This paper deals with the long-standing conflict between interpretations of thermoelectricity based on the original reversible thermodynamics of Thomson and the later irreversible thermodynamics of Onsager. It is shown that, by a slight modification of the Maxwellian relaxation treated in a previous paper [J. Goddard and K. Kamrin, “Dissipation potentials from elastic collapse,” Proc. R. Soc. A 475, 20190144 (2019)], Onsager's symmetry is simply a reflection of the underlying symmetry of equilibrium thermodynamics. It is also shown that a modern interpretation of Thomson's thermodynamics, as given recently by the present author, reveals thermoelectricity to be the analog of a fluid-mechanical transport process with the limit of thermodynamic equilibrium corresponding to the convection-dominated regime of large Péclet number.
References
1.
W.
Thomson
, “On a mechanical theory of thermo-electric currents
,” Proc. R. Soc. Edinburgh
3
, 91
–98
(1851
);see also,
W.
Thomson
, Mathematical and Physical Papers (Cambridge University Press
, Cambridge, UK
, 1882
), pp. I-237
–266
(digital copy available at https://gallica.bnf.fr).2.
L.
Onsager
, “Reciprocal relations in irreversible processes. I
,” Phys. Rev.
37
, 405
(1931
).3.
J.
Goddard
, “On the thermoelectricity of W. Thomson: Towards a theory of thermoelastic conductors
,” J. Elasticity
104
, 267
–280
(2011
).4.
J.
Thomson
, “Xl. cathode rays
,” The London, Edinburgh, Dublin Philos. Mag.
44
, 293
–316
(1897
).5.
L.
Boltzmann
, “Zur Theorie der thermoelektrischen Ersheinungen
,” Sitzungber. Akad. Wissen. Wien, Abt. II
96
, 1258
–1297
(1887
).6.
W.
Thomson
, “Account of researches in thermo-electricity
,” Proc. R. Soc. London
7
, 49
–58
(1854
);see also,
W.
Thomson
, Mathematical and Physical Papers (Cambridge University Press
, Cambridge, UK
, 1882
), pp. I-460
–468
(digital copy available at https://gallica.bnf.fr).7.
G.
Lewis
, E.
Eastman
, and W.
Rodebush
, “The heat capacity of electro positive metals and the thermal energy of free electrons
,” Proc. Natl. Acad. Sci. U. S. A.
4
, 25
–29
(1918
).8.
P.
Bridgman
, “On the application of thermodynamics to the thermo-electric circuit
,” Proc. Natl. Acad. Sci. U. S. A.
15
, 765
–768
(1929
).9.
E.
Hall
, “The Thomson effect and thermal conduction in metals
,” Proc. Natl. Acad. Sci. U. S. A.
6
, 613
–621
(1920
).10.
H.
Callen
, “The application of Onsager's reciprocal relations to thermoelectric, thermomagnetic, and galvanomagnetic effects
,” Phys. Rev.
73
, 1349
(1948
).11.
J.
Nye
, Physical Properties of Crystals: Their Representation by Tensors and Matrices
, Oxford Science Publications (Clarendon
, Oxford
, 1957
).12.
N.
Mott
, The Theory of the Properties of Metals and Alloys
(Dover Publications
, New York
, 1958
).13.
A.
Sommerfeld
, Lectures on Theoretical physics - Thermodynamics and Statistical Mechanics
(Academic Press
, New York
, 1964
), Vol. 5
.14.
15.
D.
Edelen
, “A nonlinear Onsager theory of irreversibility
,” Int. J. Eng. Sci.
10
, 481
–490
(1972
).16.
D.
Edelen
, “On the existence of symmetry relations and dissipation potentials
,” Arch. Ration. Mech. Anal.
51
, 218
–227
(1973
).17.
J.
Goddard
, “Edelen's dissipation potentials and the visco-plasticity of particulate media
,” Acta Mech.
225
, 2239
–2259
(2014
),18.
J.
Goddard
and K.
Kamrin
, “Dissipation potentials from elastic collapse
,” Proc. R. Soc. A
475
, 20190144
(2019
).19.
B.
Coleman
and W.
Noll
, “Foundations of linear viscoelasticity
,” Rev. Mod. Phys.
33
, 239
(1961
),Erratum:
Rev. Mod. Phys.
36
(4
), 1103
, 1964
.20.
B.
Coleman
and C.
Truesdell
, “On the reciprocal relations of Onsager
,” J. Chem. Phys.
33
, 28
–31
(1960
).21.
I.
Müller
, A History of Thermodynamics: The Doctrine of Energy and Entropy
(Springer Science & Business Media
, 2007
).22.
R.
Fosdick
and L.
Truskinovsky
, “About clapeyron's theorem in linear elasticity
,” in The Rational Spirit in Modern Continuum Mechanics
, edited by C.-S.
Man
and R.
Fosdick
(Springer
, 2004
), pp. 399
–426
.23.
J.
Maxwell
, “IV. On the dynamical theory of gases
,” Philos. Trans. R. Soc., London
157
, 49
–88
(1867
).24.
D.
Miller
, “Thermodynamics of irreversible processes. The experimental verification of the Onsager reciprocal relations
,” Chem. Rev.
60
, 15
–37
(1960
).25.
R. B.
Bird
, W.
Stewart
, and E.
Lightfoot
, Transport phenomena
, 1st ed. (John Wiley & Sons
, 1960
).26.
J.
Gibbs
, Scientific Papers of Josiah Willard Gibbs
, edited by H.
Bumstead
and R.
Van Name
(Longmans, Green & Co.
, 1906
), Vol. 1
, p. 455
.27.
J.
Goddard
, “The viscous drag on solids moving through solids
,” AIChE J
60
, 1488
–1498
(2014
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.
