THE
LIQUID STATE IN THE
RECIPROCAL SYSTEM:
THE VOLUME/PRESSURE RELATION, A CONTEMPORARY MATHEMATICAL TREATMENT, PART II
where
and
(Of course, From my previous paper
where
^{³}/g) (total volume/total mass)
^{º}K and that
due to the solid molecules in solution of the liquid (solid volume/total
mass)
In this paper we will consider the effect of pressure on a liquid at
temperatures below the liquid natural temperature unit, 510.8º V. Also, pressure has a
different effect on a liquid at a temperature above, rather than below,
510.8ºK. These differences will be handled in another paper._{2}For a solid under pressure P is the external pressure.
For a liquid under pressure, the volume is multipled by the square of
the solid factor, or simply _{}. So,
It follows that isothermal compressibility is
It's often easier to work
with the bulk modulus,
From my previous paper,
since
where The internal pressure of a liquid is obviously different from that of
a solid. The natural unit of pressure in the Reciprocal System is
This expression is then multiplied by the number of pressure units, _{o}^{3}.) Therefore,
Substituting eq. 10 in eq. 12, we get
n.
Using eq. 8, 9, and 10, B can be expressed as_{v}
Now let's turn to calculating the volume expansivity.
where One could plug (or 1/B) and into eq. 1 and integrate, but the resulting equation is more complex than eq. 5 and thus not useful. In summary, to calculate bulk modulus and volume expansivity of a liquid, it is necessary to determine
I selected four important liquids: acetic acid, carbon tetrachloride, ethyl acetate, and water. Here are the results, in table format.
(The values of The _{3}_{ }contributes 3 units and the CO_{2}H contributes
4. In carbon tetrachloride, each atom contributes 1 unit.
In ethyl acetate, each volumetric group contributes a unit. In water,
3 molecules of 3 atoms each act against the external pressure, for a total
of 9. All values of n, _{v}n,
and _{t}n are integral or half-integral, as required by
the nature of the Reciprocal System. This is very different from
the empirical correlations used by other investigators._{p}^{7}In the coming years I hope some member of ISUS will calculate the results for thousands of liquids following the equations given here.
1. M. Abbott, H. Van Ness, 2. R. Satz, "The Liquid State in the Reciprocal System:
The Volume/Temperature Relation, a Contemporary Mathematical Treatement,"
(The numerical results of the paper do not change, because 3. R. Satz, "The Equation of State of Solid Matter,"
4. D. Larson, 5. 6. 7. R. Reid, J. Prausnitz, B. Poling, 8. D. Larson, |