Scientia Sinica

No. 1 LU: VOLUME VISCO-ELASTIC THEORY OF FLUIDS a 39

BoB Ba Om

Wie 2 V By Be. ou?

The velocity dispersion caused by the relaxational compression 1s (see equation

(18) of reference [2]) given by

pp _BotBo oth 11+ By Bow? (18) p(Be+B% 0773) By 1+B 07 7

whose inflectional point with respect to log © occurs at wo; = 0%/v§ T. = Bo/Bo T2 - (19)

In these equations, the f’s are adiabatic compressibilities. Let Br be the isothermal compressibility. Then, we have from thermodynamics

Bo = Br/¥o = Br C/C> , (20)

and, since for the present case of thermal relaxation V=V(T, P) we see at once for non-equilibrium states with the internal state remaining unchanged

Bo =Brlre=BrePicp, (21)

where obviously C“ =C,—C®, CY’ =C,—C™. Substituting (20) and (21) into (16), we get

(CS C,=—C6, C®) wt

= 22. SE SEIN CABG TOMER (22) But, since from thermodynamics Cp = Cu + TV e?/Br, (23)

V . ; 5 where & = = og ) , and, noting that @ and B; both involve adjustment

OT /, of translational but not of rotational and vibrational motions, i.e., they depend only on the external state, CY = CY + T© V a/Br, (24) we have, since in (23) T=T, C§ Cy — Cp CH = (T V a?/Br) (Cy — CY) = (6, = 6) e®. (25)