Adiabatic cooling

The thermodynamic behavior of a rising moist air parcel can be examined in two steps the cooling of the air parcel from its initial condition to saturation followed by the cooling of the saturated air. 

Let us consider first a moist unsaturated air parcel. Assuming that the rise is adiabatic (no heat exchange with its surroundings) and reversible, then it will also be isentropic. Recall that for a reversible process dQ = T dS and therefore when dQ = 0, dS — 0 also. Under these conditions we have shown in Chapter 16 that if the air parcel is dry (no water vapor), its temperature will vary linearly with height according to (16.8) 

The water vapor and liquid water mixing ratios vv and wy. are very useful quantities in cloud physics. They do not have units and can be defined on a molar, a volume, or a mass basis. The mass basis will be used in this chapter unless otherwise indicated. Several rather complicated expressions can be simplified considerably using these mixing ratios. If necessary, (17.46) can be used to convert the water vapor mixing ratio to water vapor partial pressure. 

The constant a can be eliminated noting that initially To = otwhere pc,o is the initial air pressure of the parcel, to get 

FIGURE 17.11 Lifting condensation level as a function of initial temperature and relative humidity of the air parcel assuming that the air parcel starts initially at the ground at p = 1 atm. 

FIGURE 15.10 Dew temperature of an air parcel as a function of its temperature and relative humidity. 

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In Figure 2 the lines, volume, m /kg dry air, indicate humid volume, which includes the volume of 1.0 kg of dry gas plus the volume of vapor it carries. Enthalpy at saturation data are accurate only at the saturation temperature and humidity however, for air—water vapor mixtures, the diagonal wet bulb temperature lines are approximately the same as constant-enthalpy adiabatic cooling lines. The latter are based on the relationship ... 

Cg = humid heat for humidity H in units of kj / (kg-K) and = latent heat of vaporization at / in kj /kg. The slope of the constant-enthalpy adiabatic cooling line is —C j which is the relationship between temperature and humidity of gas passing through a totally adiabatic direct-heat dryer. The humid heat of a gas—vapor mixture per unit weight of dry gas includes the specific heat of the vapor... 

Enthalpy data are given on the basis of kilojoules per kilogram of diy air. Entbalpy-at-saturation data are accurate only at the saturation temperature and humidity. Enthalpy deviation curves permit enthalpy corrections for humidities less than saturation and show how the wet-bulb-temperature hues do not precisely coincide with constant-enthalpy, adiabatic cooling hnes. 

Note that during the cooling step the maximum amount of evaporation which is permitted by the material balance is 50 lb for the step shown. In an evaporative-cooling step, however, the actual evaporation which results from adiabatic cooling is more than this. Therefore, water must be added back to prevent the NaCl concentration from rising too high otherwise, coprecipitation of NaCl will occur. 

This type of equipment can also be used for apphcations in which the only heat removed is that required for adiabatic cooling of the incoming feed solution. When this is done and the fines-destriiction feature is to be employed, a stream of hqiiid must be withdrawn from the settling zone of the ciystaUizer and the fine ciystals must be separated or destroyed by some means other than heat addition—for example, either dUiition or thickening and plwsical separation. 

If the temperature structure, instead of being that of Fig. 17-6, differs primarily in the lower layers, it resembles Fig. 17-7, where a temperature inversion (an increase rather than a decrease of temperature with height) exists. In the forced ascent of the air parcel up the slope, dry adiabatic cooling produces parcel temperatures that are everywhere cooler than the environment acceration is downward, resisting displacement and the atmosphere is stable. 

If, instead, the air is damped adiabatically with the wet cloth, so that the state of the air varies, the cloth will settle to a slightly different temperature. Each state of air (0, x) is represented by a certain wet bulb temperature 6, which can be calculated from Eq. (4.116) or its approximation (4.123), when the partial pressures of water vapor are low compared with the total pressure. When the state of air reaches the saturation curve, we have an interesting special case. Now the temperatures of the airflow and the cloth are identical. This equilibrium temperature is called the adiabatic cooling border or the thermodynamic wet bulb temperature (6 ). 

For each of the. (bur sets of shelves, the condition of the air is changed to 60 per cent humidity along an adiabatic cooling line. 

Since complete humidification is not always attained, an allowance must be made when designing air humidification cycles. For example, if only 95 per cent saturation is attained the adiabatic cooling line should be followed only to the point corresponding to that degree of saturation, and therefore the gas must be heated to a slightly higher temperature before adiabatic cooling is commenced. 

Calculations involving to systems where the Lewis relation is not applicable are very much more complicated because the adiabatic saturation temperature and the wet-bulb temperature do not coincide. Thus the significance of the adiabatic cooling lines on the psychrometric chart is very much restricted. They no longer represent the changes which take place in a gas as it is humidified by contact with liquid initially at the adiabatic saturation temperature of the gas, but simply give the compositions of all gases with the same adiabatic saturation temperature. 

From the humidity chart, Figure 13.4 in Volume 1, air at 294 K and of 40 per cent relative humidity has a humidity of 0.006 kg/kg. This remains unchanged on heating to 366 K. At the dryer inlet, the wet bulb temperature of the air is 306 K. In the dryer, the cooling takes place along the adiabatic cooling line until 60 per cent relative humidity is reached. 

Before equation 15.22 can be applied to vacuum or adiabatic cooling crystallisation, the quantity E must be estimated, where, from a heat balance ... 

A vacuum crystalliser operates on a slightly different principle from the reduced-pressure unit since supersaturation is achieved by simultaneous evaporation and adiabatic cooling of the feedstock. A hot, saturated solution is fed into an insulated vessel maintained under reduced pressure. If the feed liquor temperature is higher than the boiling point of the solution under the low pressure existing in the vessel, the liquor cools adiabatically to this temperature and the sensible heat and any heat of crystallisation liberated by the solution evaporate solvent and concentrate the solution. 

A newly discovered, highly organized state of matter in which clusters of 20-30 component atoms are magnetically contained and adiabatically cooled to within 2-3 X 10 K of absolute zero. At this point, the motions of the contained atoms are overcome by very weak cohesive forces of the Bose-Einstein condensate. While of no apparent relevance to biochemical kinetics, the Bose-Einstein condensate represents one of the most perfect forms of self-assembly, inasmuch as aU atoms within the condensate share identical Schrodinger wave equations. 

The ability to cool (and eventually liquefy) gases by adiabatic expansion underlies industrial gas liquefaction processes. Adiabatic cooling of gaseous nozzle-jet expansions is also an important technique in modem molecular beam and mass spectrometric research. Thermodynamicist John Fenn, winner of the 2002 Nobel Prize in Chemistry, pioneered many of the techniques of adiabatic nozzle-beam cooling. 

The diagonal lines that run upward and to the left of the saturation curve in Figure 2.5 are referred to as adiabatic cooling curves. Lines for the specific volume of dry air and the saturated volume are also shown. Coordinates of points on these lines are computed by use of Equation 2.38. The humid volume of unsaturated air can be determined by linear interpolation between the two lines, based on percentage humidity. 

Derive" the equations for saturated volume, humid heat and the adiabatic cooling lines for the psychrometric chart. 

The reader should be familiar with the use of the air-water psychrometric chart (Figure 2.5). If not, the reader should take a look at some of the problems at the end of Chapters 2 and 3. By way of review, the basic chart consists of a humidity(>/)-temperature (dry-bulb) set of coordinates along with additional parameters (curves) of constant relative humidity, constant moist volume (humid volume), adiabatic cooling curves (which are the same as the wet-bulb or psychrometric lines, for water vapor only) and the 100% relative humidity curve, also called the saturated-air curve. If any two values are known, we can determine the air-moisture condition on Figure 2.5 and evaluate all other required parameters. 

The use of these relationships in constructing and applying humidity charts is best illustrated by examining a simplified case, that of adiabatic cooling or humidification. Figure 5.4 illustrates this process between air and water that is recycled through the cooling tower. In this operation air is both cooled and... 

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