Canonical formalism, fundamental equation, and generalized thermomechanics for irreversible fluids with heat transfer

Journal Article · Mon Mar 01 04:00:00 EST 1993 · Physical Review E; (United States)

DOI:https://doi.org/10.1103/PhysRevE.47.1765· OSTI ID:6701664

Sieniutycz, S; Berry, R S ^[1]

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1. Department of Chemistry, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637 (United States)

A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum '' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy [ital E], it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy.

• DOE Contract Number: FG02-86ER13488
• OSTI ID: 6701664
• Journal Information: Physical Review E; (United States), Journal Name: Physical Review E; (United States) Vol. 47:3; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
ENERGY
ENTROPY
FLUIDS
FUNCTIONS
HEAT FLOW
HEAT TRANSFER FLUIDS
IRREVERSIBLE PROCESSES
LAGRANGIAN FUNCTION
PHYSICAL PROPERTIES
POTENTIAL ENERGY
THERMODYNAMIC PROPERTIES
THERMODYNAMICS