Phase Change Operations

We will use this estimate as the first guess in the spreadsheet solution. In one cell (Cell A1 in this illustration) we insert the initial guess for 7 (342°C), and in the next cell (Bl) we insert the formula for the fourth-order polynomial on the left-hand side of the equation to be solved  

Our goal is to find the value in Cell Al that drives the value in Cell Bl to aero. We could perform the trial-and-error search manually, but if the spreadsheet program has a goalseek tool (most programs do), we would select it and use it to perform the search automatically (Set Cell Bl to 0 by varying Cell Al). Either way, at the end of the search the two cells would display values close to those shown below  

The solution is therefore [7 = 299°Cl. The heat transferred from the specified quantity of gas as it cools from 500°C to 299°C goes to convert the specified amount of feedwater into steam. 

You have now seen two ways to evaluate an expression of the type 

If a functional relation for Cp(7) is available, such as one of the polynomials of Table B.2, the integration can be carried out analytically and if tabulated specific enthalpies are available for the substance being heated or cooled, a simple subtraction replaces the integration. 

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Often there are significant differences in the phases that exit from one process operation and enter another. For example, hot effluent gases from a reactor are condensed, or partially condensed, often before entering a separation operation, such as a vapor-liquid separator (e.g., a flash vessel or a distillation tower). In process synthesis, it is common to position a phase-change operation, using temperature- and/or pressure-reduction operations, such as heat exchangers and valves. 

Figure 3.7 Flowsheet with temperature-, pressure-, and phase-change operations in the vinyl-chloride process.

Evaporator. This unit, in the form of a large kettle, with a tube bundle inserted across the bottom, performs the temperature- and phase-change operations. Saturated steam that passes through the tubes condenses as the dichloroethane liquid is heated to its boiling point and vaporized. The large vapor space is provided to enable liquid droplets, entrained in the vapor, to coalesce and drop back into the liquid pool, that is, to disengage from the vapor which proceeds to the pyrolysis furnace. 

Condenser. To produce a saturated liquid at 6°C, the phase-change operation is carried out by a condenser that transfers heat to a mild refrigerant. Then the pressure is lowered to 12 atm across a valve. 

Calorimetry is the basic experimental method employed in thennochemistry and thennal physics which enables the measurement of the difference in the energy U or enthalpy //of a system as a result of some process being done on the system. The instrument that is used to measure this energy or enthalpy difference (At/ or AH) is called a calorimeter. In the first section the relationships between the thennodynamic fiinctions and calorunetry are established. The second section gives a general classification of calorimeters in tenns of the principle of operation. The third section describes selected calorimeters used to measure thennodynamic properties such as heat capacity, enthalpies of phase change, reaction, solution and adsorption. 

In most utibty boilers, steam pressure regulation is achieved by the throttling of turbine control values where steam generated by the boiler is admitted into the steam turbine. Some modem steam generators have been designed to operate at pressures above the critical point where the phase change between Hquid and vapor does not occur. 

Heat transfer and mass transfer occur simultaneously whenever a transfer operation involves a change in phase or a chemical reaction. Of these two situations, only the first is considered herein because in reacting systems the complications of chemical reaction mechanisms and pathways are usually primary (see HeaT-EXCHANGETECHNOLOGy). Even in processes involving phase changes, design is frequendy based on the heat-transfer process alone mass transfer is presumed to add no compHcations. But in fact mass transfer effects do influence and can even limit the process rate. 

Advantages to Membrane Separation This subsertion covers the commercially important membrane applications. AU except electrodialysis are pressure driven. All except pervaporation involve no phase change. All tend to be inherently low-energy consumers in the-oiy if not in practice. They operate by a different mechanism than do other separation methods, so they have a unique profile of strengths and weaknesses. In some cases they provide unusual sharpness of separation, but in most cases they perform a separation at lower cost, provide more valuable products, and do so with fewer undesirable side effects than older separations methods. The membrane interposes a new phase between feed and product. It controls the transfer of mass between feed and product. It is a kinetic, not an equihbrium process. In a separation, a membrane will be selective because it passes some components much more rapidly than others. Many membranes are veiy selective. Membrane separations are often simpler than the alternatives. 

From the process flow sheet developed in the above exercise, identify a) those unit operations involving simple mass flows only b) those unit operations in which phase changes are occurring c) those operations in which there are chemical reactions taking place d) those operations that are batch e) those operations that are continuous. 

Thermochemistry is concerned with the study of thermal effects associated with phase changes, formation of chemical compouncls or solutions, and chemical reactions in general. The amount of heat (Q) liberated (or absorbed) is usually measured either in a batch-type bomb calorimeter at fixed volume or in a steady-flow calorimeter at constant pressure. Under these operating conditions, Q= Q, = AU (net change in the internal energy of the system) for the bomb calorimeter, while Q Qp = AH (net change in the enthalpy of the system) for the flow calorimeter. For a pure substance. 

On the other hand, operations such as distilling or freezing usually tend to separate solutions into the pure substances that were the components of the solution. The nearer alike the components are, the harder it is to separate them from the solution, but even in difficult cases, a variety of methods in succession usually brings about a separation. In nature, solutions are much more common than pure substances, and heterogeneous systems are more common than solutions. When we want pure substances, we often must prepare them from solutions through successive phase changes. 

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