Extended thermodynamic model for piezoelectric ceramics

Recently, the 14 moments model of extended thermodynamics for dense gases and macromolecular fluids has been considered and an exact solution, of the restrictions imposed by the entropy principle and that of Galilean relativity, has been obtained without using Taylor's expansions. Here, we prove the uniqueness of the above solution and exploit other pertinent conditions such as the convexity of the function h ′ related to the entropy density, the problem of subsystems and the fact that the flux in the conservation law of mass must be the moment of order 1 in the conservation law of momentum. The results present interesting aspects which were not suspected when only approximated solutions of this problem were known.

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Modified Extended Thermodynamic Model for Material Damping

10.1115/imece1999-0569 ◽

1999 ◽

Author(s):

Xia Lu ◽

S. Hanagud

Keyword(s):

Thermodynamic Model ◽

Mechanical Energy ◽

Viscous Damping ◽

Material Damping ◽

State Variables ◽

Longitudinal Vibrations ◽

Equilibrium Stress ◽

Classical State ◽

Extended Thermodynamic ◽

Non Equilibrium

Abstract During the process of damping of a structure, the mechanical energy is converted to thermal energy. Yet, the most commonly used model for material damping is the linear viscous damping. There are many attempts to develop thermodynamic models for damping. To adequately describe damping, we need more variables than the classical state variables. A simple thermodynamic model that is based on the framework of extended non-equilibrium thermodynamics is presented. Heat flux, non-equilibrium stress field and the associated non-equilibrium internal energy are used as additional variables. Longitudinal vibrations of a uniform rod are studied to present the flexibility of thermodynamic modeling for material damping.

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Solubility and hydrolysis of Tc(iv) in dilute to concentrated KCl solutions: an extended thermodynamic model for Tc4+–H+–K+–Na+–Mg2+–Ca2+–OH−–Cl−–H2O(l) mixed systems

New Journal of Chemistry ◽

10.1039/c7nj01816a ◽

2017 ◽

Vol 41 (17) ◽

pp. 9077-9086 ◽

Cited By ~ 4

Author(s):

A. Baumann ◽

E. Yalçıntaş ◽

X. Gaona ◽

M. Altmaier ◽

H. Geckeis

Keyword(s):

Thermodynamic Model ◽

Reducing Conditions ◽

Extended Thermodynamic ◽

Hydrolysis Of ◽

Mixed Systems

The solubility of Tc(iv) under strongly reducing conditions is investigated in KCl solutions with 1.5 ≤ pHm ≤ 14.5, and an extended thermodynamic model for the system Tc4+–H+–K+–Na+–Mg2+–Ca2+–OH−–Cl−–H2O(l) is provided.

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