Foundations of Continuum Thermodynamics

Šilhavý, Miroslav

doi:10.1007/978-3-642-70803-9_2

Cited by 8 publications

(4 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[1] p. 101), it is easy to show that while heat conduction always increases the entropy, it always decreases F U when approaching equilibrium at T . We conclude by discussing the link of the present analysis with Serrin's theory [3,4,33], which provides an alternative formulation of thermodynamics based on hotness (i.e., temperature) and heat flow, without assuming internal energy and entropy as primitive concepts (similar concepts were developed by Silhavy [5,6]; see also [7]). The theory is formulated using an accumulation function, A(T ), defined for cyclic processes as the total heat added in a process at temperature lower or equal than T ,…”

Section: Dual Structure Of Thermodynamicsmentioning

confidence: 99%

“…However, considerable effort has also been devoted to rigorously reformulate thermodynamics starting from temperature and heat as primitive quantities. We refer in particular to the work by Serrin and Silhavy [3][4][5][6], who derived internal energy and entropy starting from an analytical formulation of Clausius integral for cyclic processes based on temperature and a newly defined heat accumulation function. Related theories were also proposed in [7,8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dual structure of thermodynamics

Porporato

2014

Phys. Rev. E

View full text Add to dashboard Cite

Based on the properties of exponential distribution families we analyze the Fisher information of the Gibbs canonical ensemble to construct a new state function for simple systems with no mechanical work. Such a function possesses nice symmetry properties with respect to Legendre transform and provides a connection with previous alternative formulations of thermodynamics, most notably the work by Biot, Serrin and Frieden and collaborators. Logical extensions to systems with mechanical work may similarly consider generalized Gibbs ensembles.

show abstract

Section: Dual Structure Of Thermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dual structure of thermodynamics

Porporato

2014

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…May the papers [1][2][3][4][5][6] serve as examples of what has been said. Recent studies in the foundations of macroscopical Thermodynamics have also relied on the use of cycles, [7,8], as the classical tradition systematized in W. Schottky's treatise [9] used to do.…”

Section: Introductionmentioning

confidence: 99%

The Second Law of Thermodynamics and Optimal Bounds for the Efficiency of Cyclic Processes

Pradas¹

1994

Journal of Non-Equilibrium Thermodynamics

View full text Add to dashboard Cite

The paper shows the equivalence of Clausius' inequality to a certain bound on the efficiency of any general cyclic process, as well as the equivalence of the entropy inequality to a certain bound on the work performed in any general process. These bounds are expressed in terms of a geometrical characteristic of the functions accounting the absorption and emission of heat in terms of the temperatures at which the exchange takes place, namely the "baricenters" or "first moments" of these functions. Further, with the aid of general heat transfer inequalities between the system and its environment the analysis is extended to take into account the temperatures of the environment. All known bounds on efficiency and on work are shown to be consequences of the main result; in fact, they are seen to be estimates cruder than those here presented, which, in this sense, may be called optimal.

show abstract

“…Material element. In this subsection, we introduce the concept of a material element, following the scheme to be found in [4,5], We shall confine ourselves to examining the case of isothermal infinitesimal deformations. Let (i) X be a set whose elements a are called states; (ii) n be a set of functions n: [0, dn\ -> X, defined on the real interval [0, dn\ (with d > 0) that take their values in the state set; each element n e n is called a process and the interval [0, dn\ is interpreted as the time-interval during which the process takes place; dn is called the duration of the process; it' := 7r(0) and itJ := n(dn) denote the initial and the final values of it, respectively; (iii) E: X -> Sym be a mapping defined on the state set that takes its values in Sym, the space of the second-order symmetric tensors; for each state a, E{a) is interpreted as the corresponding infinitesimal strain tensor, at a fixed material point, with respect to a fixed reference configuration; (iv) S: X -> Sym be a mapping that, at each state a , delivers the corresponding stress S(a).…”

mentioning

confidence: 99%

Free-energy functions for elastic-plastic material elements

Lucchesi¹

1993

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract. Certain thermodynamic properties of elastic-plastic materials with workhardening are discussed and their corresponding free-energy functions are determined.1. Introduction. The aim of the present paper is to examine certain thermodynamic properties of elastic-plastic materials and to determine their free-energy functions. We shall confine ourselves to considering the von Mises yield criterion, infinitesimal deformations, and isothermal conditions.It is shown in [1] how, under suitable hypotheses on the spatial gradient of velocity, the infinitesimal theory of plasticity can be deduced from the general theory of materials with elastic range, a theory formulated in [2] and [3].In order to describe the constitutive response, we use the concepts of material element, state, and process (the latter is a mapping defined on a real interval, which takes its values in the set of states and specifies the possible evolution from an initial state). We formulate these concepts as in Silhavy [4,5].The following general properties of material elements, states, and processes are important to our developments. If a material element satisfies the condition of perfect accessibility (i.e., if any two states are linked by at least one process), then the second law of thermodynamics states [6] that the work done by the exterior on the material element during a closed process is nonnegative. If the second law is satisfied, at least one state function y/ exists, called free-energy function, which satisfies the dissipation inequality, i.e., the inequality saying that the work done during any process linking two states al and a2 is not less than (t//(a2) -y/{al )). In general, the function \f/ is not unique but, for each state a , the set of all free-energy functions vanishing at a0 has least and upper elements, i.e., free-energy functions y/_ and lj7 such that ^ f°r anY free-energy function with y/{o0) -0. If a material element does not meet the condition of perfect accessibility but has a base state, i.e., a state from which every other state is reachable by some process, it is still possible to formulate the second law in such a way that its prescription is equivalent to the existence of (at least) one free-energy function [7],

show abstract

Foundations of Continuum Thermodynamics

Cited by 8 publications

References 12 publications

Dual structure of thermodynamics

Dual structure of thermodynamics

The Second Law of Thermodynamics and Optimal Bounds for the Efficiency of Cyclic Processes

Free-energy functions for elastic-plastic material elements

Contact Info

Product

Resources

About