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
| dL/dθ = s″ − s′ + L/θ, | (3) |
which is exactly similar to the equation for the specific heat of a vapour maintained in the saturated condition. If we suppose that the specific heats s′ and s″ of the solid and liquid at equilibrium pressure are nearly the same as those ordinarily observed at constant pressure, the relation (3) differs from that of Person only by the addition of the term L/θ. Since s″ is greater than s′ in all cases hitherto investigated, and L/θ is necessarily positive, it is clear that the latent heat of fusion must increase with rise of temperature, or diminish with fall of temperature. It is possible to imagine the F.P. so lowered by pressure (positive or negative) that the latent heat should vanish, in which case we should probably obtain a continuous passage from the liquid to the solid state similar to that which occurs in the case of amorphous substances. According to equation (3), the rate of change of the latent heat of water is approximately 0.80 calorie per degree at 0° C. (as compared with 0.50, Person), if we assume s″ = 1, and s′ = 0.5. Putting (s″ − s′) = 0.5 in equation (2), we find L = 0 at −160° C. approximately, but no stress can be laid on this estimate, as the variation of (s″ − s′) is so uncertain.
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| Fig. 1.—F.P. or Solubility Curve: simple case. |
6. Freezing of Solutions and Alloys.—The phenomena of freezing of heterogeneous crystalline mixtures may be illustrated by the case of aqueous solutions and of metallic solutions or alloys, which have been most widely studied. The usual effect of an impurity, such as salt or sugar in solution in water, is to lower the freezing point, so that no crystallization occurs until the temperature has fallen below the normal F.P. of the pure solvent, the depression of F.P. being nearly proportional to the concentration of the solution. When freezing begins, the solvent generally separates out from the solution in the pure state. This separation of the solvent involves an increase in the strength of the remaining solution, so that the temperature does not remain constant during the freezing, but continues to fall as more of the solvent is separated. There is a perfectly definite relation between temperature and concentration at each stage of the process, which may be represented in the form of a curve as AC in fig. 1, called the freezing point curve. The equilibrium temperature, at the surface of contact between the solid and liquid, depends only on the composition of the liquid phase and not at all on the quantity of solid present. The abscissa of the F.P. curve represents the composition of that portion of the original solution which remains liquid at any temperature. If instead of starting with a dilute solution we start with a strong solution represented by a point N, and cool it as shown by the vertical line ND, a point D is generally reached at which the solution becomes “saturated.” The dissolved substance or “solute” then separates out as the solution is further cooled, and the concentration diminishes with fall of temperature in a definite relation, as indicated by the curve CB, which is called the solubility curve. Though often called by different names, the two curves AC and CB are essentially of a similar nature. To take the case of an aqueous solution of salt as an example, along CB the solution is saturated with respect to salt, along AC the solution is saturated with respect to ice. When the point C is reached along either curve, the solution is saturated with respect to both salt and ice. The concentration cannot vary further, and the temperature remains constant, while the salt and ice crystallize out together, maintaining the exact proportions in which they exist in the solution. The resulting solid was termed a cryohydrate by F. Guthrie, but it is really an intimate mixture of two kinds of crystals, and not a chemical compound or hydrate containing the constituents in chemically equivalent proportions. The lowest temperature attainable by means of a freezing mixture is the temperature of the F.P. of the corresponding cryohydrate. In a mixture of salt and ice with the least trace of water a saturated brine is quickly formed, which dissolves the ice and falls rapidly in temperature, owing to the absorption of the latent heat of fusion. So long as both ice and salt are present, if the mixture is well stirred, the solution must necessarily become saturated with respect to both ice and salt, and this can only occur at the cryohydric temperature, at which the two curves of solubility intersect.
The curves in fig. 1 also illustrate the simplest type of freezing point curve in the case of alloys of two metals A and B which do not form mixed crystals or chemical compounds. The alloy corresponding to the cryohydrate, possessing the lowest melting point, is called the eutectic alloy, as it is most easily cast and worked. It generally possesses a very fine-grained structure, and is not a chemical compound. (See Alloys.)
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| Fig. 2.—Cooling Curves of Alloys: typical case. |
To obtain a complete F.P. curve even for a binary alloy is a laborious and complicated process, but the information contained in such a curve is often very valuable. It is necessary to operate with a number of different alloys of suitably chosen composition, and to observe the freezing points of each separately. Each alloy should also be analysed after the process if there is any risk of its composition having been altered by oxidation or otherwise. The freezing points are generally best determined by observing the gradual cooling of a considerable mass, which is well stirred so long as it remains liquid. The curve of cooling may most conveniently be recorded, either photographically, using a thermocouple and galvanometer, as in the method of Sir W. Roberts-Austen, or with pen and ink, if a platinum thermometer is available, according to the method put in practice by C. T. Heycock and F. H. Neville. A typical set of curves obtained in this manner is shown in fig. 2. When the pure metal A in cooling reaches its F.P. the temperature suddenly becomes stationary, and remains accurately constant for a considerable period. Often it falls slightly below the F.P. owing to super-fusion, but rises to the F.P. and remains constant as soon as freezing begins. The second curve shows the cooling of A with 10% of another metal B added. The freezing begins at a lower temperature with the separation of pure A. The temperature
