3. Superfusion, Supersaturation.—It is generally possible to cool a liquid several degrees below its normal freezing point without a separation of crystals, especially if it is protected from agitation, which would assist the molecules to rearrange themselves. A liquid in this state is said to be “undercooled” or “superfused.” The phenomenon is even more familiar in the case of solutions (e.g. sodium sulphate or acetate) which may remain in the “metastable” condition for an indefinite time if protected from dust, &c. The introduction into the liquid under this condition of the smallest fragment of the crystal, with respect to which the solution is supersaturated, will produce immediate crystallization, which will continue until the temperature is raised to the saturation point by the liberation of the latent heat of fusion. The constancy of temperature at the normal freezing point is due to the equilibrium of exchange existing between the liquid and solid. Unless both solid and liquid are present, there is no condition of equilibrium, and the temperature is indeterminate.
It has been shown by H.A. Miers (Jour. Chem. Soc., 1906, 89, p. 413) that for a supersaturated solution in metastable equilibrium there is an inferior limit of temperature, at which it passes into the “labile” state, i.e. spontaneous crystallization occurs throughout the mass in a fine shower. This seems to be analogous to the fine misty condensation which occurs in a supersaturated vapour in the absence of nuclei (see [Vaporization]) when the supersaturation exceeds a certain limit.
4. Effect of Pressure on the F.P.—The effect of pressure on the fusing-point depends on the change of volume during fusion. Substances which expand on freezing, like ice, have their freezing points lowered by increase of pressure; substances which expand on fusing, like wax, have their melting points raised by pressure. In each case the effect of pressure is to retard increase of volume. This effect was first predicted by James Thomson on the analogy of the effect of pressure on the boiling point, and was numerically verified by Lord Kelvin in the case of ice, and later by Bunsen in the case of paraffin and spermaceti. The equation by which the change of the F.P. is calculated may be proved by a simple application of the Carnot cycle, exactly as in the case of vapour and liquid. (See [Thermodynamics].) If L be the latent heat of fusion in mechanical units, v′ the volume of unit mass of the solid, and v″ that of the liquid, the work done in an elementary Carnot cycle of range dθ will be dp(v″ − v′), if dp is the increase of pressure required to produce a change dθ in the F.P. Since the ratio of the work-difference or cycle-area to the heat-transferred L must be equal to dθ/θ, we have the relation
dθ/dp = θ (v″ − v′)/L.
(1)
The sign of dθ, the change of the F.P., is the same as that of the change of volume (v″ − v′). Since the change of volume seldom exceeds 0.1 c.c. per gramme, the change of the F.P. per atmosphere is so small that it is not as a rule necessary to take account of variations of atmospheric pressure in observing a freezing point. A variation of 1 cm. in the height of the barometer would correspond to a change of .0001° C. only in the F.P. of ice. This is far beyond the limits of accuracy of most observations. Although the effect of pressure is so small, it produces, as is well known, remarkable results in the motion of glaciers, the moulding and regelation of ice, and many other phenomena. It has also been employed to explain the apparent inversion of the order of crystallization in rocks like granite, in which the arrangement of the crystals indicates that the quartz matrix solidified subsequently to the crystals of felspar, mica or hornblende embedded in it, although the quartz has a higher melting point. It is contended that under enormous pressure the freezing points of the more fusible constituents might be raised above that of the quartz, if the latter is less affected by pressure. Thus Bunsen found the F.P. of paraffin wax 1.4° C. below that of spermaceti at atmospheric pressure. At 100 atmospheres the two melted at the same temperature. At higher pressures the paraffin would solidify first. The effect of pressure on the silicates, however, is much smaller, and it is not so easy to explain a change of several hundred degrees in the F.P. It seems more likely in this particular case that the order of crystallization depends on the action of superheated water or steam at high temperatures and pressures, which is well known to exert a highly solvent and metamorphic action on silicates.
5. Variation of Latent Heat.—C.C. Person in 1847 endeavoured to show by the application of the first law of thermodynamics that the increase of the latent heat per degree should be equal to the difference (s″ − s′) between the specific heats of the liquid and solid. If, for instance, water at 0° C. were first frozen and then cooled to −t° C., the heat abstracted per gramme would be (L′ + s′t) calories. But if the water were first cooled to −t° C., and then frozen at −t°C., by abstracting heat L″, the heat abstracted would be L″ + s″t. Assuming that the heat abstracted should be the same in the two cases, we evidently obtain L′ − L″ = (s″ − s′)t. This theory has been approximately verified by Petterson, by observing the freezing of a liquid cooled below its normal F.P. (Jour. Chem. Soc. 24, p. 151). But his method does not represent the true variation of the latent heat with temperature, since the freezing, in the case of a superfused liquid, really takes place at the normal freezing point. A quantity of heat s″t is abstracted in cooling to −t, (L″ − s″t) in raising to 0° and freezing at 0°, and s’t in cooling the ice to -t. The latent heat L″ at −t does not really enter into the experiment. In order to make the liquid freeze at a different temperature, it is necessary to subject it to pressure, and the effect of the pressure on the latent heat cannot be neglected. The entropy of a liquid φ″ at its F.P. reckoned from any convenient zero φ0 in the solid state may be represented by the expression
φ″ − φ0 = ∫ s′dθ/θ + L/θ.
(2)
Since θdφ″/dθ = s″, we obtain by differentiation the relation