Intrinsic pressure

Actually, the system capacitance and the pressure-decay rate measure the rate of capacitance discharge of the system. Because the combustion process is known to be controlled by pressure, the pressure-decay rate will disturb the combustion process. If the decay rate is greater than the intrinsic pressure-growth rate of the controlling reaction, the combustion process will not recover. This suggests that the pressure-decay rate dP/dt is the intrinsic term, rather than the capacitance term (L ). 

A further conclusion, however, remains to be drawn which is less familiar. The effect of the mutual attraction between molecules must be the same as that of a pressure existing in the liquid, and this is called the intrinsic pressure. A liquid must, therefore, oppose a resistance to forces tending to enlarge its volume or, in other words, must possess cohesion or tensile strength. We habitually overlook this fact, only because we handle liquids almost exclusively under conditions which change their shape, but do not alter their volume. If, however, we attempt to do the latter, the existence of cohesion or intrinsic pressure is easily demonstrated, and some experiments in this sense will be referred to below. 

Nevertheless, this molecular attraction exists and shows itself, when the gas is strongly compressed —and the distance between the molecules is greatly reduced—by causing deviations from Boyle s law. If we consider two layers of molecules, the distance between which is, of course, smaller than the radius of molecular attraction (Fig. 3), we see that their mutual attraction, or, in other words, the intrinsic pressure is proportional to the number of attracting molecules and to the number of attracted molecules, that is, proportional to the square... 

To connect the internal latent heat with the intrinsic pressure let us consider the forces to which a molecule of the liquid is subject. As long as it is in the interior of the liquid these are obviously equal in all directions, but the case is different when the molecule approaches the surface nearer than the radius of molecular attraction. Let O (Fig. 4) be such a molecule and describe round it a sphere with the radius C of molecular attraction then only the liquid within that sphere will have any effect on O. In the position shown the molecule is attracted downwards by the liquid contained in the segment ab (equal to AB), as the downward... 

The relations between the intrinsic pressure and other physical constants developed in the foregoing paragraphs have been found from theoretical considerations based on Laplace s theory, that is, on the assumption of cohesive forces acting over very small distances. They are of interest to us inasmuch as there is a necessary connection between intrinsic pressure and surface tension. While no numerical expression has so far been found for this, it is obvious that high intrinsic pressures must be accompanied by high surface tensions, since the surface tension is a manifestation of the same cohesive force as causes intrinsic pressure. (See, however, equation 3, p. 27, for an empirical relation between the two.)... 

By comparing the intrinsic pressures of various liquids and their solubilities in water, Walden finds that there is parallelism between the two. He... 

The attempt to show that surface tension phenomena were the cause of osmotic pressure was first made by Jager, and his theories were vigorously supported and developed by Traube, whose conclusions we shall state and examine briefly. He finds that the more a dissolved substance reduces the surface tension of water the greater is the velocity of osmosis of the solution. Hence he concludes that it is the difference in the surface tensions of solvent and solution which determines the direction and velocity of osmosis. The direction of flow Traube obtains by the following consideration let M (Fig. 7) be a membrane separating two liquids A and B. The molecules of each liquid are then drawn into its interior by the cohesion or intrinsic pressure. If the intrinsic... 

In the preceding pages we have availed ourselves of only one of the theories of surface tension, that of Laplace. It has led us directly to recognise an important property of liquids—their cohesion or intrinsic pressure—and has enabled us to establish... 

Figure 4.3 plots defect concentrations as a function of the partial pressure of oxygen, ranging from low to intrinsic pressure P to high Pq. ... 

With decreasing temperature, as we have seen, the intrinsic defect population decreases exponentially and, at low T, extrinsic disorder becomes dominant. Moreover, extrinsic disorder for oxygen-based minerals (such as silicates and oxides) is significantly alfected by the partial pressure of oxygen in the system (see section 4.4) and, in the region of intrinsic pressure, by the concentration of point impurities. In this new region, term Qj does not embody the enthalpy of defect formation, but simply the enthalpy of migration of the defect—i.e.,... 

VanderWaals argued that a> is the result of mutual attraction between the bulk of the gas and a sample near the wall of container, and might reasonably be proportional to the densities of both parts - that is to the square of the density of the gas. Since the volume of a given mass varies inversely with the density, the intrinsic pressure may be written as > = a/V2, where (a) is some constant for that particular gas... 

In the list of equations of state and of some other equations used in detonation calculations, which follows, the symbols listed by Cook (Ref 12, pp 376-78) will be used, with a few exceptions. Small v will be used for specific volume (cc per gram of expl) and small e for specific energy, although some investigators use caps. For pressure which does not include intrinsic pressure, tu, small p will be used, while P will be used for total pressure p + tu (See eq 6) and not for p/p2 listed by Cook. Some of the symbols used in equations of state are not listed by Cook... 

Intrinsic Pressure. See under Detonation (and Explosion), Equations of State, Introduction in Vol 4, p D269-L... 

H4) In the intrafibrillar phase, the pressure pi is uniform, while, in the extrafibrillar phase, water and ions are endowed, through constitutive equations, with their own intrinsic pressure. 

The Volume of Phosphorus in Liquid Compounds under Conditions of Maximum Contraction.—The volumes which liquid compounds would occupy if they remained in this state at temperatures not far removed from the absolute zero represent the closest packing possible at ordinary external pressure and under the influence of the internal or intrinsic pressure alone of non-oriented molecules, i.e. those which are not arranged in a space-lattice. These volumes can be obtained by shorter or longer extrapolations from the actual observed liquid volumes. 

In taking the lower limit of integration as zero, the effect of the size of the molecules is neglected. Tliis pull is, in equilibrium, balanced by the intrinsic pressure K of the fluid, hence ... 

The work required to pull unit area of a film of thickness d from the liquid surface (5 small compared with c) is Kd, and for unit volume so separated as successive thin films it will be K. The further work required to disintegrate these films into vapour will be small compared with K (since the main attraction is in the liquid bulk), and as the whole process is equivalent to the evaporation of 1 cm.3 of liquid, K is equaF to the latent heat of evaporation per cm.. For water, this is about 600 g. cal. or 25 2 x 10 ergs, and since 1 atm.=10 dynes per cm.2, K is about 25,000 atm. Thus the intrinsic pressures of liquids have very large values. 

Intrinsic Pressure and Solvent Pressure —We must be careful to distinguish the term solvent pressure from the internal, intrinsic oi cohesion pressure or tension already discussed in Chap III, Vol II This... 

The result for the relative intrinsic pressure denoted as pt = pt/4 gets the form... 

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