Scientia Sinica

No. 1 LU: VOLUME VISCO-ELASTIC THEORY OF FLUIDS ‘ 37

The fact that equation (10) may be inferred from equation (4) supports the author’s viewpoint that our visco-elastic theory of sound absorption phenomena should be applicable to both gases and liquids. This is not merely an assumption as is liable to be understood™!, since one can obtain KneserBourgin equations for sound absorption and dispersion directly from the corresponding equations in terms of compressibilities previously derived by the author23! from our visco-elastic equations. This will be shown in § III.

Next, consider the case of chemical relaxation supposed to exist alone, that is caused by a single chemical reaction. Let AN be the increase in number of moles, N, of a certain chemical component in the fluid element due to the chemical reaction in question. Since V=V(p,7,N ) for the chemically nonequilibrium states, this increase gives rise to a partial change of volume, which: to a first approximation is

1 ( OV

we (fee \ 2 V Van SE (12)

= Beg SS

where AW is considered to be small. When thermodynamic equilibrium is attained, s=so with

Da aoa 9 — te =— 5 Gr (AN), (13)

where (AN), is the ultimate increase of N caused by a constant pressure ap-

3 : ; no ; V plied under the given thermodynamic condition. Supposing that +> =) = P

under the given thermodynamic condition (e.g., constant temperature or constant entropy) be insensitive to the existing change of chemical composition, the substitution of (13) and the difference between (13) and (12), viz., _

n—s=-7-(ae) te N)o — an], (14)

into our equation of irreversibility (4) will yield the following equation of chemical irreversibility:

aN) a AN—(AN) (15)

a T2 This equation appears to have been first given by Liebermann'”. Since 7, is then the relaxation time of the chemical reaction in the neighbourhood of equilibrium, 1/t, may be defined, as done by Liebermann, as the rate of the equilibrium reaction. As shown by Liebermann from simple kinetic considerations, 1/t, differs from the conventional reaction rate constant by a constant of proportionality depending on the equilibrium constant of the reaction and the molar fractions of the reacting components.