Adiabatic condensation

The asymmetric spin boson model presents a significantly more challenging non-adiabatic condensed phase test problem due to the asymmetry in forces from the different surfaces. Approximate mean field methods, for example, will fail to reliably capture the effects of these different forces on the dynamics. 

By the compression of 1 gr. of saturated water vapour at 100° to saturated water vapour at 101°, we have an emission of 1-2 cal. If this heat is not allowed to escape, we do not obtain saturated water vapour at 101°, but superheated steam at a correspondingly higher temperature. Conversely, if we allow saturated water vapour to expand adiabatically, condensation takes place. We may mention that this spontaneous condensation of water vapour, which for a slight expansion takes place only in the presence of dust particles or ions, has been successfully employed in counting the number of ions or nuclei in the vapour. 

Adiabatic condensation. The question here is whether we can force condensation by some adiabatic change in the volume. An adiabatic process in a closed system must satisfy the combined laws in the form of (7.1.14) that is, we must have AS > 0. In Table 7.1 we find the entropy of saturated steam to be = 7.355 J/(gK) so, to achieve an... 

One common approximation is to separate the nuclear and electronic degrees of freedom. Since the nuclei are considerably more massive than the electrons, it can be assumed that the electrons will respond mstantaneously to the nuclear coordinates. This approximation is called the Bom-Oppenlieimer or adiabatic approximation. It allows one to treat the nuclear coordinates as classical parameters. For most condensed matter systems, this assumption is highly accurate [11, 12]. 

Acrolein reacts slowly in water to form 3-hydroxypropionaldehyde and then other condensation products from aldol and Michael reactions. Water dissolved in acrolein does not present a hazard. The reaction of acrolein with water is exothermic and the reaction proceeds slowly in dilute aqueous solution. This will be hazardous in a two-phase adiabatic system in which acrolein is suppHed from the upper layer to replenish that consumed in the lower, aqueous, layer. The rate at which these reactions occur will depend on the nature of the impurities in the water, the volume of the water layer, and the rate... 

In a typical adiabatic polymerization, approximately 20 wt % aqueous acrylamide is charged into a stainless steel reactor equipped with agitation, condenser, and cooling jacket or coils. To initiate the polymerization, an aqueous solution of sodium bisulfite [7631-90-5] is added, followed by the addition of a solution of ammonium persulfate [7727-54-0] N2HgS20g. As the polymerization proceeds, the temperature rises to about 90°C, and then begins to fall at the end of the polymerization. The molecular weight obtained depends primarily on the initiator concentration employed. 

A useful method for a binary mixture employs an analysis based on the McCabe-Thiele graphical method. In addition to the usual assumptions of adiabatic column and equimolal overflow on the trays, the following procedure assumes neghgible holdup of hquid on the trays, in the column, and in the condenser. 

These mechanisms can be observed in many common situations. For example, fog via mixing can be seen in the discharge of breath on a cold day. Fog via adiabatic expansion can be seen in the low-pressure area over the wing of an airplane landing on a humid summer day and fog via condensation can be seen in the exhaust from an automobile air conditioner (if you follow closely enough behind another car to pick up the ions or NO molecules needed for nucleation). All of these occur at a veiy low supersaturation and appear to be keyed to an abundance of foreign nuclei. All of these fogs also quickly dissipate as heat or unsaturated gas is added. 

If an ascending air parcel reaches saturation, the addition of latent heat from condensing moisture will partially overcome the cooling due to expansion. Therefore, the saturated adiabatic lapse rate (of cooling) is smaller than y. ... 

A low-pressure process has been developed by ICl operating at about 50 atm (700 psi) using a new active copper-based catalyst at 240°C. The synthesis reaction occurs over a bed of heterogeneous catalyst arranged in either sequential adiabatic beds or placed within heat transfer tubes. The reaction is limited by equilibrium, and methanol concentration at the converter s exit rarely exceeds 7%. The converter effluent is cooled to 40°C to condense product methanol, and the unreacted gases are recycled. Crude methanol from the separator contains water and low levels of by-products, which are removed using a two-column distillation system. Figure 5-5 shows the ICl methanol synthesis process. 

The process of adiabatic saturation in Section 24.4 assumed that the spray water temperature had no effect on the final air condition. If, however, a large mass of water is used in comparison with the mass of air, the final condition will approach the water temperature. If this water is chilled below the dew point of the entering air, moisture will condense out of the air, and it will leave the washer with a lower moisture content (see Figure 24.7). 

In order that hot condenser water may be re-used in a plant, it is normally cooled by contact with an air stream. The equipment usually takes the form of a tower in which the hot water is run in at the top and allowed to flow downwards over a packing against a countercurrent flow of air which enters at the bottom of the cooling tower. The design of such towers forms an important part of the present chapter, though at the outset it is necessary to consider basic definitions of the various quantities involved in humidification, in particular wet-bulb and adiabatic saturation temperatures, and the way in which humidity data are presented on charts and graphs. While the present discussion is devoted to the very important air-water system, which is in some ways unique, the same principles may be applied to other liquids and gases, and this topic is covered in a final section. 

The other entries in Table 13.2 show that heat removal is not a problem for most ring-opening and condensation polymerizations. Polycaprolactam (also called Nylon 6) is an addition polymer, but with rather similar bond energies for the monomer and the polymer. The reaction exotherm is small enough that large parts are made by essentially adiabatic reaction in a mold. An equilibrium between monomer and polymer does exist for polycaprolactam, but it occurs at commercially acceptable molecular weights. 

The application of open sorption systems can provide dehumidification by the adsorption of water vapor and sensible cooling by adiabatic humidification (after a cold recovery for the dried air) at temperatures between 16 °C and 18 °C. Conventional systems have to reach temperature as low as 6 °C or lower in order to start dehumidification by condensation. For comfort reasons this cold air has to be heated up to about 18 °C before released into the building. This shows that open sorption systems can provide in general an energetically preferable solution. 

Adiabatic operation. If adiabatic operation leads to an acceptable temperature rise for exothermic reactors or an acceptable decrease for endothermic reactors, then this is the option that would normally be chosen. If this is the case, then the feed stream to the reactor requires heating and the effluent stream requires cooling. The heat integration characteristics are thus a cold stream (the reactor feed) if the feed needs to be increased in temperature or vaporized, and a hot stream (the reactor effluent) if the product needs to be decreased in temperature or condensed. The heat of reaction appears as increased temperature of the effluent stream in the case of exothermic reaction or decreased temperature in the case of endothermic reaction. 

Cold shot. Injection of cold fresh feed for exothermic reactions or preheated feed for endothermic reactions to intermediate points in the reactor can be used to control the temperature in the reactor. Again, the heat integration characteristics are similar to adiabatic operation. The feed is a cold stream if it needs to be increased in temperature or vaporized and the product a hot stream if it needs to be decreased in temperature or condensed. If heat is provided to the cold shot or hot shot streams, these are additional cold streams. 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

However, if the PES are multidimensional, as is the case for reactions in the condensed phase, the adiabatic approach is inconvenient for practical calculations, especially for nonadiabatic reactions. 

A rather general method of the calculation of the tunneling taking account of the dissipation was given in Ref. 82. The cases of rather strong dissipation were considered in Refs. 81 and 82, where it was assumed that a thermodynamical equilibrium in the initial potential well exists. The case of extremely weak friction has been considered using the equations for the density matrix in Ref. 83. A quantum analogue of the Focker-Planck equation for the adiabatic and nonadiabatic processes in condensed media was obtained in Refs. 105 and 106. 

The brief review of the newest results in the theory of elementary chemical processes in the condensed phase given in this chapter shows that great progress has been achieved in this field during recent years, concerning the description of both the interaction of electrons with the polar medium and with the intramolecular vibrations and the interaction of the intramolecular vibrations and other reactive modes with each other and with the dissipative subsystem (thermal bath). The rapid development of the theory of the adiabatic reactions of the transfer of heavy particles with due account of the fluctuational character of the motion of the medium in the framework of both dynamic and stochastic approaches should be mentioned. The stochastic approach is described only briefly in this chapter. The number of papers in this field is so great that their detailed review would require a separate article. 

Freeder, B. G. et al., J. Loss Prev. Process Ind., 1988, 1, 164-168 Accidental contamination of a 90 kg cylinder of ethylene oxide with a little sodium hydroxide solution led to explosive failure of the cylinder over 8 hours later [1], Based on later studies of the kinetics and heat release of the poly condensation reaction, it was estimated that after 8 hours and 1 min, some 12.7% of the oxide had condensed with an increase in temperature from 20 to 100°C. At this point the heat release rate was calculated to be 2.1 MJ/min, and 100 s later the temperature and heat release rate would be 160° and 1.67 MJ/s respectively, with 28% condensation. Complete reaction would have been attained some 16 s later at a temperature of 700°C [2], Precautions designed to prevent explosive polymerisation of ethylene oxide are discussed, including rigid exclusion of acids covalent halides, such as aluminium chloride, iron(III) chloride, tin(IV) chloride basic materials like alkali hydroxides, ammonia, amines, metallic potassium and catalytically active solids such as aluminium oxide, iron oxide, or rust [1] A comparative study of the runaway exothermic polymerisation of ethylene oxide and of propylene oxide by 10 wt% of solutions of sodium hydroxide of various concentrations has been done using ARC. Results below show onset temperatures/corrected adiabatic exotherm/maximum pressure attained and heat of polymerisation for the least (0.125 M) and most (1 M) concentrated alkali solutions used as catalysts. 

Dry air rising in the atmosphere has to expand as the pressure in the atmosphere decreases. This pV work decreases the temperature in a regular way, known as the adiabatic lapse rate, Td, which for the Earth is of order 9.8 Kkm-1. As the temperature decreases, condensable vapours begin to form and the work required for the expansion is used up in the latent heat of condensation of the vapour. In this case, the lapse rate for a condensable vapour, the saturated adiabatic lapse rate, is different. At a specific altitude the environmental lapse rate for a given parcel of air with a given humidity reaches a temperature that is the same as the saturated adiabatic lapse rate, when water condenses and clouds form Clouds in turn affect the albedo and the effective temperature of the planet. Convection of hot, wet (containing condensable vapour) air produces weather and precipitation. This initiates the water cycle in the atmosphere. Similar calculations may be performed for all gases, and cloud layers may be predicted in all atmospheres. 

The gas leaving an ammonia oxidation unit in a continuous process is cooled rapidly to 20°C and contains 9 mol % NO, 1% N02, 8% O2, and 82% N2 (all the water formed by reaction is assumed to be condensed). It is desirable to allow oxidation of NO to N02 in a continuous reactor to achieve a molar ratio of N02 to NO of 5 before absorption of the N02 to make HNO3. Determine the outlet temperature of the reactor, if it operates adiabatically (at essentially 6.9... 

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