Version 1
: Received: 3 January 2017 / Approved: 3 January 2017 / Online: 3 January 2017 (10:21:50 CET)
How to cite:
Hollestelle, H. Thermodynamics of a Set of Closed Curved Surfaces and Noether’s Theorem. Preprints2017, 2017010012. https://doi.org/10.20944/preprints201701.0012.v1
Hollestelle, H. Thermodynamics of a Set of Closed Curved Surfaces and Noether’s Theorem . Preprints 2017, 2017010012. https://doi.org/10.20944/preprints201701.0012.v1
Hollestelle, H. Thermodynamics of a Set of Closed Curved Surfaces and Noether’s Theorem. Preprints2017, 2017010012. https://doi.org/10.20944/preprints201701.0012.v1
APA Style
Hollestelle, H. (2017). Thermodynamics of a Set of Closed Curved Surfaces and Noether’s Theorem<strong> </strong>. Preprints. https://doi.org/10.20944/preprints201701.0012.v1
Chicago/Turabian Style
Hollestelle, H. 2017 "Thermodynamics of a Set of Closed Curved Surfaces and Noether’s Theorem<strong> </strong>" Preprints. https://doi.org/10.20944/preprints201701.0012.v1
Abstract
For a set of closed curved surfaces that resemble a Langmuir monolayer an energy is defined that depends only on the curvature of the surfaces interacting with the dimensions normal to the surfaces, that is, the thickness of these surfaces. The thickness, or depth, of the surfaces originates because of surface-particles with chains, that move freely on the inside of the surfaces at a certain depth. This is a purely geometrical description that does not depend on the introduction of ad hoc constants like the elastic constant. With a statistical mechanical model the equations of state are calculated for a gas of non-connected sphere-like surfaces in a volume. There are two states of which the lower temperature state is depending mostly on the interaction energy and surface properties, and the higher temperature state is depending mostly on sphere kinetic and volume properties. This results in aggregation of the sphere-like surfaces from many small ones to few large ones when lowering temperature and vice versa. The model allows for the calculation of the partition function and, when the emergence of the curvature - depth interaction is described as a phase-transformation, for the application of Noether’s theorem. Because of these properties the model is interesting in its own right apart from being an addition to existing elastic descriptions of surfaces.
Keywords
thermodynamics; surfaces; curvature
Subject
Physical Sciences, Thermodynamics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
4 June 2020
Commenter:
Harmen Hollestelle
The commenter has declared there is no conflict of interests.
Comment:
Published peer reviewed in The Int. Jrnl of Science and Technoledge, Jan. 2017, open access (the earliest version unpublished working paper around 1991, the author likes to thank the admirable late Prof. N. G. van Kampen for support at that early period).
Commenter: Harmen Hollestelle
The commenter has declared there is no conflict of interests.