Pressure curves

The agreement between the two columns is excellent.f Vapour pressure curves. The general form of the vapour pressure curves is given by equations (13). All empirical equations which have yet been proposed (for the literature, see Winkel-mann, vol. iii. p. 903 et seq.) must therefore coincide with the complete equation for all temperatures at which they are in agreement with experiment. The vapour pressure curve of a 

It is not sufficient even for an approximate calculation to know the form of the function L for a limited range of temperature (see p. 407). The value of the constant C depends to a considerable extent on the form of the function L at very low temperatures. For the calculation of C it is therefore necessary to know the values of the specific heats at very low temperatures. These have recently been determined in Nemst s laboratory for a number of solid substances, but unfortunately almost exclusively for substances which volatilise only at very high temperatures. Iodine is apparently the only substance whose vapour pressure and specific heats at low temperatures are both known. In this case the vapour pressure constant c can therefore be calculated with a certain degree of approximation. The calculation is as follows  

The specific heat of solid iodine, according to Nemst and Lindemann is given by 

The molecular specific heat of iodine vapour c, is 3 bR according to the kinetic theory. At room temperature it is somewhat higher than this, but we shall neglect this increase, as it probably 

This equation contains only the two constants Lq and 0, which can therefore be calculated if we know the value of the vapour pressure of solid iodine at two temperatures. According to Ramsay and Young, we have  

---

In practice, however, it is recommended to adjust the coefficient m, in order to obtain either the experimental vapor pressure curve or the normal boiling point. The function f T ) proposed by Soave can be improved if accurate experimental values for vapor pressure are available or if it is desired that the Soave equation produce values estimated by another correlation. 

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

The vapour pressure of a liquid increases with rising temperature. A few typical vapour pressure curves are collected in Fig. 7,1, 1. When the vapour pressure becomes equal to the total pressure exerted on the surface of a liquid, the liquid boils, i.e., the liquid is vaporised by bubbles formed within the liquid. When the vapour pressure of the liquid is the same as the external pressure to which the liquid is subjected, the temperature does not, as a rale, rise further. If the supply of heat is increased, the rate at which bubbles are formed is increased and the heat of vaporisation is absorbed. The boiling point of a liquid may be defined as the temperature at which the vapour pressure of the liquid is equal to the external pressure dxerted at any point upon the liquid surface. This external pressure may be exerted by atmospheric air, by other gases, by vapour and air, etc. The boiling point at a pressure of 760 mm. of mercury, or one standard atmosphere, may be termed the normal boiling point. 

The effect of superheated steam may be illustrated by reference to baizaldehyde, which boils at 178° at 760 mm. It distils with steam at 97-9° (Pj = 703-5 mm. and pg = 56-5 mm.) and the distillate contains 32-1 per cent, of benzaldehyde by weight. If one employs steam superheated to 133°, the vapour pressure of benzaldehyde (extrapolated from the boUing point - pressure curve) is 220 mm. hence pj = 540 (water), Pg = 220 (benzaldehyde), and... 

The reason for the constancy and sharpness of the melting j)oint of a pure crystalline solid can be appreciated upon reference to Fig. 7,10, 1, in which (a) is the vapour pressure curve of the solid and (6) that of the liquid form of the substance. Let us imagine a vessel, maintained at constant temperature, completely filled with a mixture of the above liquid and solid. The molecules of the solid can only pass into the liquid and the molecules of the liquid only into the solid. We may visualise two competitive processes taking place (i) the solid attempting to evaporate but it can only pass into the liquid, and (ii) the liquid attempting to distil but it can only pass into the solid. If process (i) is faster, the solid will melt, whereas if process (ii) proceeds with greater speed the... 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

System flow resistance as a function of flow rate is needed to select the proper fan size. For calculation of system pressure drop see References 5—8. The resistance pressure curve for a typical system (Fig. 4a) shows that the pressure required to force air through the system increases with the flow rate. 

Fig. 7. Control of fan performance with inlet vane control. SoHd lines marked A and N show normal performance without vanes (vanes wide open). As vanes are progressively closed, static and power curves are modified as indicated by dashed lines. Intersection ( - ) of the system resistance curve with these reduced pressure curves at points B, C, D, and E shows how imparting more spin to the inlet air reduces flow. Projecting points A to E vertically downward to the corresponding power curve locates fan power points A through E7 Power savings achieved over throttling control can be estimated by projecting points B through E vertically downward to the A power curve and comparing the value with that from the proper reduced power curve. To...

Fig. 6. Typical capillary pressure curves in air displacement cake dewatering of a fine coal suspension at varying dewatering times from top curve down the...

Fig. 10. Viscosity—pressure curve for typical petroleum oils (—) paraffinic (-) aUcycHc and ( ) soHd. To convert MPa to atm, divide by 0.101.

There are significant differences in various data sets pubtished for oleum vapor pressure. A review of existing vapor pressure data plus additional data from 10 to 8600 kPa (1.45 to 1247 psi) over the entire concentration range of oleum is available (93), including equations for vapor pressure versus temperature. Vapor pressure curves for oleum calculated from these equations are shown in Figure 19. Additional vapor pressure data from 0.06 to 14 kPa (0.5—110 torr) is given in the titerature (92). 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

For very small AP, flux is linear with pressure. Figure 7 shows a graph of flux versus pressure. Curve A is the pure water flux from equation 1, curve B is the theoretical permeate flux (TPE) for a typical process. As the gel layer forms, the flux deviates from the TPF following equation 7 and curve D results. Changing the hydrodynamic conditions changes K and results in a different operating curve, curve C. 

It has good capacity and drying capabiHty as illustrated by the vapor pressure curves in Figure 5. At 25°C, the dew point attainable in gases dried with 95% sulfuric acid is less than —75°C. 

The Clapeyron equation is most often used to represent the relationship between the temperature dependence of a pure hquid s vapor pressure curve and its latent heat of vaporization. In this case, dT is the slope of the vapor pressure—temperature curve, ADis the difference between the... 

FIG. 6-12 Correction factor for PoiseiiiUe s equation at low pressures. Curve A experimental curve for glass capillaries and smooth metal tubes. (From Brown, et al, J. Appl. Phys., 17, 802 [1.946].) Curve B experimental curve for iron pipe (From Biggie, Couiiesy of E. I. du Pont de Nemours [Pg.641]

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

Although there have been few data collected, postshock temperatures are very sensitive to the models which specify y and its volume dependence, in the case of the Gruneisen equation of state (Boslough, 1988 Raikes and Ahrens, 1979a Raikes and Ahrens, 1979b). In contrast, the absolute values of shock temperatures are sensitive to the phase transition energy Ejp of Eq. (4.55), whereas the slope of the versus pressure curve is sensitive to the specific heat (see, e.g.. Fig. 4.28). 

Figure 4 shows vapor pressure curves of rare-earth metals[24], clearly showing that there is a wide gap between Tm and Dy in the vapor pressure-temperature curves and that the rare-earth elements are classified into two groups according to their volatility (viz.. Sc, Y, La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, and Lu, non-volatile elements, and Sm, Eu, Tm, and Yb, volatile elements). Good correlation between the volatility and the encapsulation of metals was recently... 

Static pressure curve A graphical representation of the static pressure and volume flow of a fan at a set speed. 

Assume that a boiler feed water is being pumped at 180 °F. Read the chart in Figure 3-46 and the water vapor pressure curve, and follow over to read NPSH reduction = 0.45 feet. A pump selected for the sertice requires 6 feet cold water service NPSHr ... 

The three modve steam pressure curves, 100%-90%-80%, are obtained from the ejector manufacturer as is the performance curve of sucdon pressure versus percent of ejector design capacity. This latter curve for an actual installation would show actual absolute suction pressures versus pounds per hour or cubic feet per minute of air or percent design capacity. 

Calculate the pump dowTitime for a system of vessels and piping with a volume of 500 liters. The final pressure is to be 0.01 torr, starting at atmospheric. From the speed-pressure curve of a manufacturer s pump at 0.01 torr, speed is 2.0 liters/sec. At atmospheric pressure, = 2.V5 liters/sec with P"q = 760 torr. From the manufacturer s data, Rps = 15 and = 0.5 liters. 

Vapor Pressure Curves. (Courtesy Ingersoll-Rand Co.)... 

A-6 Altitude and Atmospheric Pressures, 578 A-7 Vapor Pressure Curves, 579 A-8 Pressure Conversion Chart, 580 A-9 Vacuum Conversion, 581 A-10 Decimal and Millimeter Equivalents of Fractions, 582 A-11 Particle Size Measurement, 582 . A-12 Viscosity Conversions, 583 A-13 Viscosity Conversion, 584 A-14 Commercial Wrought Steel Pipe Data, 585 A-15 ... 

Overhead temperature for essentially pure products at 10 psig = 223°F from vapor pressure curve. 

---