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TEMPERATURĘ C0EFFIC1ENT

rang* for mercury. Slotte proposes several empirical formulse, induding

^ ⁼ (* + *)“

where c, a and n are constants.

Thoipe and Rodger propose c

8 i-f «t + pt*

which is similar to Poiseuille's eąuation. ^Ehinn, from theoretical considerations, derives

- = A e-WT

Vt

where T is the absolute temperaturę, Q is the critical increment of energy reąuired to form a " loose spot" in the liąuid, R is the gaspfónstant, N the Avogadro number and A is a OOnstant.

Dunn's theory, which was applied first to\di|fusion in solution, is that unless a ** loose spot ” ||ć)irs among the solvent molecules, the osmotic pressure of the dissolving solute will not be sufficient tp drive it forward. If P is the osmotic pressure, the diffusion ratę, D, varies as P times the number of 'llipse spots.” If the " loose spots ” are p^fributed |t i random, we have

D = P. Ae~Q/^RT; or, sińce P tfaries with temperaturę,

D == RTA*-Q/^RT.

Applying Stokes’ law¹ to the passage Of a I molecule through the solvent, we have

or - ==> Ae~W, V

N 677-37/'

where r is the radius.

¹ To be discussed -later.

Q may also be regarded as the quantity of energy reąuired to overcome the attraction on any molecule of all its ńeighbours. Andrade and Sheppard independently derive a similar eąuation from probability considerations, and the latter points out that a number of other workers had used a similar escpression before the work of Dunn.

v Sheppard’s linę of reasoning is that, in shear, there is an eąuilibrium between def ormed and undeformed, and orientated and unorięntated molecules* This leads to an expression in which the logarithm of the fluidity is found to vary ljnearly with the reciprocal of the temperaturę (absolute) in the following way:

If the total number of molecules is N, and the number of " deformed " molecules n, then

N — n _pi^e~^tlKt * Ia~

where p_x and p% are the probabilities of the molecules in the respective States, c is the difference in the potential energies of the moleculeś in the two States, and k is the Boltzmann constant = R/N.

Sheppard assumes that pjpi is approximately independent of temperaturę, and that the fluidity is proportional to the ratio of unorientated to orientated molecules (».«., the less the molecules change when sheared, the morę easily they will shear). Hence he concludes that

<f> = Afl-K/r,

A being the proportionality constant, and K being

cjk,

It is not necessary to take the explanations of the physical meanings of these constants too seriously. A great many diiferent explanation$ of the