Pressure, correction for

Another pressure correction for percent loss can also be applied, as described in the ASTM test method. 

Later, we will make equilibrium calculations that involve activities, and we will see why it is convenient to choose the ideal gas as a part of the standard state condition, even though it is a hypothetical state/ With this choice of standard state, equations (6.94) and (6.95) allow us to use pressures, corrected for non-ideality, for activities as we make equilibrium calculations for real gases.s... 

Edmister (1948) published a generalised plot showing the isothermal pressure correction for real gases as a function of the reduced pressure and temperature. His chart, converted... 

Fig. 1.30. Typical pressure correction for a Pirani gage for different gas species (courtesy of Alcatel).

Fig. 8. The BP86 free-energy (G) profiles at 423 K with and without pressure corrections for associative (a) and dissociative (b) pathways (solid line is without pressure corrections, open bar is with pressure corrections).

Gaseous equilibria are expressed in terms of fugacities which can be regarded as partial pressures corrected for nonideality. Several other... 

The slope of the vapour pressure versus temperature curve, dP dT, can be obtained experimentally (see nnex 2). The most accurate method is to take tangents to the pressure (corrected for the presence of pad gas) versus temperature data from a closed test, or to fit the data to the following relationship161 ... 

The partial molal free energies of transfer are related to the fugacities in pure liquid, f° (vapor pressure corrected for deviation from die perfect gas law ), and in solution, by the equations,... 

The osmotic pressure of a solute is the hydrostatic pressure that must be applied to a solution in order to increase the activity, a. (or fugacity, designated f, introduced by G. N. Lewis as a measure of thermodynamic escaping tendency . It is an effective gas pressure corrected for deviations from the perfect gas laws) of the solvent sufficiently to balance its decrease caused by the presence of the solute. Equilibrium is established through a membrane permeable only to the solvent. This pressure is, by integrating... 

Derive an explicit formula for the osmotic pressure, correct for the lowest solute concentrations. 

Refer to the portion of Figure 4.6 where the source tank fluid level is below the center line of the impeller in either the system connected in parallel or in the system connected in series. At the surface of the wet well (point 1), the pressure acting on the liquid is equal to the atmospheric pressure Patm minus the vapor pressure of the liquid Py. This pressure is, thus, the atmospheric pressure corrected for the vapor pressure and is the pressure pushing on the liquid surface. Imagine the suction pipe devoid of liquid if this is the case, then this pressure will push the fluid up the suction pipe. This is actually what happens as soon as the impeller starts moving and pulling the liquid up. As soon as a space is evacuated by the impeller in the suction pipe, liquid rushes up to flU the void this is not possible, however, without a positive NPSH to push the liquid. Note that before the impeller can do its job, the fluid must, first, reach it. Thus, the need for a driving force at the inlet side. 

TABLB LXIII. PRESSURE CORRECTIONS FOR HYDROGEN BIjJBCTRODB IN MILLIVOLTS... 

Historically, van der Waals himself did not apply his equation of state to Langmuir monolayers, but others did. For instcince. already in 1925 Volmer and Mahnert formulated [1.1.5.23] , which is equivalent to [3.4.28] if the pressure correction is zero and the excluded area constant. Langmuir s relation [3.3.4] does not agree with the positive sign of the pressure correction for attraction between the molecules. 

One point rejected due to failure of a statistical test. Pressures corrected for dimer. 

Edmister (1948) published a generalized plot showing the isothermal pressure correction for real gases as a function of the reduced pressure and temperature. His chart, converted to SI units, is shown as Eigure 3.2. Edmister s chart was based on hydrocarbons but can be used for other materials to give an indication of the likely error if the ideal gas specific heat values are used without corrections. 

The pressure correction for each // / // ° can, however, be readily evaluated. If the liquid solution is ideal (so that = 1), a further simplification results ... 

Once the distribution of mass among the various aqueous species in solution has been calculated, there are a number of different geochemical modeling options available (Fig. 1). The most commonly used option is to increase the temperature and pressure and re-calculate the distribution of species and saturation states of minerals, as initially discussed by Kharaka and Mariner (1977). The effects of increasing pressure on the complexation of the aqueous species was not included at that time but has now been added based on the correlations of Aggarwal et al. (this issue). Including this correction is important because the dissociation constant of complexes can vary by a factor of three over 1 kilobar. The pressure correction for aqueous complexes results in reducing the enhanced solubility of minerals from that predicted without this correction (22). 

The hydrostatic test pressure is 1.25 times the design pressure corrected for temperature, rather than the usual 1.5. Division 2 establishes upper limits for the test pressure relative to the yield strength at test temperature. The pneumatic test pressure is 1.15 times the design pressure corrected for temperature rather than 1.25 required by Division 1. Division 2 has no provision for proof tests to establish the maximum allowable working pressure. But Appendix 6, Experimental Stress Analysis, provides for the determination of the critical or governing stresses for unusual geometries for which theoretical stress analysis is inadequate. 

The size of the correction factor depends on the concentration of gas molecules defined in terms of moles of gas particles per liter n/V). The higher the concentration, the more likely a pair of gas particles will be close enough to attract each other. For large numbers of particles, the number of interacting pairs of particles depends on the square of the number of particles and thus on the square of the concentration, or (pjVf. This can be justified as follows In a gas sample containing N particles, there are W 1 partners available for each particle, as shown in Fig. 5.28. Since the 1 2 pair is the same as the 2 1 pair, this analysis counts each pair twice. Thus, for N particles, there are W(W — 1)/2 pairs. If is a very large number, W — 1 approximately equals N, giving possible pairs. Thus the pressure, corrected for the attractions of the particles, has the form... 

Comment Notice that the term 1.003 atm is the pressure corrected for molecular volume. This value is higher than the ideal value, 1.000 atm, because the volume in which the molecules are free to move is smaller than the container volume, 22.41 L. Thus, the molecules collide more frequently with the container walls. The term 0.013 atm corrects for intermolecular forces. The intermolecular attractions between molecules reduce the pressure to 0.990 atm. We conclude, therefore, that the intermolecular attractions are the main cause of the slight deviation of Cl2(s) from ideal behavior under the stated experimental conditions. 

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