Pressure, deviations

Figure 4-84. Regenerator pressure deviation during expander bypass valve malfunction.

It consists of a spring-loaded cut-off valve which is held open in the open position under normal conditions. Should the pressure deviate sufficiently, the diaphragm will move and disengage the trigger mechanism, releasing the latch on the valve, which will close under the force of the spring. 

At very low pressures, deviations from the ideal gas law are caused mainly by the attractive forces between the molecules and the compressibility factor has a value less than unity. At higher pressures, deviations are caused mainly by the fact that the volume of the molecules themselves, which can be regarded as incompressible, becomes significant compared with the total volume of the gas. 

Further correction of volume for an atmospheric pressure deviation from one atmosphere may be done by applying Boyle s Law, which states that the volume of a gas without change of temperature varies inversely with the pressure applied to it. 

Finally, we observe that the eventual decrease in the decomposition rate is related to the exhaustion of the reactant. An inhibition of the decomposition process which is sometimes found before the yield has reached 100% may be ascribed to strain and surface energy which is stored in the reactant and the product. If the increase in these energies as a function of the advancement of the reaction surpasses the available driving force (e.g., the X(g) pressure deviation from the equilibrium pressure), the reaction comes to a stop. A pertinent discussion of decomposition reactions is given in [F.C. Tompkins (1976)]. 

The accuracy of the pressure and temperature measurements was verified by measuring the vapor pressure curves and critical points for pentane and for toluene. Vapor pressures were measured by observing the formation of a liquid phase as pentane or toluene was injected into the constant-volume view cell under isothermal conditions. The observation of critical opalescence was used to determine the critical point. The measured vapor pressures and critical points are given in Table I. Vapor pressures deviate from... 

Clearly, when B22 = B, the term in square brackets equals 1, and the pressure deviation from the Raoult s-law value has the sign of fin this is normally negative. When the virial coefficients are not equal, a reasonable assumption is that species 2, taken here as the heavier species (the one with the smaller vapor pressure) has the more negative second virial coefficient. This has the effect of making the quantity in parentheses negative and the quantity in square brackets < 1. However, if this latter quantity remains positive (the most likely case), the sign of fin still determines the sign of the deviations. 

Here Raoult s law acts as the limiting demarcation criterion between ideal and real or non-ideal liquid mixtures. As Figure 32.4(a) indicates, in practice, non-ideal (real) liquid mixtures do not show linear behaviour but their vapour pressure deviates from (i.e. above or below) the line AB. 

Classical thermodynamics discourses equilibria in solutions of noninteracting micromolecules, within and between phases, under constant and variable concentration, volume, temperature, and pressure. Deviations observed with macromolecules necessitated new theory modeled after a lattice in which segments of linear macromolecules, instead of the whole molecule, interchange positions with identical segments and with solvent molecules without... 

These potentials are standardised, that is, they only apply to systems at unit activity, 25°C, and latm pressure. Deviation from these conditions will result in quite different values being obtained. For example, if two pieces of zinc are dipped into zinc sulphate solutions of different concentration (the solutions being connected via a salt bridge), a difference in potential will be measurable between the two electrodes. The electrode in the more concentrated solution will be the cathode and that in the dilute solution the anode. This is a differential concentration cell, many examples of which are found in corroding systems. Thus, any electrochemical series may be produced for a given environment, that is metals and alloys may be arranged in order of corrosion resistance to that environment. Table 1 illustrates this point for alloys immersed in flowing seawater [3],... 

Related Calculations. When reactants enter at a temperature different from that of the exiting products, the enthalpy changes that are due to this temperature difference should be computed independently and added to A7/2°98K, along with the pressure deviations of enthalpy. 

The major change from IPTS-68 to ITS-90 has been the elimination of the normal (i.e., 1-atm) boiling points that were previously used as fixed points. This change was made because the temperature of a boiling point is much more sensitive to the ambient pressure than that of a freezing point. The latter is defined as the equilibrium temperature of coexisting pure solid and liquid at one standard atmosphere (101 325 Pa), and corrections can be made for small pressure deviations (the effect is only about 5 mK per atm). ... 

Nitrogen adsorption isotherms measurements were performed at 77 K on a Micrometries ASAP 2010M and on a Fisons Sorptomatic 1990. Each isotherm point is acquired when the pressure variation, within a fixed time, is lower than a fixed pressure deviation. 

At first, equilibrium time was increased in order to try to eliminate the low-pressure deviation. This proved to be impossible. The upward shift of the isotherm predicted in Fig 2 was only observed when the initial equilibrium times were very short. Once a reasonable equilibrium time was reached (in the order of several hours per point) the isotherm stayed identical. Even for equilibrium times as high as 12 hours per point the isotherm did not shift towards the Dubinin-Radushkevich line. From this, it was concluded that the deviation for low partial pressures was not an experimental artifact. In fact, this has already been suggested by several authors [6,7], but little attention has been given to these results. Partly because their observations and conclusions were mainly directed towards the fractal characterisation of porous materials. 

From PV = nRT, we expect PV/RT lo equal one tor one mole or ideal gas at any temperature and pressure. Since volume deviates positively from ideal behavior and pressure deviates negatively, if PV/RT is greater than one tor one mole cf gas, then the deviation due to molecular volume must be greater than the deviation due to the intermolecular forces. If PV/RT is lasa than one for one mole of gas, then the deviation due to intermolecular forces must be greater than the deviation due to molecular volume. 

B is correct. Since the reaction was exothermic, the vapor pressure deviated negatively from Raoult s law. Depending upon the ratios of the liquids in solution, the vapor pressure could be lower than either or just lower than B. (A has a higher boiling point thus a lower vapor pressure.) The boiling point must have gone up from B because the vapor pressure went down from B. 

D is correct. An ideal gas has a PV/RT equal to one. Real volume is greater than predicted by the ideal gas law, and real pressure is less than predicted by the ideal gas law. Volume deviations are due to the volume of the molecules, and pressure deviations are due to the intermolecular forces. Thus, a negative deviation in this ratio would indicate that the intermolecular forces are having a greater affect on the nonideal behavior than the volume of the molecules, (see the graph on page 27)... 

At high relative pressures, deviations from the straight line may exist. The three possible cases of the versus f plot are shown in Fig. 3.7 [16]. The shape of these curves can provide considerable insight concerning the shape and dimension of the pore. 

Adopting the Newton s viscosity law (1.69) derived from continuum mechanical principles [102] (sec. 2-4.2), the thermod3mamic pressure deviates slightly from the mean pressure. It follows that the mean pressure is approximated as ... 

Real gases approach ideal gas behavior at low pressures. Deviations from ideality increase at higher pressures and lower temperatures, that is, as the density goes up. The ideal gas equation cannot predict the transition from gas to liquid since, according to the equation, the volume at a fixed pressure would decrease continuously and proportionately to the absolute temperature as the temperature is decreased. This, of course, is not what is observed in reality. 

Here, too, the deviations from Raoult s law are positive for both components over the entire composition range at 45°C (Figures 1.7 and 1.8). The partial pressure deviations are large enough to result in a maximum in the total pressure (Figure 1.7). The binary thus forms a maximum pressure, or minimum temperature, azeotrope, a phenomenon discussed in more detail later in this section. In this binary, the concentration of ethanol is higher in the vapor than in the liquid below the azeotrope and is lower in the vapor than in the liquid above the azeotrope. At the azeotropic point, the concentrations in the liquid and vapor are identical (Figure 1.9). 

The behavior of B(p) and C(p) for propane is shown in Figure 7. The number of PpT data used here for adjusting the equation of state is 843, with different least-squares weightings than in Refs. 3 and 5. Overall deviations, with equal weighting for all points, are 2.07 bar for the mean of absolute pressure deviations and 0.34% for the rms of relative density deviations. 

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