322 
10 
in which case (3) gives 
ae ov aie dv = Pe (v) Y 
(19) z 
Se RD EE 1 oy Gece r 
gabe ah ig aaee is = 7; (S ) 
I.e.: In order that the pressure Pp be determined by the specific 
volume v alone, the same need not be true for the internal energy Ww but 
U must be the sum of two terms ies 1h. of whi.ch De depends on the 
specific volume v alcne and ee on the specific entropy AS alone -- and 
there can be no "interaction energy" involving v, S together. 
In many compression and shock provlems involving solids and liquids 
those can be treated as such "interactionlcss" substances. 
In this case the specific entropy iG disappears from the differ- 
ential equation of the continuous case, which assumes the form (15), and 
also from the shock conditions (10), (14). These equations are sufficient 
to determine the variation of x, Vv, P, 3 i.e. the visible motion of 
matter and the mechanical forces acting upon it. They depend only on the 
Oe term of the inner energy U (cf. (18)). oa oy Buel Se TT’ come in 
only in (11), which becomes 
y t = or = ey area 
Re 7 Zee 3 (piv Pal (v7 va) ‘ (gba eee | 
(20) ‘ 
= P, +p.) (v,-v2) 
= iG ea jee i: { b dv 
V, 
Thus (8) is not needed in the case of continuous motion, and (11) 
is not needed in the case of shocks. However (8) and (11) express the con- 
servation of energy, so we see: For an "interactionless" inner energy (18) 
the visible motion and the mechanical forces can be determined by themselves, 
without using the conservation of energy. 
