1 Nonlinear Thermoelasticity.- 2 Simplification and Approximation.- 1 Homogeneous and Dissipationless Thermoelasticity.- 2 Linearized Thermoelasticity.- Synopsis.- 3 Efficiency Within Nonlinear Thermoelasticity.- 4 Efficiency Within Homogeneous and Dissipationless Thermoelasticity.- 5 Efficiency Within Linearized Thermoelasticity.- 6 Versions of a Second Law of Thermodynamics.- 1 Nonlinear Thermoelasticity.- 2 Homogeneous and Dissipationless Thermoelasticity.- 3 Linearized Thermoelasticity.- 4 Nonstandard Linearized Thermoelasticity.- References.
The aim of this book is to comment on, and clarify, the mathematical aspects of the theory of thermodynamics. The standard presentations of the subject are often beset by a number of obscurities associated with the words "state", "reversible", "irreversible", and "quasi-static". This book is written in the belief that such obscurities are best removed not by the formal axiomatization of thermodynamics, but by setting the theory in the wider context of a genuine field theory which incorporates the effects of heat conduction and intertia, and proving appropriate results about the governing differential equations of this field theory. Even in the simplest one-dimensional case it is a nontrivial task to carry through the details of this program, and many challenging problems remain open.
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