Evaporation enthalpy, 3.27

Many other mixed-feed arrangements are possible which combine the individual advantages of each type of arrangement. Figure 3.13 shows a three-stage evaporator in temperature-enthalpy terms, assuming that inlet and outlet solutions are at saturated conditions... 

When the dryer is seen as a heat exchanger, the obvious perspective is to cut down on the enthalpy of the air purged with the evaporated water. Minimum enthalpy is achieved by using the minimum amount of air and cooling as low as possible. A simple heat balance shows that for a given heat input, minimum air means a high inlet temperature. However, this often presents problems with heat-sensitive material and sometimes with materials of constmction, heat source, or other process needs. AH can be countered somewhat by exhaust-air recirculation. 

If the amount of evaporation is small, the change in enthalpy in the Hquid phase can be taken as a result of temperature change alone. Using an average (av) hquid flow rate, the following is derived ... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The specific enthalpies ia equation 9 can be determined as described earUer, provided the temperatures of the product streams are known. Evaporative cooling crystallizers operate at reduced pressure and may be considered adiabatic (Q = 0). As with of many problems involving equiUbrium relationships and mass and energy balances, trial-and-error computations are often iavolved ia solving equations 7 through 9. 

Although the T-s diagram is veiy useful for thermodynamic analysis, the pressure enthalpy diagram is used much more in refrigeration practice due to the fact that both evaporation and condensation are isobaric processes so that heat exchanged is equal to enthalpy difference A( = Ah. For the ideal, isentropic compression, the work could be also presented as enthalpy difference AW = Ah. The vapor compression cycle (Ranldne) is presented in Fig. H-73 in p-h coordinates. 

FIG. 11-79 Pressure enthalpy diagram for typical two-stage system with two evaporating temperatures, flash-gas removal, and intercooling. 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partiaUv for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihriugliue [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

The heat requirements in batch evaporation are the same as those in continuous evaporation except that the temperature (and sometimes pressure) of the vapor changes during the course of the cycle. Since the enthalpy of water vapor changes but little relative to temperature, the difference between continuous and batch heat requirements is almost always negligible. More important usually is the effect of variation of fluid properties, such as viscosity and boiling-point rise, on heat transfer. These can only be estimated by a step-by-step calculation. 

Example 4 Evaporative Cooling Air at 95 F dry-bulb temperature and 70 F wet-bulb temperature contacts a water spray, where its relative humidity is increased to 90 percent. The spray water is recirculated makeup water enters at 70 F. Determine exit dry-bulb temperature, wet-bulb temperature, change in enthalpy of the air, and quantity of moisture added per pound of dry air. 

Endotliermic Decompositions These decompositions are mostly reversible. The most investigated substances have been hydrates and hydroxides, which give off water, and carbonates, which give off CO9. Dehydration is analogous to evaporation, and its rate depends on the moisture content of the gas. Activation energies are nearly the same as reaction enthalpies. As the reaction proceeds in the particle, the rate of reaction is impeded hy resistance to diffusion of the water through the already formed product. A particular substance may have sever hydrates. Which one is present will depend on the... 

If an evaporation temperature (Pc) is pre-selected as a parametric independent variable, then the temperatures and enthalpies at c and e are found from (b) above the temperature T(, is also determined. If there is no heat loss, the heat balance in the HRSG between gas states 4 and 6 is... 

These techniques help in providing the following information specific heat, enthalpy changes, heat of transformation, crystallinity, melting behavior, evaporation, sublimation, glass transition, thermal decomposition, depolymerization, thermal stability, content analysis, chemical reactions/polymerization linear expansion, coefficient, and Young s modulus, etc. 

Brooke [234] provides calculation techniques using enthalpy of the air to determine water evaporated, air flow, and blow-down quantities. 

Pressure, temperature, and enthalpy or total heat values may be obtained from tables or diagrams covering each particular refrigerant. Table 11-12 presents a few comparative values of boiling points (evaporator temperature) and corresponding pressures as taken from such data. 

Refrigerating Effect. This is the heat absorbed in the evaporator per lb of refrigerant. It is determined by the difference in enthalpy of a lb of refrigerant vapor leaving the evaporator and that of a lb of liquid just upstream (ahead) of the expansion valve at the evaporator. From Figure 11-48A,... 

Enthalpy,Btu/lb., h Temperature at 3 i Condensing Pi is Evaporating Pressure P2 is Condensing Pressure... 

It carries very large amounts of heat as enthalpy of evaporation or latent heat in relatively small weights of steam ... 

Then if hfg = enthalpy of evaporation of the steam at the pressure involved. 

High-pressure condensate forms at the same temperature as the high-pressure steam from which it condenses, as the enthalpy of evaporation (latent heat) is transferred from it. When this condensate is discharged through a steam trap to a lower pressure the energy it contains is greater than it can hold while remaining as liquid water. The excess... 

A more informative diagram is the pressure-enthalpy chart which shows the liquid and vapour states of the fluid (Figure 2.6). In this diagram, a fluid being heated passes from the suhcooled state (a), reaches hoiling point (h) and is finally completely evaporated (c) and then superheated (d). The distance along the sector h-c shows the proportion which has heen evaporated at any enthalpy value. 

No heat is being added or removed in this process, so the enthalpy must remain constant, and the process is shown as a movement along the line of constant enthalpy. Latent heat will be taken in by the water, from the sensible heat of the air, until the mixture reaches saturation, when no more water can be evaporated. 

The wet hulh is now 18.9°C and the enthalpy is 53 kj/kg. A second-stage evaporative cooler with an efficiency of 75% will bring this down to 21°C dry hulh (point ). 

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