Viskosität und Wärmeleitfähigkeit: Boltzmann-Gas

Physik Online ◽  
2018 ◽  
Author(s):  
Siegfried Hess ◽  
Manfred Faubel
Keyword(s):  
Boltzmann Gas

scholarly journals The estimation of electric moment in solution by the temperature coefficient method. Part I.—Experimental method and the electric moments of some benzyl compounds

1933 ◽  
Vol 142 (846) ◽  
pp. 173-197 ◽  
Keyword(s):  
Single Molecule ◽  
Polar Solvent ◽  
Fundamental Equation ◽  
Absolute Temperature ◽  
Electric Moment ◽  
Avogadro’S Number ◽  
Boltzmann Gas ◽  
Different Temperatures ◽  
The Moment ◽  
Coefficient Method

The theory of the estimation of the electric moment of molecules dissolved in a non-polar solvent is now well known. The fundamental equation is P 2∞ = 4 π /3 N (α 0 + μ 2 /3 k T) (1) in which the symbols have the following significance: P 2∞ the total polarizability of the solute per grain molecule at infinite dilution, N Avogadro’s number, α 0 the moment induced in a single molecule by unit electric field, k the Boltzmann gas constant, T the absolute temperature, and μ the permanent electric moment of the molecule. This equation is of the form P 2∞ = A + B/T, (2) where A = 4 π /3 Nα 0 and B = 4 π /9 . N μ 2 / k , from which it follows that if A and B are constant, i. e ., independent of temperature, then each may be evaluated from a series of measurements of P 2∞ at different temperatures or alternatively B (and hence μ ) may be obtained from one value of P 2∞ at one temperature, provided that A can be obtained by some independent method.

scholarly journals Relativistic Rotating Boltzmann Gas Using the Tetrad Formalism

2015 ◽  
Vol 58 (1) ◽  
pp. 89-108 ◽  
Author(s):  
Victor E. Ambrus ◽  
Robert Blaga
Keyword(s):  
Lattice Boltzmann ◽  
Thermal Equilibrium ◽  
Explicit Calculation ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Tetrad Formalism ◽  
Equilibrium Stress ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Gas ◽  
Stress Energy

Abstract We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013) 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this formalism to rel- ativistic lattice Boltzmann simulations. We present in detail the transformation to the comoving frame, the choice of tetrad, as well as the explicit calculation and analysis of the components of the equilibrium particle ow four-vector and of the equilibrium stress-energy tensor.

scholarly journals Theory of existence and uniqueness for the nonlinear Maxwell-Boltzmann equation I

1977 ◽  
Vol 16 (3) ◽  
pp. 379-414 ◽  
Author(s):  
Aleksander Glikson
Keyword(s):  
Boltzmann Equation ◽  
Existence And Uniqueness ◽  
Broad Class ◽  
Physical Space ◽  
Uniqueness Result ◽  
Cauchy Problems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Boltzmann Gas ◽  
Definition Of

A review of the development of the theory of existence and uniqueness of solutions to initial-value problems for mostly reduced versions of the nonlinear Maxwell-Boltzmann equation with a cut-off of intermolecular interaction, precedes the formulation and discussion of a somewhat generalized initial-value problem for the full nonlinear Maxwell-Boltzmann equation, with or without a cut-off. This is followed by a derivation of a new existence-uniqueness result for a particular Cauchy problem for the full nonlinear Maxwell-Boltzmann equation with a cut-off, under the assumption that the monatomic Boltzmann gas in the unbounded physical space X is acted upon by a member of a broad class of external conservative forces with sufficiently well-behaved potentials, defined on X and bounded from below. The result represents a significant improvement of an earlier theorem by this author which was until now the strongest obtained for Cauchy problems for the full Maxwell-Boltzmann equation. The improvement is basically due to the introduction of equivalent norms in a Banach space, the definition of which is connected with an exponential function of the total energy of a free-streaming molecule.

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