Critical temperature of a gas

The critical temperature, of a gas is the temperature above which the gas cannot be liquefied no matter how high the pressure. 

Originally it was considered that to obtain a gas in the liquid state the sole necessity was pressure however, all gases possess a physical property known as critical temperature The critical temperature of a gas is that temperature above which the gas cannot be liquefied, however great the pressure to which it is subjected. 

Gases are almost always less dense than liquids because the molecules are so far apart. (Density is the mass in a given volume.) As the pressure on a gas increases, it gets denser because the molecules are squeezed closer together. After a certain point, the molecules are so close together that the gas turns into a liquid. But at a very high temperature, called the critical temperature of a gas, the gas won t turn into liquid no matter how high the pressure. At that point it s called a supercritical fluid. 

The effect of temperature, however, is more important than that of the pressure because for each gas there is a certain temperature above which it cannot be liquefied, no matter how high a pressure may be applied. This temperature is known as the critical temperature. Thus, the critical temperature of a gas maybe defined, as that temperature above which it cannot be liquefied howsoever high the pressure may be. For instance, the critical temperature of carbon dioxide is 31.1 C. This means that it is not possible to liquefy carbon dioxide above 31.1 C by any means. 

The P-V Isotherms of Carbon Dioxide The importance of critical temperature of a gas was first discovered by T. Andrews in his experiments on pressure-volume relationships (isotherms) of carbon dioxide gas at a series of temperatures. The isotherms of carbon dioxide determined by him at different temperatures is shown in the figure given above. Consider first the isothermal at the lowest temperature, viz., 13.1 C. The point A represents carbon dioxide in gaseous state occupying a certain volume under a certain pressure. On increasing the pressure, its volume diminishes as is indicated by the curve AB. At B which represents a pressure of 49.8 atm, liquefaction of the gas commences and thereafter a rapid decrease in volume takes place at the same pressure, as more and more of the gas is converted into the liquid state. At C, the gas has been completely liquefied. Now, as the liquid is only slightly compressible, further increase of pressure produces only a very small decrease in volume. A steep line CD that is almost vertical shows this. 

The critical temperature of a gas is such a temperature that above it, no pressure, however great, will liquefy the gas. The critical pressure is that pressure at which gas at the critical temperature begins to liquefy. (See Table 2, also p. 657 1... 

The critical temperature of a gas is the absolute temperature, denoted T, above which the liquid phase cannot be formed no matter how great a pressure is applied to the system. 

The initial temperature of a gas condensate lies between the critical temperature and the cricondotherm. The fluid therefore exists at initial conditions in the reservoir as a gas, but on pressure depletion the dew point line is reached, at which point liquids condense in the reservoir. As can be seen from Figure 5.22, the volume percentage of liquids is low, typically insufficient for the saturation of the liquid in the pore space to reach the critical saturation beyond which the liquid phase becomes mobile. These... 

The absolute values of the solubilities of gases are not at present calculable from any general law, although W. M. Tate (1906) finds in the case of aqueous solutions a relation with the viscosities of the solution (/x ), and water (/x0), the critical temperatures of the gas (T0), and of water (T. ), and the absorption coefficients ... 

CRITICAL TEMPERATURE. 1. This term is most commonly used to denote the maximum temperature at which a gas (or vapor) may be liquefied by application of pressure alone. Above this temperature Ihe substance exists only as a gas. 2. The critical temperature of a superconducting transition takes place in zero magnetic field. 

Recently, considerable attention has been paid to the use of compressed gases and liquids as solvents for extraction processes (Schneider et al., 1980 Dain-ton and Paul, 1981 Bright and McNally, 1992 Kiran and Brennecke, 1992), although the law of partial pressures indicates that when a gas is in contact with a material of low volatility, the concentration of solute in the gas phase should be minimal and decrease with increased pressure. Nevertheless, deviations from this law occur at temperatures near the critical temperature of the gas, and the concentration of solute in the gas may actually be enhanced as well as increased with pressure. 

The Van der Waals equation is one of those happy approximations which somehow make reasonable predictions well outside the region in which their assumptions are valid. It can even be used to predict the critical constants of a gas. A Van der Waals gas should have a critical pressure and temperature given respectively by... 

The melting behavior for TPP in the presence of compressed pentane (Figure 1) is characterized by an interrupted three-phase, SLG equilibrium line which terminates at a LCEP. This behavior is characteristic of a gas and a solid with low mutual solubility, and is expected when the triple-point temperature of the solid is much greater than the critical temperature of the gas (3). At temperatures just above the LCEP temperature, TPP does not melt in the presence of compressed pentane, and gas-solid equilibrium is observed at pressures up to two hundred atmospheres (Figure 3). 

Critical Constants of a Gas The most characteristic property of gases is that their molecules lie far apart from one another and are in continuous rapid motion. Each molecule, therefore, leads almost an independent existence. This is particularly so when temperature is high and pressure is low. 

In 1881, van der Waals showed that if the pressure, volume and temperature of a gas are expressed in terms of its critical pressure, critical volume and critical temperature, we can obtain an important generalisation called the principle of corresponding states. 

The specific surface area of a ceramic powder can be measured by gas adsorption. Gas adsorption processes may be classified as physical or chemical, depending on the nature of atomic forces involved. Chemical adsorption (e.g., H2O and AI2O3) is caused by chemical reaction at the surface. Physical adsorption (e.g., N2 on AI2O3) is caused by molecular interaction forces and is important only at a temperature below the critical temperature of the gas. With physical adsorption the heat erf adsorption is on the same order of magnitude as that for liquefaction of the gas. Because the adsorption forces are weak and similar to liquefaction, the capillarity of the pore structure effects the adsorbed amount. The quantity of gas adsorbed in the monolayer allows the calculation of the specific surface area. The monolayer capacity (V ,) must be determined when a second layer is forming before the first layer is complete. Theories to describe the adsorption process are based on simplified models of gas adsorption and of the solid surface and pore structure. 

At the plateau the maximum uptake value of the adsorbent is therefore reached. The type I or Langmuir isotherm describes the formation of a single monolayer on the surface of the porous material. No multilayers of hydrogen are formed at 77 K, because the interaction strength between single layers is too weak at temperatures higher than the critical temperature of H2. Therefore a type I isotherm is typically obtained for porous materials at adsorption temperatures higher than the critical temperature of the gas. 

Simple systems will be considered first. We shall start with (sub-)monolayer adsorption, that is adsorption in which all the adsorbate molecules are in contact with the adsorbent. It is noted that for gases (sub-) monolayer adsorption is met only at low relative pressures for relative pressures approaching unity, invariably condensation in more than one layer takes place. Physical adsorption at temperatures above the critical temperature of the gas is also restricted to a maximum of one complete monolayer. For adsorption from solution (chapter 2) monolayer adsorption is more usually the rule. 

We consider application of Eqs. (I.6-16)-(1.6-I8) to (he calculation of the solubility of naphthalene (component 2) in carbon dioxide (component I) at 3S°C and at high pressures. Data for these conditions (Tsekhanskaya et al.T) are shown as open circles in Fig. 1.6-2. Particularly noteworthy is the dramatic enhancement In solubility—several orders of magnitude—that occurs with increasing pressure near foe critical pressure of foe solvent gas. The solubility enhancement, which obtains for temperatures slightly higher than the critical temperature of a solvent gas (the critical temperature of COi is 3l°C), is the basis for certain "supercritical extraction processes ase Paulaitis et a1.Ba for discussions of fols topic. 

IIL There are three real equal roots present. At and above the point where a = / y, there can only be one value of v for any assigned value of p. This point K (Fig. 143) is no other than the well-known critical point of a gas. Write pe, vc, Tc, for the critical pressure, volume, and temperature of a gas. From (2),... 

A supercritical fluid is formed whenever a substance is heated above its critical temperature. The critical temperature of a substance is the temperature above which a distinct liquid phase cannot exist, regardless of pressure. The vapor pressure of a substance at its critical temperature is itscriticalpressure. At temperatures and pressures above its critical teniperaiure and pressure (its critical point), a substance is called a supercritical fluid. Supercritical fluids have densities, viscosities, and other properties that are intermediate between those of the substance in its gaseous and liquid states. Table 29-1 compares some properties of supercritical fluids to those of typical gases and liquids. I hesc properties are important in gas. liquid, and supercritical fluid chromatography and extractions. 

All of these equations predict that the amount adscffbed increases monotonically with increasing pressure. Experimental adsorption isotherms attmn a masdmum value in the amount adsorbed and then fall to zero. At the critical temperature of the gas, the maximum in the isotherm occurs at a pressure of about 10 bars and the zero occurs at a much higher pressure of several hundred bars. For subcritical gases, the maximum occurs at lower pressure and for supercritical gases the maximum occurs at higher pressure. 

The critical pressure of a gas denoted is the vapor pressure of the liquid at the critical point. Hence, below the critical temperature any substance at a pressure above its vapor pressure will be liquid. 

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