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Properties of the Hugoniot function

Published online by Cambridge University Press:  28 March 2006

Robert D. Cowan
Affiliation:
Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico

Abstract

Differentiation of the Hugoniot function $H (p,v) = E(p,v)-E(p_0,v_0)+\frac {1}{2}(p + p_0)(v_0 - v)$ and use of the first and second laws of thermodynamics leads to the relation dH = T dS+dA, where dA is the element of area in the (p, v) plane swept out (in a counter-clockwise direction) by the line segment (p0, v0) → (p, v) as the point (p, v) is moved from some point (p1, v1) to a neighbouring point (p1+dp1, v1+dv1). This relation, together with rather general assumptions regarding the shape of the isentropic curves dS = 0 for the material behind the shock, makes possible the geometrical derivation of a number of properties of the function H and of the Hugoniot curves dH = 0.

Type
Research Article
Copyright
© 1958 Cambridge University Press

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References

Bethe, H. A. 1942 The theory of shock waves for an arbitrary equation of state, OSRD Report no. 545 (unclassified).Google Scholar
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Cowan, R. D. 1953 Phys. Rev. 92, 1079 (A).
Hugoniot, H. 1889 J. éc. polyt. Paris 58, 1.
Weyl, H. 1949 Comm. Pure Appl. Math. 2, 103.