Heat of condensation

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

The adsorbed state often seems to resemble liquid adsorbate, as in the approach of the heat of adsorption to the heat of condensation in the multilayer region. For this reason, a common choice for the standard state of free adsorbate is the pure liquid. We now have... 

When plotted according to the linear form of the BET equation, data for the adsorption of N2 on Graphon at 77 K give an intercept of 0.004 and a slope of 1.7 (both in cubic centimeters STP per gram). Calculate E assuming a molecular area of 16 for N2. Calculate also the heat of adsorption for the first layer (the heat of condensation of N2 is 1.3 kcal/mol). Would your answer for Vm be much different if the intercept were taken to be zero (and the slope the same) Comment briefly on the practical significance of your conclusion. 

Now in principle each layer will have its own values of a, q, and v, and consequently the summation of Equation (2.11) cannot be carried out unless simplifying assumptions are made. Brunauer, Emmett and Teller made three such assumptions (a) that in all layers except the first the heat of adsorption is equal to the molar heat of condensation q, (b) that in all layers except the first the evaporation-condensation conditions are identical, i.e. that... 

Similar results with graphitized carbon blacks have been obtained for the heat of adsorption of argon,krypton,and a number of hydrocarbons (Fig. 2.12). In all these cases the heat of adsorption falls to a level only slightly above the molar heat of condensation, in the vicinity of the point where n = n . 

In this condenser, part of the stripper off-gases are condensed (the heat of condensation is used to generate low pressure steam). The carbamate formed and noncondensed NH and CO2 are put into the reactor bottom and conversion of the carbamate into urea takes place. The reactor is sized to allow enough residence time for the reaction to approach equiUbrium. The heat required for the urea reaction and for heating the solution is suppHed by additional condensation of NH and CO2. The reactor which is lined with 316 L stainless steel, contains sieve trays to provide good contact between the gas and Hquid phases and to prevent back-mixing. The stripper tubes are 25-22-2 stainless steel. Some strippers are still in service after almost 30 years of operation. 

The generated water vapor rises through a screen (demister) placed to remove entrained saline water droplets. Rising further, it then condenses on the condenser tube bank, and internal heat recovery is achieved by transferring its heat of condensation to the seawater feed that is thus being preheated. This internal heat recovery is another of the primary advantages of the MSF process. The energy performance of distillation plants is often evaluated by the performance ratio, PR, typically defined as... 

Methods of Liquefaction and Solidification. Carbon dioxide may be Hquefted at any temperature between its triple poiat (216.6 K) and its critical poiat (304 K) by compressing it to the corresponding Hquefaction pressure, and removing the heat of condensation. There are two Hquefaction processes. In the first, the carbon dioxide is Hquefted near the critical temperature water is used for cooling. This process requires compression of the carbon dioxide gas to pressures of about 7600 kPa (75 atm). The gas from the final compression stage is cooled to about 305 K and then filtered to remove water and entrained lubricating oil. The filtered carbon dioxide gas is then Hquefted ia a water-cooled condenser. 

The results of a specific case study are shown in Fig. 26-49. This depicts the change in inbreathing volume flow rate as a function of time. The middle curve describes the case when the tank is filled with dry air that is, no condensation occurs. When the air is saturated with water vapor at 55°C (131°F) and condensation occurs, the top curve is obtainea. The bottom line represents the volume flow rate brought about by thermal contraction alone, not including the amount condensed. Because of the heat of condensation released, this fraction is less than the volume flow rate without condensation, but this effect is more than compensated for by the additional volume flow rate due to condensation. 

Adsorption onto a solid is always accompanied by a liberation of heat. For physical adsorption, this exothermic heat of adsorption is always greater than the heat of condensation of the adsorbate. 

Pure vapor or substantially pure vapor can be considered condensed isothermally, and during the condensate range the latent heat of condensation is uniform. 

Consider a process which has two process hot streams (Hj and H2), two process cold streams (Cj and C2), a heating utility (HUi which is a saturated vapor that loses its latent heat of condensation) and a cooling utility (CUi). The problem data are given in Table 9.8. The cost of the heating utility is 4/10 kJ added while the cost of the coolant is 7/10 kJ. The minimum allowable temperature difference is lO C. Employ graphical, algebraic and... 

Ehie to the dilute nature of the stream, we may assume that the latent heat of condensation for MEK is much smaller than the sensible heat removed from the gas. Therefore, we can apply the procedure presented in Section 10.5. Once a value is selected for ATj ", Eq. (10.19) can be used to determine T and Eqs. (10.3b) and (10.7) can be employed to calculate the value of Since the bounds on p (and consequently on AT ) are tight, we will iterate over two values of 0.96 and 1.00 (Ar2 " = 90.0 and 94.5 K). The other iterative variable is AT, . Both variables are used to trade off fixed versus operating costs. As an illustration, consider the following iteration AT," = 5 K and... 

Calorific value The measure of the heating capacity of a fuel, usually expressed as the available heat resulting from the complete combustion of that fuel in kj kg or kj nr Gross calorific value includes the heat of condensation of the water vapor in a hydrogen fuel net calorific value excludes this. 

In condensation one fluid remains at constant temperature throughout the length of the exchanger while the fluid B that is absorbing the latent heat of condensation is rising in temperature to an outlet of tg. Note that as fluid A condenses, it does not flow the length of the travel path. Fluid A drops to the bottom of the exchanger and flows out the outlet at temperature Tg, which is the same as Tj, the tempera-... 

Buoyancy caused by the release of latent heat of condensation of water. As will be seen in Section 7.7, water releases a substantial amount of energy when it condenses. 

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