Thermodynamics of Shock Waves

  • Jerry W. Forbes
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)


The use of continuum thermodynamic parameters (i.e. quantity per gram) doesn’t change thermodynamic equations. Therefore, the continuum thermodynamic state parameters will be used. Following Callen [1], the first law of thermodynamics using continuum variables for E, v, Q is:
$$ \mathrm{ dE} = \mathrm{ d}{{\mathrm{ W}}_1} + \mathrm{ dQ} = - \mathrm{ P} \ \mathrm{ dv} + \mathrm{ dQ} $$
which states that the change in internal energy is equal to work done plus heat flow. In general the first law can include dissipative forces, which allows for irreversible as well as reversible processes. Thermodynamics used in this class is the description of equilibrium final states.


Sound Speed Fundamental Relation Release Wave Consistent Equation Reference Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    H.B. Callen, Thermodynamics (Wiley, New York, 1960)zbMATHGoogle Scholar
  2. 2.
    J.M. Walsh, R.H. Christian, Equation of state of metals from shock wave measurements. Phys. Rev. 97(6), 1544 (1955)CrossRefGoogle Scholar
  3. 3.
    W. Kaplan, Advanced Calculus (Addison-Wesley, Reading, 5th printing, 1959), p. 446Google Scholar
  4. 4.
    B. Hartmann, Determination of the bulk modulus and compressive properties of solids, in Methods of Chemistry: Determination of Elastic and Mechanical Properties, ed. by B.W. Rossiter, R.C. Baetzold (Wiley, New York, 1991), pp. 267–300Google Scholar
  5. 5.
    R.W. Warfield, Static high-pressure measurements on polymers, in Methods of Experimental Physics, ed. by R.A. Fava, vol. 16C (Academic, New York, 1980), pp. 91–116Google Scholar
  6. 6.
    R.E. Barker Jr., Gruneisen numbers for polymeric solids. J. Appl. Phys. 38(11), 4234–4242 (1967)CrossRefGoogle Scholar
  7. 7.
    S. Neel, Shock Compression of a Heterogeneous, Porous Polymer Composite. Ph.D. thesis (Georgia Tech, 2010)Google Scholar
  8. 8.
    G.E. Duvall, G.R. Fowles, in High Pressure Physics and Chemistry, ed. by R.S. Bradley, vol. 2 (Academic, New York, 1963)Google Scholar
  9. 9.
    S.A. Sheffield, Shock Induced Reaction in Carbon Disulfide. Ph.D. thesis, Washington State University, WSU SDL 78–03, Jun 1978Google Scholar
  10. 10.
    A. Dewaele, P. Loubeyre, M. Mezouar, Equations of state of six metals above 94 GPa. Phys. Rev. B 70, 094112 (2004)CrossRefGoogle Scholar
  11. 11.
    D.J. Andrews, Equation of state of the alpha and epsilon phases of iron. J. Phys. Chem. Solids 34, 825–840 (1973)CrossRefGoogle Scholar
  12. 12.
    J.M. Winey, G.E. Duvall, M.D. Knudson, Y.M. Gupta, Equation of state and temperature measurements for shocked nitromethane. J. Chem. Phys. 113(17), 7492 (2000)CrossRefGoogle Scholar
  13. 13.
    G.I. Pangilinan, Y.M. Gupta, Temperature determination in shocked condensed materials using Raman scattering. Appl. Phys. Lett. 70(8), 967–969 (1997)CrossRefGoogle Scholar
  14. 14.
    D.J. Pastine, J.W. Forbes, Accurate relations determining the volume dependence of the Quasiharmonic Gruneisen parameter. Phys. Rev. Letters 21, 1582 (1968)CrossRefGoogle Scholar
  15. 15.
    M. Cowperthwaite, Significance of some equations of state obtained from shock wave data. Am. J. Phys. 34, 1025 (1966)CrossRefGoogle Scholar
  16. 16.
    J.N. Johnson, D.B. Hayes, J.R. Asay, Equations of state and shock induced transformations in solid I-solid II liquid bismuth. J. Phys. Chem. Solids 35, 501 (1974)CrossRefGoogle Scholar
  17. 17.
    J.R. Asay, D.B. Hayes, Shock-compression and release behavior near melt states in aluminum. J. Appl. Phys. 46(11), 4789–4799 (1975)CrossRefGoogle Scholar
  18. 18.
    J.H. Rose, J.R. Smith, F. Guinea, J. Ferrante, Universal features of the equation of state of metals. Phys. Rev. B 29, 2963–2969 (1984)CrossRefGoogle Scholar
  19. 19.
    P. Vinet, J. Ferrante, J.H. Rose, J.R. Smith, Compressibility of solids. J. Geophys. Res. 92, 9319–9325 (1987)CrossRefGoogle Scholar
  20. 20.
    R.E. Cohen, O. Guseren, R.J. Hemley, Accuracy of equation-of-state formulations. Am. Mineral. 85, 338–344 (2000)Google Scholar
  21. 21.
    R. Jeanloz, Universal equation of state. Phys. Rev. B 38, 805–807 (1988)CrossRefGoogle Scholar
  22. 22.
    W.B. Holzapfel, Physics of solids under strong compression. Reports on Progress in Physics, 59, 29–90 (1996)Google Scholar
  23. 23.
    D.E. Grady, Equation of State for Solids, Shock Compression of Condensed Matter – 2011, AIP Conference Proceedings, vol. 1426, eds. by M.L. Elert, W.T. Buttler, J.P. Borg, J.L. Jordan, T.J. Vogler (Meleville, New York, 2012)Google Scholar
  24. 24.
    P.M. Morse, Diatomic molecules according to the wave mechanics. II vibrational levels. Phys. Rev. 34, 57–64 (1929)zbMATHCrossRefGoogle Scholar
  25. 25.
    A.D. Chijioke, W.W. Nellis, I.F. Silvera, High-pressure equations of state of Al, Cu, Ta, and W. J. Appl. Phys. 98, 073526 (2005)CrossRefGoogle Scholar
  26. 26.
    DR. Lide (ed.), Handbook of Chemistry and Physics, 85th edn. (CRC press, 2004–2005)Google Scholar
  27. 27.
    S.P. Marsh, LASL Shock Hugoniot Data (U. CA Press, Berkeley/Los Angeles, 1980)Google Scholar
  28. 28.
    S. Meenakshi, B.S. Sharma, Analysis of universal equations of state for solids. Indian J. Phys. 73(5), 663–668 (1999)Google Scholar
  29. 29.
    C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1968)Google Scholar
  30. 30.
    S.B. Segletes, Thermodynamic stability of the Mie-Gruneisen equation of state and its relevance to hydrocode computations. J. Appl. Phys. 70(5), 2489–2499 (1991)CrossRefGoogle Scholar
  31. 31.
    R. Menikoff, B.J. Plohr, The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61(1), 75–130 (1999)MathSciNetCrossRefGoogle Scholar
  32. 32.
    J.M. Winey, Y.A. Gruzdkov, Z.A. Dreger, B.J. Jensen, Y.M. Gupta, Thermomechanical model and temperature measurements for shocked ammonium perchlorate single crystals. J. Appl. Phys. 91(9), 5650 (2002)CrossRefGoogle Scholar
  33. 33.
    S.A. Sheffield, Response of liquid carbon disulfide to shock compression. II. Experimental design and measured Hugoniot information. J. Chem. Phys. 81(7), 3048–3063 (1984)CrossRefGoogle Scholar
  34. 34.
    D.H. Dolan, J.N. Johnson, Y.M. Gupta, Nanosecond freezing of water under multiple shock wave compression: Continuum modeling and wave profile measurements. J. Chem. Phys. 123, 064702 (2005)CrossRefGoogle Scholar
  35. 35.
    D.H. Dolan, Time dependent freezing of water under multiple shock wave compression, Ph.D. thesis, Washington State University, May 2003Google Scholar
  36. 36.
    J.W. Walsh, M.H. Rice, Dynamic compression of liquids from measurements on strong shock waves. J. Chem. Phys. 26(4), 815–823 (1957)CrossRefGoogle Scholar
  37. 37.
    M.H. Rice, J.W. Walsh, Equation of state of water to 250 kilobar. J. Chem. Phys. 26(4), 824–830 (1957)CrossRefGoogle Scholar
  38. 38.
    G.A. Gurtman, J.W. Kirsch, C.R. Hastings, Analytical equation of state for water compressed to 300 kbar. J. Appl. Phys. 42, 851 (1971)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Energetics Technology CenterSt. CharlesUSA

Personalised recommendations