Critical pressure, definition

The quantity zoi will depend very much on whether adsorption sites are close enough for neighboring adsorbate molecules to develop their normal van der Waals attraction if, for example, zu is taken to be about one-fourth of the energy of vaporization [16], would be 2.5 for a liquid obeying Trouton s rule and at its normal boiling point. The critical pressure P, that is, the pressure corresponding to 0 = 0.5 with 0 = 4, will depend on both Q and T. A way of expressing this follows, with the use of the definitions of Eqs. XVII-42 and XVII-43 [17] ... 

Besides critical temperature, another term requires definition, that is, critical pressure which is the pressure which must be exerted on a gas cooled to its critical temperature to produce liquefaction. 

The maximum superheat which can be achieved with a nonboiling liquid is definitely pressure sensitive. This is evident in Fig. 18 and also in Fig. 28. Both plots show that the possible superheat (and therefore the possible values of ATc) decreases to zero as the critical pressure is approached. This is in agreement with the equation-of-state theory and also the nucleation-rate theory. 

For a pure substance, the critical temperature may be defined as the temperature above which the gas cannot be liquefied, regardless of the pressure applied. Similarily, the critical pressure of a pure substance is defined as the pressure above which liquid and gas cannot coexist, regardless of the temperature. These definitions of critical properties are invalid for systems with more than one component. 

The definition of the critical point as applied to a pure substance does not apply to a two-component mixture. In a two-component mixture, liquid and gas can coexist at temperatures and pressures above the critical point, Notice that the saturation envelope exists at temperatures higher than the critical temperature and at pressures higher than the critical pressure. We see now that the definition of the critical point is simply the point at which the bubble-point line and the dew-point line join. A more rigorous definition of the critical point is that it is the point at which all properties of the liquid and the gas become identical. 

As a minimum, a distillation assembly consists of a tower, reboiler, condenser, and overhead accumulator. The bottom of the tower serves as accumulator for the bottoms product. The assembly must be controlled as a whole. Almost invariably, the pressure at either the top or bottom is maintained constant at the top at such a value that the necessary reflux can be condensed with the available coolant at the bottom in order to keep the boiling temperature low enough to prevent product degradation or low enough for the available HTM, and definitely well below the critical pressure of the bottom composition. There still remain a relatively large number of variables so that care must be taken to avoid overspecifying the number and kinds of controls. For instance, it is not possihle to control the flow rates of the feed and the top and bottom products under perturbed conditions without upsetting holdup in the system. 

Since an azeotrope by definition has either a higher or a lower vapor pressure than that of any of the components, the azeotropic vapor pressure curve will always lie above or below the curves of the components. This is indicated schematically in Figure 1 where A and B are vapor pressure curves of the components and C is the vapor pressure of the azeotrope. If curve C crosses either A or B, the azeotropic vapor pressure is no longer greater or less than any of the components and the system will become nonazeotropic at the point of intersection. On the other hand, if the azeotropic curve is parallel to the other curves the system will be azeotropic up to the critical pressure. 

By definition, an SCF is a gas compressed to a pressure greater than its critical pressure (Pc) and heated to a temperature higher than its critical temperature (Tc). For example, the critical point for carbon dioxide occurs at a pressure of 73.8 bar and a temperature of 31.1 °C, as depicted in Figure 3.7. In this phase, regardless of the pressure applied, the fluid will not transcend to the liquid phase. 

The aim of this Chapter is the development of an uniform model for predicting diffusion coefficients in gases and condensed phases, including plastic materials. The starting point is a macroscopic system of identical particles (molecules or atoms) in the critical state. At and above the critical temperature, Tc, the system has a single phase which is, by definition, a gas or supercritical fluid. The critical temperature is a measure of the intensity of interactions between the particles of the system and consequently is a function of the mass and structure of a particle. The derivation of equations for self-diffusion coefficients begins with the gaseous state at pressures p below the critical pressure pc. A reference state of a hypothetical gas will be defined, for which the unit value D = 1 m2/s is obtained at p = 1 Pa and a reference temperature, Tr. Only two specific parameters, Tc, and the critical molar volume, VL, of the mono-... 

All the results presented so far give reason to conclude that the avalanche-like destruction of a foam column at definite temperature, pressure drop and foam dispersity, depends mainly on the equilibrium pressure reached. However, in order to establish the mechanism of action of the critical pressure drop, further studies of single foam films and foams are required. They should be performed under conditions that reveal the role of all elements of the foam (films, borders and vertexes) in the process of foam destruction. 

The critical loci of binary systems composed of normal paraffin hydrocarbons are shown in Figure 29. This diagram clearly shows that the critical pressure for a mixture can be greater than the critical pressure of each pure component It will be recalled that the pseudo-critical pressure used in correcting for the jion-ideal behavior of gases (equation 20, Chapter 2) is by definition between the critical pressures of the constituents in a two-component system. Obviously, there is no relation between the actual critical pressure of a mixture and the pseudo-critical pressure. Similarly, there is no relation between the actual critical temperature and pseudo-critical temperature. 

Every pure substance has a definite critical temperature, critical pressure, and critical density. We shall discuss the relationships between these quantities and the molecular weight in greater detail in a later paragraph. We may mention at this stage that Guldberg found the normal boiling point of all substances to be a nearly constant fraction of their critical temperature measured on the absolute scale. The table on p. 57 shows how far this rule is obeyed. ... 

Let us now focus upon the critical temperature and consider a few of the definitions that can describe this invariant point. It is important to note that the critical point is defined by the temperature only the value of the critical pressure appears to have a lesser or secondary significance. The critical (or supercritical) fluid region exists at all pressures at or above the critical temperature for a pure substance. Above this critical temperature, there exists only one phase, completely independent of the pressure. That is, no matter how high (or how low) you cause the pressure to be, the one phase wiU not condense to a hquid. 

Upper Limit of Vaporisation Curve.—On continuing to add heat to a liquid contained in a closed vessel, the pressure of the vapour will continuously increase. Since with increase of pressure the density of the vapour must increase, and since with rise of temperature the density of the liquid must decrease, a point will be reached at which the densities of liquid and vapour become identical the system cea es -to49nJieterogeneous, and-passes into one homogeneous phase. The temperature at which this occurs is called the critical temperature. To this temperature there will, of course, correspond a certain definite pressure, called the critical pressure. The curve representing the equilibrium between liquid and vapour must, therefore, end abruptly at the critical point- At temperatures above this point no pressure, however great, can cause the formation of the liquid phase at temperatures above the critical point the vapour becomes a gas. In the case of water, the critical temperature is 374 , and the critical pressure 217-5 atm. at the point representing these conditions the vapour-pressure curve of water must end. The lower determined by the range of tiie m gfa f-A... 

The 1-g curve has a definite upper limit at the critical pressure and temperature, since it is not possible to distinguish between liquid and gas above this pressure and temperature. 

A quantity often used in calculations on real gases is the Pitzer acentric factor, co. Pitzer defined the factor as a means of characterizing deviation from spherical symmetry for use in corresponding state modeP . The acentric factor is obtained from experimental data, as follows co = og P[) —1.0 in which P is the reduced pressure P/P at the reduced temperature of 0.7°C, P being the critical pressure. This definition is consistent with acentric factor values of zero for rare gases. 

This behavior occurs until a certain high temperature is reached denoted and called the critical temperature. At that temperature, the constant pressure plateau shrinks into a single point (point C) called the critical point The molar volume at that point is called critical molar volume and the pressure is the critical pressure P. A gas cannot be condensed to a liquid at temperatures above and there is no clear distinction between the liquid and gaseous phases because the two states cannot coexist with a sharp boundary between them. Experimentally, if a certain amount of gas and liquid is placed inside a pressurized container with transparent quartz windows and kept below T, two layers will be observed, separated by a sharp boundary. As the tube is warmed, the boundary becomes less distinct because the densities, and therefore the refractive indices, of the liquid and gas approach a common value. When the T is reached, the boundary becomes invisible and the iridescent aspect exhibited by the fluid is called critical opalescence. Hence the following definitions can be drawn for the critical constants of a real gas. 

In ordinary drying, the liquid in a specimen evaporates, and the resulting surface (interfacial) tension can distort the structure. In critical point drying [425], heating a specimen in a fluid above the critical temperature to above the critical pressure permits the specimen to pass through the critical point (that temperature and pressure where the densities of the liquid and vapor phases are the same and they coexist and thus there is no surface tension). By definition, a gas cannot condense to a liquid at any pressure above the critical temperature. The critical pressure is the minimum pressure required to condense a liquid from the gas phase at just... 

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