Skip to main content
SpringerLink
Log in
Book cover

Lectures on Quantum Statistics pp 141–170Cite as

Real Gas Quantum Statistics

  • Chapter
  • First Online:

  • 1120 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 953))

Abstract

From the classical kinetic theory of gases we know the equation of state of the ideal gas, βp = n (see Chap. 1). For real gases, the interaction forces between the molecules lead to corrections to the ideal gas equation of state. We mention the classical theory by van der Waals and the systematic expansions with respect to density, called virial expansions.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Beth, E., and G.E. Uhlenbeck. 1937. The Quantum Theory of the Non-Ideal Gas. II. Behaviour at Low Temperatures. Physica 4: 915–924.

    Article  ADS  Google Scholar 

  • Blochinzew, D.J. 1953. Quantenmechanik. Berlin: Deutscher Verlag der Wissenschaften.

    Google Scholar 

  • Bobrov, V.B., and S. Trigger. 2018. Bose–Einstein Condensate and Singularities of the Frequency Dispersion of the Permittivity in a Disordered Coulomb System. Theoretical and Mathematical Physics 194: 404–414.

    Article  MathSciNet  Google Scholar 

  • Chetverikov, A.P., W. Ebeling, and M.G. Velarde. 2009. Local Electron Distributions and Diffusion in Anharmonic Lattices Mediated by Thermally Excited Solitons. European Physical Journal B 70: 217–227.

    Article  ADS  Google Scholar 

  • Costa, É., N.H.T. Lemes, M.O. Alves, R.C.O. Sebastião, and J.P. Braga. 2013. Quantum Second Virial Coefficient Calculation for the 4He Dimer on a Recent Potential. Journal of the Brazilian Chemical Society 24: 363–368.

    Article  Google Scholar 

  • Ebeling, W. 1974. Statistical Derivation of the Mass Action Law or Interacting Gases and Plasmas. Physica 73: 573–584.

    Article  ADS  Google Scholar 

  • Ebeling, W., H.J. Hoffmann, and G. Kelbg. 1967. Quantenstatistik des Hochtemperatur-Plasmas im Thermodynamischen Gleichgewicht. Contributions to Plasma Physics 7: 233–248.

    Google Scholar 

  • Ebeling, W., W.D. Kraeft, and D. Kremp. 1976. Theory of Bound States and Ionisation Equilibrium in Plasmas and Solids. Berlin: Akademie-Verlag.

    Google Scholar 

  • Ebeling, W., W.D. Kraeft, and G. Röpke. 2012. On the Quantum Statistics of Bound States within the Rutherford Model of Matter. Annals of Physics 524: 311–326.

    Article  Google Scholar 

  • Feynman, R.P. 1972. Statistical Mechanics. Reading: Benjamin.

    Google Scholar 

  • Friedman, H.L. 1962. Ionic Solution Theory. New York: Interscience.

    Google Scholar 

  • Friedman, H.L., and W. Ebeling. 1979. Theory of Interacting and Reacting Particles. Rostocker Physikalische Manuskripte 4: 330–348.

    Google Scholar 

  • Hill, T.L. 1956. Statistical Mechanics. New York: McGraw Hill.

    MATH  Google Scholar 

  • Hirschfelder, J.O., C.F. Curtis, and R.B. Bird. 1954. Molecular Theory of Gases and Liquids. New York. Wiley.

    MATH  Google Scholar 

  • Hoffmann, H.J., and W. Ebeling. 1968a. On the Equation of State of Fully Ionized Quantum Plasmas. Physica 39: 593–598.

    Article  ADS  Google Scholar 

  • Hoffmann, H.J., and W. Ebeling. 1968b. Quantenstatistik des Hochtemperatur-Plasmas im Thermodynamischen Gleichgewicht. II. Die Freie Energie im Temperaturbereich 106 bis 108 ∘K. Contributions to Plasma Physics 8 (1): 43–56.

    Google Scholar 

  • Huang, K. 1963. Statistical Mechanics. New York: Wiley.

    Google Scholar 

  • Huang, K. 2001. Introduction to Statistical Physics. London: Taylor & Francis.

    MATH  Google Scholar 

  • Kelbg, G., and H.J. Hoffmann. 1964. Quantenstatistik Realer Gase und Plasmen. Annalen der Physik 469: 310–318.

    Article  ADS  MathSciNet  Google Scholar 

  • Kilimann, K., and W. Ebeling. 1990. Energy Gap and Line Shifts for H-Like Ions in Dense Plasmas. Zeitschrift fr Naturforschung 45a: 613–617.

    Google Scholar 

  • Kilpatrick, J.E., W.E. Keller, E.F. Hammel, and N. Metropolis. 1954. Second Virial Coefficients of He3 and He4. Physical Review 94: 1103–1110.

    Article  ADS  Google Scholar 

  • Kraeft, W.D., W. Ebeling, D. Kremp. 1969. Complex Representation of the Quantumstatistical Second Virial Coefficient. Physics Letters A 29: 466–467.

    Article  ADS  Google Scholar 

  • Kraeft, W.D., D. Kremp, W. Ebeling, and G. Röpke. 1986. Quantum Statistics of Charged Particle Systems. Berlin: Akademie-Verlag.

    Book  Google Scholar 

  • Kremp, D., and W.D. Kraeft. 1972. Analyticity of the Second Virial Coefficient as a Function of the Interaction Parameter and Compensation Between Bound and Scattering States. Physics Letters A 38: 167–168.

    Article  ADS  Google Scholar 

  • Kremp, D., W.D. Kraeft, and W. Ebeling. 1971. Quantum-Statistical Second Virial Coefficient and Scattering Theory. Physica 51: 146–164.

    Article  ADS  MathSciNet  Google Scholar 

  • Kremp, D., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.

    MATH  Google Scholar 

  • Landau, L.D., and E.M. Lifshitz. 1976. Statistical Physics (Part I). Moscow: Nauka.

    Google Scholar 

  • Landau, L.D., and E.M. Lifshitz. 1980. Statistical Physics. Oxford: Butterworth-Heinemann.

    MATH  Google Scholar 

  • Langin, T.K., T. Strickler, N. Maksimovic, P. McQuillen, T. Pohl, D. Vrinceanu, et al. 2016. Demonstrating Universal Scaling for Dynamics of Yukawa One-Component Plasmas After an Interaction Quench. Physical Review E 93: 023201.

    Article  ADS  Google Scholar 

  • Morita, T. 1959. Equation of State of High Temperature Plasma. Progress in Theoretical Physics 22: 757–774.

    Article  ADS  Google Scholar 

  • Ott, T., M. Bonitz, L.G. Stanton, and M.S. Murillo. 2014. Coupling Strength in Coulomb and Yukawa One-Component Plasmas. Physics of Plasmas 21: 113704.

    Article  Google Scholar 

  • Pines, D., and P. Nozieres. 1966. The Theory of Quantum Liquids. New York: Benjamin.

    MATH  Google Scholar 

  • Rogers, F.J., H.C. Graboske, and D.J. Harwood. 1970. Bound Eigenstates of the Static Screened Coulomb Potential. Physical Review A 1: 1577–1586.

    Article  ADS  Google Scholar 

  • Slater, J.C. 1939. Introduction to Chemical Physics. New York: Mc Graw Hill.

    Google Scholar 

  • Uhlenbeck, G.E., and E. Beth. 1936. The Quantum Theory of the Non-Ideal Gas I. Deviations From the Classical Theory. Physica 3: 729–745.

    Article  ADS  Google Scholar 

  • Yukawa, H. 1935. On the Interaction of Elementary Particles. I. Proceedings of the Physico-Mathematical Society of Japan 17: 48–57.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB Physik, Humboldt Universität zu Berlin, Berlin, Germany

    Werner Ebeling

  2. Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Thorsten Pöschel

Authors
  1. Werner Ebeling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thorsten Pöschel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ebeling, W., Pöschel, T. (2019). Real Gas Quantum Statistics. In: Lectures on Quantum Statistics. Lecture Notes in Physics, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-030-05734-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation