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  1. A-Z
  2. Annalen der Physik
  3. 1969
  4. Band 477
  5. Heft 7-8
  6. On Existence of Rev...
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On Existence of Reversible Adiabatic Surfaces
Autor(in)

Dutta, M.

Referenz

1 Caratheodory, C., Math. Ann. 67 (1909) 355

2 Caratheodory, C., Über die Bestimmung der Energie und der absoluten Temperatur mit reversiblen Prozessen. Berlin Ber. (1925) 39.

3 Born, M., Phys. Zs. 22 (1921) 218, 249, 282.

4 Lande, A., Axiomatische Begründung der Thermodynamik durch Caratheodory, Handbuch d. Phys., Bd. IX, Kapitel 1 - 4, (1966), 281 - 300.

5 Bucdahl, H. A., Amer. J. of Physics 17 (1949) 91.

6 Ehrenfest-Afanassjewa, T., Z. f. Phys. 33 (1925) 933;

7 Hocking, J. G., and G. S. Young, Topology, Addison-Wesley Pub. Co. (1961).

8 Dutta, M., T. Mukerjee and L. Debnath, Elements of General Topology, World Press, Calcutta (1964).

9 Hurewicz, W., and H. Wallman, Dimension Theory, Princeton University Press (1948).

Landsberg, P. T., Reviews of Modern Physics 28 (1956) 563.

Lew, J. S., Journ. of Math. Anal. and Applications 16 (1966) 363.

Turner, L. A., Amer. Journ. of Physics 28 (1960) 781.

Whaples, G., Journ. of Rat. Mech. and Anal. 1 (1952) 301.

Z. f. Phys. 34 (1925) 583.

Zemansky, M. W., Amer. Journ. of Physics 39 (1966) 919.

Seitenbereich

0321 - 0325

Zusammenfsg.

From the notion of equivalence relation and classes induced by them, the sets of points related by reversible processes restricted suitably are shown to be disjoint. By definition, each of thr above sets is arcwise-connected and so connected by HAUSDORFF'S theorem. Adiabatic processes are defined to be those in which, changes of states of a system are entirely by changing the deformation coordinates. First and second laws of thermodynamics are introduced just after CARATHÉODORY. Then by arguments of abstract mathematics every points in an r. a. set in an (<I>n</I> + 1)-dimensional space has been shown to gave a neighbourhood homeomorphics to a <I>n</I>-dimensional sphere, i. e., an r. a. set is an <I>n</I>-dimensional manifold having one-to-one correspondence with the deformation space. Thus, the existance of reversible adiabatic surfaces has been established.

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