In this paper we introduce the Isotherm Length-Work theorem using the Helmholtz potential metric and the virial expansion of pressure in inverse power of molar volume. The theorem tells us what length of a thermodynamical system described by equation of state through virial expansion along isotherms actually is with such a metric. We also give explicit solutions for thermodynamic length along isotherms in the case of first, second and third order expansion
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Arnold (1967) Mathematical Methods of Classical Mechanics Springer Verlag Berlin
H.B. Callen (1960) Thermodynamics Wiley New York
C. Caratheodory (1909) ArticleTitleUnterschungen uber die Grundlagen der Thermodynamyk Mathematishe Annalen 67 355–386 Occurrence Handle10.1007/BF01450409
Caratheodory C. (1955). Unterschungen uber die Grundlagen der Thermodynamyk. Gesammelte Mathematische Werke, B.2., Munchen, 131–177.
J.W. Gibbs (1961) The Scientific Papers Dover Publ. New York
R. Hermann (1973) Geometry, Physics and Systems Dekker New York
R. Mrugala (1978) ArticleTitleGeometrical Formulation of Equilibrium Phenomenological Thermodynamics Reports Math. Phys. 14 IssueID3 419–427 Occurrence Handle10.1016/0034-4877(78)90010-1
R. Mrugala (1996) ArticleTitleOn a Riemannian metric on contact thermodynamic spaces Reports Math. Phys. 38 IssueID3 339–348 Occurrence Handle10.1016/S0034-4877(97)84887-2
Preston S. Notes on the geometrical structures of thermodynamics, manuscript to be submitted, 2004.
G. Ruppeiner (1979) ArticleTitleThermodynamics: A Riemannian geometric model Phys. Rev. A 20 IssueID4 1608–1613 Occurrence Handle10.1103/PhysRevA.20.1608
G. Ruppeiner (1995) ArticleTitleRiemannian geometry in thermodynamic fluctuation theory Rev. Modern Phys. 67 IssueID3 605–659 Occurrence Handle10.1103/RevModPhys.67.605
P. Salamon R.S. Berry (1983) ArticleTitleThermodynamic length and dissipated availability Phys. Rev. Lett. 51 IssueID13 1127–1130 Occurrence Handle10.1103/PhysRevLett.51.1127
P. Salamon J. Nulton E. Ihrig (1984) ArticleTitleOn the relation between entropy and energy versions of thermodynamics length J. Chem. Phys. 80 436 Occurrence Handle10.1063/1.446467
P. Salamon B. Andresen P.D. Gait R.S. Berry (1980) ArticleTitleThe significance of Weinhold’s length J. Chem. Phys. 73 IssueID2 1001–1002 Occurrence Handle10.1063/1.440217
M. Santoro (2005) ArticleTitleWeinhold’s length in an isentropic Ideal and quasi-Ideal Gas Chem. Phys. 310 IssueID1–3 269–272 Occurrence Handle10.1016/j.chemphys.2004.10.042
M. Santoro (2005) ArticleTitleWeinhold’s length in an isochoric thermodynamic system at constant heat capacity Chem. Phys. 313 IssueID1–3 331–334 Occurrence Handle10.1016/j.chemphys.2005.01.025
M. Santoro (2004) ArticleTitleThermodynamic length in a two-dimensional thermodynamic state space J. Chem. Phys. 121 IssueID7 2932–2936 Occurrence Handle10.1063/1.1774156 Occurrence Handle15291603
Weinhold F. (1976). Metric Geometry of equilibriumthermodynamics p. I-V, J. Chem. Phys. 63(6):2479–2483, 2484–2487, 2488–2495, 2496–2501 (1976); 65(2):559–564.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Santoro, M. On the Helmholtz Potential Metric: The Isotherm Length-Work Theorem. J Stat Phys 120, 737–755 (2005). https://doi.org/10.1007/s10955-005-7006-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-005-7006-1