• Українська
  • English

< | >

Current issue   Ukr. J. Phys. 2016, Vol. 61, N 5, p.400-412
doi:10.15407/ujpe61.05.0400    Paper

Humenyuk Y.A.

Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
(1, Svientsitskii Str., Lviv 79011, Ukraine; e-mail: josyp@ph.icmp.lviv.ua)

Thermodynamic Quantities of a Low-Density Gas in the Weakly Nonequilibrium Heat-Conduction Steady State

Section: General Problems of Theoretical Physics
Original Author's Text: English

Abstract: A low-density gas in the heat-conduction steady state is considered. Within the theory of continuous media, corrections to the pressure and the internal energy are obtained, which are related to the local temperature gradients of several orders. Corresponding expressions are derived for the compressibilities along and across the heat flux as well as for heat capacities. The expression for the nonequilibrium entropy is shown to obey the second law of thermodynamics. The free energy calculated is found out not to satisfy properties of a thermodynamic potential.

Key words: heat flux, temperature gradients, equation of state, nonequilibrium entropy, steady-state thermodynamics.

References:
1. S.R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962).
2. I. Gyarmati, Non-Equilibrium Thermodynamics. Field Theory and Variational Principles (Springer, Berlin, 1970).   CrossRef
3. S. Chapman and T.G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, Cam-bridge, 1970).
4. V.P. Silin, Introduction to the Kinetic Theory of Gases (Nauka, Moscow, 1971) (in Russian).
5. R. Balescu, Equilibrium and Non-Equilibrium Statistical Mechanics (Wiley-Interscience, New York, 1975).
6. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974).
7. M.A. Leontovich, Zhurn. Exp. Teor. Fiz. 8, 844 (1938).
8. M.A. Leontovich, Introduction to Thermodynamics. Statistical Physics (Nauka, Moscow, 1983) (in Russian).
9. H. Grad, Comm. Pure Appl. Math. 2, 311 (1949).
10. H. Grad, in Handbuch der Physik, edited by S. Fl¨ugge (Springer, Berlin, 1958).   PubMed
11. D. Jou, J. Casas-V’azquez, and G. Lebon, Rep. Prog. Phys. 51, 1105 (1988).   CrossRef
12. Extended Thermodynamic Systems, edited by S. Sieniutycz and P. Salamon (Taylor and Francis, New York, 1992).
13. I. M¨uller and T. Ruggeri, Rational Extended Thermodynamics (Springer, New York, 1999).
14. D. Jou, J. Casas-V’azquez, and G. Lebon, Rep. Prog. Phys. 62, 1035 (1999).   CrossRef
15. D. Jou, J. Casas-V’azquez, and G. Lebon, Extended Irreversible Thermodynamics (Springer, Berlin, 2001).   CrossRef
16. J. Casas-V’azquez and D. Jou, Phys. Rev. E 49, 1040 (1994).   CrossRef
17. R. Dom’ınguez and D. Jou, Phys. Rev. E 51, 158 (1995).   CrossRef
18. J. Camacho and D. Jou, Phys. Rev. E 52, 3490 (1995).   CrossRef   PubMed
19. J. Casas-V’azquez and D. Jou, Rep. Prog. Phys. 66, 1937 (2003).   CrossRef
20. D. Jou and A. Salhoumi, Phys. Lett. A 283, 163 (2001).   CrossRef
21. L.S. Garc’ıa-Col’ın and Fuentes y Mart’ınez G.J., J. Stat. Phys. 29, 387 (1982).   CrossRef
22. R.E. Nettleton, J. Phys. A: Math. Gen. 21, 3939 (1988).   CrossRef
23. R.E. Nettleton, J. Phys. A: Math. Gen. 22, 5281 (1989).   CrossRef
24. R.E. Nettleton, Phys. Rev. A 42, 4622 (1990).   CrossRef   PubMed
25. A.R. Vasconcellos, R. Luzzi, and L. S. Garc’ıa-Col’ın, Phys. Rev. A 43, 6622 (1991).   CrossRef   PubMed
26. L.S. Garc’ıa-Col’ın, A.R. Vasconcellos, and R. Luzzi, J. Non-Equilib. Thermodyn. 19, 24 (1994).
27. R.E. Nettleton, J. Chem. Phys. 106, 10311 (1997).   CrossRef
28. R.E. Nettleton, J. Chem. Phys. 93, 8247 (1990).   CrossRef
29. B.N. Miller and P.M. Larson, Phys. Rev. A 20, 1717 (1979).   CrossRef
30. B.C. Eu, J. Chem. Phys. 108, 5834 (1998).   CrossRef
31. Y. Oono and M. Paniconi, Prog. Theor. Phys. Suppl. 130, 29 (1998).   CrossRef
32. S.-i. Sasa and H. Tasaki, J. Stat. Phys. 125, 126 (2006).   CrossRef
33. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).   CrossRef
34. G.E. Crooks, Phys. Rev. E 60, 2721 (1999).   CrossRef   PubMed
35. G.E. Crooks, Phys. Rev. E 61, 2361 (2000).   CrossRef
36. T.S. Komatsu, N. Nakagawa, S.-i. Sasa, and H. Tasaki, Phys. Rev. Lett. 100, 230602 (2008), arXiv:0711.0246v4.   CrossRef   PubMed
37. T.S. Komatsu, N. Nakagawa, S.-i. Sasa, and H. Tasaki, J. Stat. Phys. 142, 127 (2011), arXiv:1009.0970v2.   CrossRef
38. S.-i. Sasa, J. Stat. Mech.: Theory Exper. 01004 (2014).
39. T.S. Komatsu, N. Nakagawa, S.-i. Sasa, and H. Tasaki, J. Stat. Phys. 134, 401 (2009), arXiv:0805.3023v1.   CrossRef
40. T.S. Komatsu and N. Nakagawa, Phys. Rev. Lett. 100, 030601 (2008), arXiv:0708.3158v1.   CrossRef   PubMed
41. N. Nakagawa, Phys. Rev. E 85, 051115 (2012), arXiv:1109.1374v4.   CrossRef   PubMed
42. N. Nakagawa and S.-i. Sasa, Phys. Rev. E 87, 022109 (2013), arXiv:1211.6203v2.   CrossRef   PubMed
43. T. Sagawa and H. Hayakawa, Phys. Rev. E 84, 051110 (2011), arXiv:1109.0796v4.   CrossRef   PubMed
44. J.H. Ferziger and H.G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972).
45. H.-D. Kim and H. Hayakawa, J. Phys. Soc. Jpn. 72, 1904 (2003), arXiv:0202003v5.
46. H.-D. Kim and H. Hayakawa, J. Phys. Soc. Jpn. 72, 2473 (2003), arXiv:cond-mat/0203036v5.   CrossRef
47. H.-D. Kim, Phys. Rev. E 71, 041203 (2005), arXiv:cond-mat/0501142v2.   CrossRef   PubMed
48. T.H. Nishino and H. Hayakawa, J. Phys. Soc. Jpn. 74, 2655 (2005), arXiv:cond-mat/0506491v2.   CrossRef
49. H. Hayakawa, T.H. Nishino, and H.-D. Kim, e-print arXiv:cond-mat/0412011v1 (2004).
50. S. Taniguchi, M. Nakamura, M. Sugiyama, M. Isobe, and N. Zhao, J. Phys. Soc. Jpn. 77, 014004 (2008).   CrossRef
51. C.S. Kim and G.P. Morriss, Phys. Rev. E 80, 061137 (2009).   CrossRef   PubMed
52. T. Taniguchi and G.P. Morriss, Phys. Rev. E 68, 026218 (2003).   CrossRef   PubMed
53. G.P. Morriss, T. Chung, and C. Angstmann, Entropy 10, 786 (2008).   CrossRef
54. G.P. Morriss and D. Truant, Entropy 14, 1011 (2012).   CrossRef
55. G.P. Morriss and D.P. Truant, Phys. Rev. E 87, 062144 (2013), arXiv:1305.2911v1.   CrossRef   PubMed
56. G.P. Morriss, e-print arXiv:1409.3259v1 (2014).
57. I.P. Bazarov, Thermodynamics (Vysshaya Shkola, Moscow, 1983) (in Russian).
58. R. Kubo, Thermodynamics (North-Holland–Wiley, Amsterdam–New York, 1968).
59. V.B. Kobylyanskyi, Statistical Physics (Vyshcha Shkola, Kyiv, 1972) (in Ukrainian).
60. Y.A. Humenyuk, Preprint of ICMP NASU, ICMP–15–06U, Lviv, 2015 (in Ukrainian).