Constant pressure method

This apparatus is similar to that used in the constant volume method, the test rubber sheet dividing the cell into high and low pressure cavities. The difference is that the low pressure side is connected to a device to measure the volume increase as gas diffuses to the low pressure side while the high pressure is kept constant. In ISO 2782 [24] and BS 903, Part A30 [25], a graduated capillary tube is used to measure the volume change. 

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An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. 

As commented in Section 2.1, the vertical capillary type of apparatus requires considerable care to set up and operate. A horizontal capillary results in a little more simple apparatus compared to a vertical capillary but in either case there is the extra necessity in the constant pressure method to accurately calibrate the capillary. Generally, the most convenient procedure is to use the constant volume method with an apparatus equipped with modern pressure transducers. 

ISO 2782 Rubber, Vulcanized - Determination of Permeability to Gases - Constant Pressure Method... 

BS 903, Part A 30. 1975. Determination of the Permeabihty of Rubber to Gases (Constant Pressure Method). 

For a multicomponent system, it is possible to simulate at constant pressure rather than constant volume, as separation into phases of different compositions is still allowed. The method allows one to study straightforwardly phase equilibria in confined systems such as pores [166]. Configuration-biased MC methods can be used in combination with the Gibbs ensemble. An impressive demonstration of this has been the detennination by Siepmaim et al [167] and Smit et al [168] of liquid-vapour coexistence curves for n-alkane chain molecules as long as 48 atoms. 

Air Permeability. Air permeabiUty is an important parameter for certain fabric end uses, eg, parachute fabrics, boat sails, warm clothing, rainwear, and industrial air filters. Air permeabiUty of a fabric is related to its cover, or opacity. Both of these properties are related to the amount of space between yams (or fibers in the case of nonwovens). The most common method for specifying air permeabiUty of a fabric involves measuring the air flow per unit area at a constant pressure differential between the two surfaces of the fabric. This method, suitable for measuring permeabiUty of woven, knitted, and nonwoven fabrics, is described in ASTM D737. Units for air permeabiUty measured by this method are generally abbreviated as CFM, or cubic feet per square foot per minute. 

Inflated Diaphragm Method (ASTM D3886). This method is appHcable both to woven and knitted fabrics. The specimen is abraded by mbbing either unidirectionally or multidirectionally against an abradant having specified surface characteristics. The specimen is supported by an inflated mbber diaphragm under a constant pressure. Evaluation of abrasion resistance can be either by determination of the number of cycles required to wear through the center of the fabric completely or by visual examination of the specimens after a specified number of cycles. 

The batch-suspension process does not compensate for composition drift, whereas constant-composition processes have been designed for emulsion or suspension reactions. It is more difficult to design controUed-composition processes by suspension methods. In one approach (155), the less reactive component is removed continuously from the reaction to keep the unreacted monomer composition constant. This method has been used effectively in VT)C-VC copolymerization, where the slower reacting component is a volatile and can be released during the reaction to maintain constant pressure. In many other cases, no practical way is known for removing the slower reacting component. 

Heat Capacity. The multiple property estimation methods for constant pressure ideal-gas heat capacities cover a broad range of organic compounds (188,216,217). Joback s method (188) is the easiest to use however, usage of all these methods has been recommended only over the range 280—1100 K (7). An accurate method for ideal-gas heat capacities (constant pressure), limited to hydrocarbons, has been presented (218) that involves a fit of seven variables, and includes steric, ring, branching, alkene, and even allene corrections. 

Another instance in which the constant-temperature method is used involves the direc t application of experimental KcO values obtained at the desired conditions of inlet temperatures, operating pressure, flow rates, and feed-stream compositions. The assumption here is that, regardless of any temperature profiles that may exist within the actu tower, the procedure of working the problem in reverse will yield a correct result. One should be cautious about extrapolating such data veiy far from the original basis and be carebil to use compatible equilibrium data. 

For conditions approaching constant pressure at the orifice entrance, which probably siiTuJates most industri appheations, there is no independently verified predictive method. For air at near atmospheric pressure sparged into relatively inviscidhqiiids (11 - 100 cP), the correlation of Kumar et al. [Can. J. Chem. Eng., 54, 503 (1976)] fits experimental data well. Their correlation is presented here as Fig. 14-92. 

To include the volume as a dynamic variable, the equations of motion are determined in the analysis of a system in which the positions and momenta of all particles are scaled by a factor proportional to the cube root of the volume of the system. Andersen [23] originally proposed a method for constant-pressure MD that involves coupling the system to an external variable, V, the volume of the simulation box. This coupling mimics the action of a piston on a real system. The piston has a mass [which has units of (mass)(length) ]. From the Fagrangian for this extended system, the equations of motion for the particles and the volume of the cube are... 

Although constrained dynamics is usually discussed in the context of the geometrically constrained system described above, the same techniques can have many other applications. For instance, constant-pressure and constant-temperature dynamics can be imposed by using constraint methods [33,34]. Car and Parrinello [35] describe the use of the extended Lagrangian to maintain constraints in the context of their ab initio MD method. (For more details on the Car-Parrinello method, refer to the excellent review by Gain and Pasquarrello [36].)... 

A good method for a simple calibration facility is a system where a constant airflow is produced by using two water containers and an arrangement of a virtually constant pressure head, The constant water flow into the second container displaces an equal airflow out of the container (Fig. 12.21). With this arrangement the difficult measurement of a small airflow is changed into a much easier and accurate measurement of a small water flow. 

The simplest method to measure gas solubilities is what we will call the stoichiometric technique. It can be done either at constant pressure or with a constant volume of gas. For the constant pressure technique, a given mass of IL is brought into contact with the gas at a fixed pressure. The liquid is stirred vigorously to enhance mass transfer and to allow approach to equilibrium. The total volume of gas delivered to the system (minus the vapor space) is used to determine the solubility. If the experiments are performed at pressures sufficiently high that the ideal gas law does not apply, then accurate equations of state can be employed to convert the volume of gas into moles. For the constant volume technique, a loiown volume of gas is brought into contact with the stirred ionic liquid sample. Once equilibrium is reached, the pressure is noted, and the solubility is determined as before. The effect of temperature (and thus enthalpies and entropies) can be determined by repetition of the experiment at multiple temperatures. 

Figure 8-114. Bubble cap pressure drop constant (Bolles Method). Used by permission, Bolles, W. L., Pet. Processing, Feb. thru May (1956).

Thus, in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process." Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

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