Humidity adiabatic saturation temperature

Adiabatic-Saturation Temperature, or Constant-Enthalpy Lines If a stream of air is intimately mixed with a quantity of water at a temperature t, in an adiabatic system, the temperature of the air will drop and its humidity will increase. If t, is such that the air leaving the system is in equihbrium with the water, t, will be the adiabatic-saturation temperature, and the line relating the temperature and humidity of the air is the adiabatic-saturation line. The equation for the adiabatic-saturation line is... 

Experimentally it has been shown that for air-water systems the value of Tj /Zc c, the psychrometric ratio, is approximately equal to 1. Under these conditions the wet-bulb temperatures and adiabatic-saturation temperatures are substantially equal and can be used interchangeably. The difference between adiabatic-saturation temperature and wet-bulb temperature increases with increasing humidity, but this effect is unimportant for most engineering calculations. An empirical formula for wet-bulb temperature determination of moist air at atmospheric pressure is presented by Liley [Jnt. J. of Mechanical Engineering Education, vol. 21, No. 2 (1993)]. 

For systems other than air-water vapor, the value of h /k c, may differ appreciably from unity, and the wet-bulb and adiabatic-saturation temperatures are no longer equal. For these systems the psychrometric ratio may be obtained by determining h /k from heat- and mass-transfer an ogies such as the Chilton-Colburn analogy [Ind. Eng. Chem., 26, 1183 (1934)]. For low humidities this analogy gives... 

Example 1 Compare Wet-Bulb and Adiabatic-Saturation Temperatures For tne air-water system at atmospheric pressure, the measured values of dry-bulh and wet-hulh temperatures are 85 and 72 F respectively. Determine the absolute humidity and compare the wet-bulb temperature and adiabatic-saturation temperature. Assume that h /k is given by Eq. (12-4). 

Since the Schmidt number, Prandtl number, latent heat of vaporization, and humid heat are all essentially independent of pressure, the adiabatic-saturation-temperature and wet-bulb-temperature hues will be substantially equal at pressures different from atmospheric. 

Humidity charts for other solvent vapors may be prepared in an analogous manner. There is one important difference involved, however, in that the wet-bulb temperature differs considerably from the adiabatic-saturation temperatures for vapors other than water. 

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. 

In the system just considered, neither the humidity nor the temperature of the gas is appreciably changed. If the gas is passed over the liquid at such a rate that the time of contact is sufficient for equilibrium to be established, the gas will become saturated and both phases will be brought to the same temperature. In a thermally insulated system, the total sensible heat falls by an amount equal to the latent heat of the liquid evaporated. As a result of continued passage of the gas, the temperature of the liquid gradually approaches an equilibrium value which is known as the adiabatic saturation temperature. 

Making a heat balance over the column, it is seen that the heat of vaporisation of the liquid must come from the sensible heat in the gas. The temperature of the gas falls from 6 to the adiabatic saturation temperature 6S, and its humidity increases from to Jfv (the saturation value at 9S). Then working on the basis of unit mass of dry gas ... 

If an unsaturated gas is brought into contact with a liquid which is at the adiabatic saturation temperature of the gas, a simultaneous transfer of heat and mass takes place. The temperature of the gas falls and its humidity increases (Figure 13.2). The temperature of the liquid at any instant tends to change and approach the wet-bulb temperature corresponding to the particular condition of the gas at that moment. For a liquid other than water, the adiabatic saturation temperature is less than the wet-bulb temperature and therefore in the initial stages, the temperature of the liquid rises. As the gas becomes humidified, however, its wet-bulb temperature falls and consequently the temperature to... 

Two methods of changing the humidity and temperature of a gas from Aidj. JP x i to B(()2. J 2) may be traced on the humidity chart as shown in Figure 13.11. The first method consists of saturating the air by water artificially maintained at the dew point of air of humidity (line AC) and then heating at constant humidity to 82 (line CB). In the second method, the air is heated (line AD) so that its adiabatic saturation temperature corresponds with the dew point of air of humidity JP2- It is then saturated by water at the adiabatic saturation temperature (line DC) and heated at constant humidity to 82 (line CB). In this second method, an additional operation — the preliminary heating—is carried out on the air, hut the water temperature automatically adjusts itself to the required value. 

In a humidifier in which the make-up liquid is only a small proportion of the total liquid circulating, its temperature approaches the adiabatic saturation temperature 0S, and remains constant, so that there is no temperature gradient in the liquid. The gas in contact with the liquid surface is approximately saturated and has a humidity Jf... 

The approach to the adiabatic saturation temperature in turn is correlated with the moisture content of the solids. Additives that will modify the moisture content of the Ca(0H)2 solids in equilibrium with a gas phase of a given relative humidity would then be expected to change the reactivity of the Ca(0H)2 towards S02. 

As shown in the results section, the relative humidity of the gaseous phase is the most important variable in the reaction of SO2 with dry Ca(0H)2 solids. These results are in agreement with results reported in the literature for SO2 removal in the bag filters of spray dryer pilot and commercial plants C3, 5-9). In the spray dryer plants, the moisture content of the gases is normally indicated as approach to the adiabatic saturation temperature (difference between the temperature of the gas and the adiabatic saturation temperature) rather than relative humidity. 

The temperature and dew point of the air entering a certain dryer are 130 and 60°F (328 and 289 K), respectively. Using a humidity chart (Fig. 19.9), find the following properties of the air its humidity, its percentage humidity, its adiabatic-saturation temperature, its humidity at adiabatic saturation, its humid heat, and its humid volume. 

Find the adiabatic-saturation temperature. Find the adiabatic-cooling line (these are the straight lines having negative slope) that passes through point A, interpolating a line if necessary, and read the abscissa of the point (point B) where this line intersects the 100 percent humidity line. This abscissa is the adiabatic-saturation temperature. In the present case, it is 80°F (300 K). 

This result (which is far from obvious) allows us to perform adiabatic cooling calculations with relative ease using the psychrometric chart. First locate the initial state of the air on the chart then locate the final state on the constant wet-bulb temperature line that passes through the initial state (or on the 100% humidity curve if cooling below the adiabatic saturation temperature takes place) and finally perform whatever material and energy balance calculations are required. Example 8.4-7 illustrates such a calculation for an adiabatic humidification operation. 

Determine the absolute humidity and the adiabatic saturation temperature of the entering air. 

If the outlet temperature is low enough, the air leaves saturated with water. The temperature corresponding to this condition is called the adiabatic saturation temperature and is found at the intersection of the adiabatic saturation curve with the 100% relative humidity curve. 

This equation has to be reversed and solved iteratively to obtain Y j (absolute humidity at adiabatic saturation) and hence Ta, (the calculation is divergent in the opposite direction). Approximate direct formulas are available from various sources, e.g., British Standard BS 1339 (2002) and Liley (Int. J. Mech. Enge. Educ. 21(2), 1993). The latent heat of evaporation evaluated at the adiabatic saturation temperature is... 

FIG. 12-7 Mollier psychrometric chart (from PSYCHIC software program) showing determination of adiabatic saturation temperature plots humidity (abscissa) against enthalpy (lines sloping diagonally from top left to bottom right). Courtesy AspenTech.)... 

In a similar way, adiabatic saturation temperature can be calculated from Eq. (12-6) by taking the first guess as -40°C and assuming the humid heat to be 1.05 kj/(kg K) including the vapor ... 

The ratio (h/M Ay)> termed the psychrometric ratio, lies between 0.96 and 1.005 for air-water vapor mixtures thus it is nearly equal to the value of humid heat c,. If the effect of humidity is neglected, the adiabatic saturation and wet-bulb temperatures and T, respectively) are almost equal for the air-water system. Note, however, that and are conceptually quite different. The adiabatic saturation temperature is a gas temperature and a thermodynamic entity while the wet-bulb temperature is a heat and mass transfer rate-based entity and refers to the temperature of the liquid phase. Under constant drying conditions, the surface of the drying material attains the wet-bulb temperature if the heat transfer is by pure convection. The wet-bulb temperature is independent of surface geometry as a result of the analogy between heat and mass transfer. 

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