Continuum Mechanics and Thermodynamics

, Volume 24, Issue 4–6, pp 339–346 | Cite as

Quantum size effects on classical thermosize effects

Original Article

Abstract

Thermosize effects have been proposed in literature by considering the quantum size effects (QSE) induced by the wave character of particles. These effects appear only if nano and macro domains are connected to each other when they are under a temperature gradient. QSE are noticeable in nano domain while they are almost negligible in macro domain. This difference causes thermosize effects, which may be called quantum thermosize effects (QTSE) because of their pure quantum origin. On the other hand, also classical thermosize effects (CTSE) appear as a result of different transport regimes in nano and macro domains, and they can be noticeable even if QTSE are negligible. As long as the mean free path (l) is much greater than the mean de Broglie wave length of particles (λ), which is almost the case in practice λ/l < 1, the principal effects are CTSE. QSE cause only small corrections on CTSE when the scale is down to nanoscale. On the other hand, in literature, QTSE and CTSE have been examined individually although it is not possible to observe QTSE alone in practice except for the extreme case of \({\lambda /l \gg 1}\) . Furthermore, the constant pressure assumption and the Knudsen law have been used during the derivations of QTSE and CTSE, respectively, although the proper assumption at nanoscale is the modified Knudsen law, which considers QSE. In this study, QSE on CTSE are considered and the modified Knudsen law is derived and used to obtain the more realistic results for thermosize coefficients. The results can be used for a possible experimental verification of thermosize effects as well as to design some new devices based on these effects.

Keywords

Thermosize effects Quantum size effects Nano thermodynamics Knudsen law 

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References

  1. 1.
    Goddard W.A., Brenner D.W., Lyshevski S.E., Iafrate G.J.: Handbook of Nanoscience, Engineering, and Technology. CRC Press, Boca Raton (2003)Google Scholar
  2. 2.
    Wolf E.L.: Nanophysics and Nanotechnology. Wiley, Weinheim (2006)CrossRefGoogle Scholar
  3. 3.
    Kang J.W., Hwang H.J.: Nanoscale carbon nanotube motor schematics and simulations for micro electro-mechanical machines. Nanotechnology 15, 1633–1638 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    Schöll E.: Theory of Transport Properties of Semiconductor Nanostructures. Chapman & Hall, London (1998)CrossRefGoogle Scholar
  5. 5.
    Roldughin V.I., Zhdanov M.V.: Effect of surface forces on the gas flow in nanosized capillaries. Colloid J. 65, 598–601 (2003)CrossRefGoogle Scholar
  6. 6.
    Skoulidas A.I., Ackerman D.M., Johnson J.K., Sholl D.S.: Rapid transport of gases in carbon nanotubes. Phys. Rev. Lett. 89, 1–4 (2002)CrossRefGoogle Scholar
  7. 7.
    Molina M.I.: Ideal gas in a finite container. Am. J. Phys. 64, 503–505 (1996)ADSCrossRefGoogle Scholar
  8. 8.
    Pathria R.K.: An ideal quantum gas in a finite-sized container. Am. J. Phys. 66, 1080 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    Dai W.S., Xie M.: Quantum statistics of ideal gases in confined space. Phys. Lett. A 311, 340–346 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    Dai W.S., Xie M.: Geometry effects in confined space. Phys. Rev. E 70, 016103 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    Sisman A., Muller I.: The Casimir-like size effects in ideal gases. Phys. Lett. A 320, 360–366 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    Sisman A.: Surface dependency in thermodynamics of ideal gases. J. Phys. A Math. Gen. 37, 11353 (2004)ADSMATHCrossRefGoogle Scholar
  13. 13.
    Pang H., Dai W.S., Xie M.: The difference of boundary effects between Bose and fermi systems. J. Phys. A Math. Gen. 39, 2563–2571 (2006)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Sisman A., Ozturk Z.F., Firat C.: Quantum boundary layer: a non-uniform density distribution of an ideal gas in thermodynamic equilibrium. Phys. Lett. A 362, 16–20 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    Dai W.S., Xie M.: Interacting quantum gases in confined space: Two- and three-dimensional equations of state. J. Math. Phys. 48, 123302 (2007)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Dai W.S., Xie M.: Upper limit on the transition temperature for non-ideal Bose gases. Ann. Phys. 322, 1771–1775 (2007)ADSMATHCrossRefGoogle Scholar
  17. 17.
    Firat C., Sisman A.: Universality of quantum boundary layer for a Maxwellian gas. Phys. Scr. 79, 1–5 (2009)CrossRefGoogle Scholar
  18. 18.
    Ozturk Z.F., Sisman A.: Quantum size effects on the thermal and potential conductivities of ideal gases. Phys. Scr. 80, 065402 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    Firat C., Sisman A., Ozturk Z.F.: Thermodynamics of gases in nano cavities. Energy 35, 814–819 (2010)CrossRefGoogle Scholar
  20. 20.
    Nie W.J., He J.Z., Du J.: Performance characteristic of a Stirling refrigeration cycle in micro/nano scale. Phys. A 388, 318–324 (2009)CrossRefGoogle Scholar
  21. 21.
    Nie W.J., He J.Z., He X.J.: A micro-/nano thermosize refrigerator and its performance analysis. Appl. Phys. 103, 114909 (2008)Google Scholar
  22. 22.
    Nie W.J., He J.Z.: Performance analysis of a thermosize micro/nano heat engine. Phys. Lett. A 372, 1168–1173 (2008)ADSMATHCrossRefGoogle Scholar
  23. 23.
    Nie W., Liao Q., Zhang C., He J.: Micro-/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristics. Energy 35, 4658–4662 (2010)CrossRefGoogle Scholar
  24. 24.
    Su G., Chen L., Lin T., Chen J.: Thermosize effects of ideal fermi gases confined in micro/nano-scale tubes. J. Low Temp. Phys. 163, 275–283 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    Nie W., He J.: Quantum boundary effect on the work output of a micro-/nanoscaled Carnot cycle. J. Appl. Phys. 105, 1–5 (2009)CrossRefGoogle Scholar
  26. 26.
    Babac G., Sisman A.: Thermodynamic cycles based on classical thermosize effects. Int. J. Comput. Theor. Nano Sci. 8(9), 1–7 (2011)Google Scholar
  27. 27.
    Babac G., Sisman A.: Classical thermosize effects in degenerate quantum gases. Int. J. Comput. Theor. Nano Sci. 8(11), 1–4 (2011)Google Scholar
  28. 28.
    Babac, G., Sisman, A.: Thermosize effects and thermodynamic analysis of a thermosize power cycle. In: Joint European Thermodynamics Conference, 22–24 June, Copenhagen (2009)Google Scholar
  29. 29.
    Babac, G., Sisman, A.: A Mesoscale power cycle based on classical thermosize effects. In: 23rd International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy ECOS2010, 14–17 June, Lausanne (2010)Google Scholar
  30. 30.
    Babac, G., Sisman, A.: Classical thermosize effects for bose gases. In: 24th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy ECOS2011, 4–7 July, Novi sad (2011)Google Scholar
  31. 31.
    Karniadakis G.E., Aluru N., Beskok A.: Micro and Nano Flows: Fundamentals and Simulation. Springer, New York (2005)Google Scholar
  32. 32.
    Reif F.: Fundemantals of Statistical and Thermal Physics. McGraw-Hill, New York (1965)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Energy InstituteIstanbul Technical UniversityMaslak, IstanbulTurkey

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