Critical temperature definition

The vapor definition introduces another concept, that of critical temperature. Critical temperature is defined as that temperature above which a gas will not liquefy regardless of any increase in pressure. Critical pres sure is defined as the pressure required at the critical temperature to cause the gas to change state. 

There is, for every gas or vapour, a definite temperature, above which it is impossible, by increase of pressure alone, to effect a liquefaction of that gas or vapour. This is called the critical temperature (6 ). 

If the temperature is changed the miscibility of the liquids alters, and at a particular temperature the miscibility may become total this is called the critical solution temperature. With rise of temperature the surface of separation between the liquid and vapour phases also vanishes at a definite temperature, and we have the phenomenon of a critical point in the ordinary sense. According to Pawlewski (1883) the critical temperature of the... 

Combustion is sometimes described as a chemical reaction giving off significant energy in the form of heat and light. It is easy to see that for this Arrhenius reaction, representative of gaseous fuels, the occurrence of combustion by this definition might be defined for some critical temperature between 600 and 1200 K. 

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. 

It is somewhat confusing that the term critical diameter is also used by those interested in the potential of an energetic material to undergo thermal runaway. Because, by definition, the energetic material releases heat when it decomposes, it has the potential to increase its local environmental temperature. Depending on the decomposition kinetics of the material, at some critical dimension the charge can self-heat to catastrophic reaction. This can be referred to in terms of the critical diameter or, more often, in terms of the initial environmental temperature that allows this scenario, the critical temperature . 

It would be of considerable interest to have data for the surface and interfacial tensions of a pair of liquids such as nicotine and water which are miscible in all proportions except within a definite temperature range. Here we should expect to find curves of the type shown in the figure, where a and h represent the surface tensions of the two phases within the critical region and c their interfacial tension. The latter has no meaning either above or below the critical temperatures and must have a maximum at some intermediate point. 

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. 

Covacs6 proposed another definition of the fractional free-volume. As the extrapolated volume of supercooled liquids reaches the crystalline state, vc, at temperature rc > 0 K, it is possible to compare this critical temperature with rg , the limit glass temperature at infinitely slow cooling. Free-volume in the crystalline state is assumed to be zero. In this case the value /g according to Doolittle may be compared with /g, c, which characterizes the excess free-volume of glass as compared with the crystalline state ... 

When the temperature has been increased to 374°C (point C), the vapor pressure has reached 218 atm—the container must be very strong The density of the vapor is now so great that it is equal to that of the remaining liquid. At this stage, the surface separating the liquid from its vapor vanishes and from this point on, we can no longer identify the liquid phase. Instead, a single uniform phase fills the container. Because a substance that fills any container it occupies is by definition a gas, we conclude that we have reached the critical temperature, Tc, of water the... 

The above relationship predicts a monotonic increase in p with increasing temperature as shown in Figure 3 for three different gases. Hence, the maximum amount of gas (by the Gibbs definition) adsorbed on the surface of the adsorbent can be attained at a lower pressure by operating close to the critical temperature of the adsorbed gas. Application of even higher pressures then p will result in a large increase in the... 

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-... 

A molar activation energy EA of diffusion is defined as the product EA = wl eRTc, with the critical temperature, Tc, of the system. This definition takes into account the connection between the interaction terms of the model, w, and w/e and IS units, as shown in section 6.3.4. At the critical temperature, Tc, a pure translational amount, w,-w, e, of the relative energy density is responsible for the magnitude of Dc. 

Since in Fig. 19 critical temperatures have been estimated by a rough extrapolation only, this study [39] could not make too definitive statements about the shift of the critical temperature due to confinement. A more extensive study has been possible for the bond fluctuation model [55], extracting both critical temperatures and the coexistence curves by use of the finite size scaling technique [236-239,280]. Figs.21, 22 present the results for chain length N=32. While mean field theory Eqs. (36) and (37) in Sect. 2.1 has predicted a crossover from... 

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