Constant-pressure process

There is an apparent paradox here that as the cooled cycle contains an irreversible process (constant pressure mixing), its efficiency might be expected to be lower than the original uncooled cycle. The answer to this paradox follows from consideration of all the irreversibilities in the cycle and we refer back to the analysis of Section 3.2.1.1, for the rational efficiency of the [CHT]ru cycle. The irreversibility associated with the heat supply is unchanged, as given in Eq. (3.3), but the irreversibility associated with the heat rejection between temperatures T(, and T) = Ta becomes... 

A basic method for determining the energy change involved with many chemical processes is calorimetry. A calorimeter is an insulated container used to carry out a chemical process. A thermometer is used to measure temperature changes that take place during the process. A simple constant-pressure calorimeter is shown in Figure 10.3. This type of calorimeter derives its name from the fact that it is open to the atmosphere and the pressure remains constant during the process. Constant-pressure... 

The measurement of heat using a simple calorimeter such as that shown in Fig. 9.7 is an example of constant-pressure calorimetry, since the pressure (atmospheric pressure) remains constant during the process. Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution. Recall that under these conditions the change in enthalpy equals the heat. 

The analogous result for the entropy change of the system in a reversible isobaric process (constant pressure) is... 

For such a process the pressure p of the surroundings remains constant and is equal to that of the system in its initial and final states. (If there are transient pressure changes within the system, they do not cause changes in the surroundings.) One may then write... 

D) CONSTANT-TEMPERATURE CONSTANT-PRESSURE (ISOTHERMAL-ISOBARIC) PROCESSES... 

The constant-temperature constant-pressure situation yields an analogous result. One can write for the reversible process... 

Figure 4.3a shows schematically how the Gibbs free energy of liquid (subscript 1) and crystalline (subscript c) samples of the same material vary with temperature. For constant temperature-constant pressure processes the criterion for spontaneity is a negative value for AG, where the A signifies the difference final minus initial for the property under consideration. Applying this criterion to Fig. 4.3, we conclude immediately that above T , AGf = Gj - G. is negative... 

Filtration. In many mineral processing operations, filtration follows thickening and it is used primarily to produce a soHd product that is very low in moisture. Filtration equipment can be either continuous or batch type and either constant pressure (vacuum) or constant rate. In the constant pressure type, filtration rate decreases gradually as the cake builds up, whereas in the constant rate type the pressure is increased gradually to maintain a certain filtration rate as the cake resistance builds. The size of the device is specified by the required filter surface area. 

Most continuous vacuum filters are the constant pressure type. Their main use is in dewatering concentrated slurries such as concentrates. They belong to three classes the disk, dmm, and horizontal filters. Disk, and to a lesser extent, dmm filters, are the mainstay for most final dewatering. These filters remove most fine particles from a process stream. 

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. 

The aqueous emulsion polymerization can be conducted by a batch, semibatch, or continuous process (Fig. 5). In a simple batch process, all the ingredients are charged to the reactor, the temperature is raised, and the polymerization is mn to completion. In a semibatch process, all ingredients are charged except the monomers. The monomers are then added continuously to maintain a constant pressure. Once the desired soflds level of the latex is reached (typically 20—40% soflds) the monomer stream is halted, excess monomer is recovered and the latex is isolated. In a continuous process (37), feeding of the ingredients and removal of the polymer latex is continuous through a pressure control or rehef valve. 

Combustors All gas turbine combustors perform the same function They increase the temperature of the high-pressure gas at constant pressure. The gas turbine combustor uses veiy little of its air (10 percent) in the combustion process. The rest of the air is used for cooling and mixing. The air from the compressor must be diffused before it enters the combustor. The velocity leaving the compressor is about 400-500 ft/sec (130-164 m/sec), and the velocity in the combustor must be maintained at about 10-30 ft/sec (3-10 iTi/sec). Even at these low velocities, care must be taken to avoid the flame to be carried downstream. To ensure this, a baffle creates an eddy region that stabi-hzes the flame and produces continuous ignition. The loss of pressure in a combustor is a major problem, since it affecls both the fuel consumption and power output. Total pressure loss is in the range of 2-8 percent this loss is the same as the decrease in compressor efficiency. 

In the gas turbine (Brayton cycle), the compression and expansion processes are adiabatic and isentropic processes. Thus, for an isentropic adiabatic process 7 = where Cp and c are the specific heats of the gas at constant pressure and volume respectively and can be written as ... 

The process demands that a constant pressure be held on the header at various loads (flow). Specifically, the control system operates as follows ... 

Whilst temperature rises at constant pressure cause a decrease in viscosity, pressure rises at constant temperature cause an increase in viscosity since this causes a decrease in free volume. It is in fact found that within the normal processing temperature range for a polymer it is possible to consider an increase in pressure as equivalent, in its effect on viscosity, to a decrease in temperature. 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

The term r/ax, is a constant and independent of filtration conditions. We find that the ratio of constant C2 at pressure 1.5 atm. to constant C, for the process under pressure at 0. 5atm. is as follows Then A2/A, = 10... 

When the space above the suspension is subjected to compressed gas or the space under the filter plate is under a vacuum, filtration proceeds under a constant pressure differential (the pressure in the receivers is constant). The rate of filtration decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over the filter medium. 

For a constant pressure drop and temperature filtration process all the parameters in Equation 9, except V and x, are constant. Integrating Equation 9 over the limits of 0 to V, from 0 to x, we obtain ... 

Table 3.3 summarizes the history of the development of wave-profile measurement devices as they have developed since the early period. The devices are categorized in terms of the kinetic or kinematic parameter actually measured. From the table it should be noted that the earliest devices provided measurements of displacement versus time in either a discrete or continuous mode. The data from such measurements require differentiation to relate them to shock-conservation relations, and, unless constant pressures or particle velocities are involved, considerable accuracy can be lost in data processing. 

Intermetallics also represent an ideal system for study of shock-induced solid state chemical synthesis processes. The materials are technologically important such that a large body of literature on their properties is available. Aluminides are a well known class of intermetallics, and nickel aluminides are of particular interest. Reactants of nickel and aluminum give a mixture with powders of significantly different shock impedances, which should lead to large differential particle velocities at constant pressure. Such localized motion should act to mix the reactants. The mixture also involves a low shock viscosity, deformable material, aluminum, with a harder, high shock viscosity material, nickel, which will not flow as well as the aluminum. 

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