c=constant). For moderately dense gases the virial coefficients of the virial expansion …
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 80A05
zbMATH DE Number: 3936740
zbMATH Keywords: third-order-approximation
zbMATH Keywords: supply-free balance equations
zbMATH Keywords: extended thermodynamics
zbMATH Keywords: thirteen field-densities
zbMATH Keywords: entropy principle
zbMATH Keywords: hyperbolicity
zbMATH Keywords: material frame-indifference
zbMATH Keywords: Objective constitutive quantities
zbMATH Keywords: Gibbs equation
zbMATH Keywords: linearized balance equations
zbMATH Keywords: iterative procedure
zbMATH Keywords: bulk viscosity
zbMATH Keywords: ideal gas
zbMATH Keywords: caloric equation of state
zbMATH Keywords: virial expansion
zbMATH Keywords: Virial coefficients
zbMATH Keywords: monoatomic gases
zbMATH Keywords: van der Waals gas
reviewed by: Wolfgang Muschik
MaRDI profile type: Publication
cites work: Extended thermodynamics of classical and degenerate ideal gases
cites work: Systems of Conservation Equations with a Convex Extension
cites work: Method of Lagrange multipliers for exploitation of the entropy principle
cites work: Q3232200
cites work: Q5842362
full work available at URL: https://doi.org/10.1007/bf00250680
OpenAlex ID: W2108840516
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description: scientific article; zbMATH DE number 3936740