Page:EB1911 - Volume 27.djvu/924

 unsaturated vapour is represented by the branch DE, which is similar to the isothermal of a gas obeying Boyle’s law. When the saturation-pressure is reached at D the vapour begins to condense, and the volume diminishes without further increase of pressure, giving the isopiestic branch DCB. At B, when the vapour is completely liquefied, further compression produces a rapid rise of pressure, as shown by the branch BA, representing the behaviour of the liquid. . 1. A, James Thomson Isothermal; B, Isothermals of CO2 (Andrews).

It is possible, however, to trace the branch DN for the supersaturated vapour continuously beyond D without liquefaction in the absence of nuclei. It is similarly possible to trace the liquid branch ABM beyond B to lower pressures in the absence of dissolved gases. As the temperature is raised, the length of the branch BD, representing the increase of volume in passing from the liquid to the gas, diminishes, as shown in fig. 1, B, which represents the isothermals of CO2, according to Andrews (Phil. Trans. 1869). Above the critical temperature, the discontinuities at B and D disappear from the isothermal curve, and it is impossible to obtain separation of the two states, liquid and gas, however great the pressure applied. The critical pressure is the vapour-pressure of the liquid at the critical temperature. It is possible to obtain a perfectly continuous passage from the gaseous to the liquid state by keeping the vapour at a pressure greater than the critical pressure while it is cooled from a temperature above the critical point, at which it would expand indefinitely (if the pressure were reduced) without separation into two phases, to a temperature below the critical point, at which expansion would produce separation into liquid and vapour as soon as the pressure was reduced to the saturation value. It was maintained by Andrews, on the basis of these and similar observations, that the gaseous and liquid states were merely widely separated forms of the same condition of matter, since one could be converted into the other without any breach of continuity or sudden evolution of heat or change of volume; just as an amorphous solid in the process of fusion becomes gradually more and more plastic as the temperature is raised, and passes into the state of a viscous liquid with continually diminishing viscosity. The same idea was further developed by James Thomson (Proc. R.S., 1871), who suggested that the discontinuity of the isothermal at temperatures below the critical point was only apparent. He supposed that the extensions of the liquid and vapour curves BM, DN, in fig. 1, A, representing the states of superheated liquid and supersaturated vapour, might theoretically be joined by a continuous Curve MN, representing a homogeneous transformation, which, however, could not be realized in practice, as the state of the substance corresponding to this part of the curve would be unstable. Maxwell (Nature, 1875) showed that the straight line BCD representing the saturation-pressure must cut off loops BMC, CND, of equal area from this imaginary isothermal; otherwise it would be theoretically possible to obtain a balance of work without any difference of temperature by taking the substance through the isothermal cycle BCDNCMB. The theoretical isothermal of James Thomson is qualitatively represented by an equation of the type devised by Van der Waals, in which the mutual attraction of the molecules of a gas is regarded as equivalent to an internal pressure of the form a/v2, which he supposes identical with the capillary pressure of the liquid. It has been found, however, that this simple expression is not sufficiently exact. It is probable that it is not merely a question of varying attraction between similar molecules. A vapour should rather be regarded as containing a certain proportion of compound or coaggregated molecules, which partially dissociate when the pressure is diminished or the temperature raised. A liquid similarly contains dissolved molecules of vapour, and the state of equilibrium is more nearly analogous to that between conjugate saturated solutions (e.g. water and phenol).

3. Effect of Capillary Pressure on Ebullition.—It was remarked at a very early date that water and other liquids could be raised under atmospheric pressure several degrees above their normal boiling-points in a clean glass vessel without ebullition occurring, and that, when a bubble was formed, it would expand explosively, producing the phenomenon of “bumping”; but that, if metallic filings or other bodies capable of supplying small bubbles of air were introduced, ebullition would proceed quietly at the normal temperature. L. Dufour succeeded in raising small drops of water, suspended in an oil mixture of suitable density, to a temperature of nearly 180° C. under atmospheric pressure. Similar observations lead to the conclusion that the phenomenon of ebullition, or boiling with the formation of bubbles, depends essentially on the presence of air or dissolved gas to provide nuclei for the starting-points of the bubbles. This is a natural consequence of the capillary pressure due to surface tension. The vapour-pressure p inside a small spherical bubble of radius r must exceed the pressure P in the liquid just outside the bubble by 2T/r, where T is the surface tension of the liquid. The capillary pressure 2T/r may be. very large if r is small. It is often stated on the strength of this relation that a bubble of radius r in a liquid will not expand indefinitely and rise to the surface as in ebullition, until the vapour-pressure p inside the bubble exceeds the external pressure P by 2T/r. But this neglects the effect of the air or gas contained in the bubble, which plays an essential part in the phenomenon. A bubble of vapour containing no air or gas could not exist at all in stable equilibrium in a liquid. If its radius r were such as to make 2T/r greater than p−P, it would collapse entirely. A bubble containing gas, on the contrary, is in stable equilibrium when its radius r is such that the pressure of the gas and vapour inside it balance the external pressure P together with the capillary pressure 2T/r. Any diminution of r produces an increase in the pressure of the gas which is more than sufficient to balance the increase of the capillary pressure 2T/r. Supposing that the external pressure and temperature remain constant, the partial pressure of the gas inside the bubble varies inversely as the volume of the bubble, and may be represented by a/r&#8202;3. The size of the bubble is determined by the equation p+a/r&#8202;3=P+2T/r. The equilibrium is always stable if p is less than P. If p is greater than P, the equilibrium becomes unstable (and the bubble expands indefinitely), when the gas-pressure a/r&#8202;3 is one-third of the capillary pressure 2T/r. This follows immediately by differentiating the above equation with respect to r, assuming the difference p−P to remain constant. Substituting 2T/3r for a/r&#8202;3 we obtain the condition of stability,

In other words, the temperature of a liquid containing bubbles of radius r will rise until the excess pressure given by (1) is reached, and ebullition will begin as soon as the excess pressure amounts to two-thirds of the capillary pressure, and will not be delayed until the full capillary pressure is reached, as might appear at first sight. Bubbles 1 millimetre in diameter in water at P＝760 mm. become unstable when the temperature reaches 100·05° C. approximately. To obtain a superheat of 10° C, where the excess pressure is 316 mm., the bubbles must not exceed about th mm. diameter. The condensation of a vapour is also retarded by the effect of capillary pressure, but the relation in this case is somewhat different.

4. Effect of Capillary Pressure on Vapour-Pressure.—It was observed by Sir W. Thomson (Lord Kelvin) (Phil. Mag. iv. 42, p. 448, 1871) that if a capillary tube of radius r is immersed in a liquid of surface tension T, and the liquid rises to a height h above the plane surface (the whole being enclosed in a vessel of uniform temperature containing only the vapour of the liquid) the pressure of the vapour at the curved surface of the meniscus in the capillary tube will be less than that at the plane surface by the amount, gh/v, where g is the acceleration of gravity, and 1/v is the density of the vapour. But the vapour must be in equilibrium with the liquid at both surfaces. Otherwise perpetual motion would ensue