Enthalpies and humidities

Considering the nature of the isothermals for the three conditions dealt with previously, at constant temperature 0 the relation between enthalpy and humidity for an unsaturated... 

Thus, the isothermal is a straight line of slope [Cw(9 — On) + A] with respect to the humidity axis. At the reference temperature 90, the slope is X at higher temperatures, the slope is greater than X, and at lower temperatures it is less than X. Because the latent heat is normally large compared with the sensible heat, the slope of the isothermals remains positive down to very low temperatures. Since the humidity is plotted as the ordinate, the slope of the isothermal relative to the X-axis decreases with increase in temperature. When 9 > Bq and Jf > Jf0, the saturation humidity, the vapour phase consists of a saturated gas with liquid droplets in suspension. The relation between enthalpy and humidity at constant temperature 9 is ... 

Considering the countercurrent flow of water and air in a tower of height z (Figure 13.15), the mass rate of flow of air per unit cross-section G is constant throughout the whole height of the tower and, because only a small proportion of the total supply of water is normally evaporated (1 -5 per cent), the liquid rate per unit area ll can be taken as constant. The temperature, enthalpy, and humidity will be denoted by the symbols 6, H, and Tf respectively, suffixes G, L, 1, 2, and / being used to denote conditions in the gas and liquid, at the bottom and top of the column, and of the air in contact with the water. 

Following this procedure, enthalpy and humidity data at saturation conditions can be computed for a range of temperatures. Table 5.4 gives the required data for this example. 

From Fig. 4.26 in American engineering units the initial and final values of the enthalpies and humidities are... 

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... 

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... 

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. 

Next we draw the saturation curve in the hj -x coordinate system. Vapor pressures can be calculated with Eqs. (4.106) and (4.108) or taken directly from the tables. The humidity x corresponding to the saturation pressure pi,(t) is calculated with Eq. (4.83) noting that p = 0.875 bar. The enthalpy of humid saturated air is calculated with Eq. (4.94) ... 

So the state point of air in the Mollier diagram is shifted in a direction where the dependency between the enthalpy and the humidity change according to the Eq. (4.133) is valid. This result is illustrated in Eig. 4.12. 

Equations 13.16 to 13.18 give the enthalpy in terms of the temperature and humidity of the humid gas for the three conditions 0 = 0a, 0 > 0O, and 0 <0a respectively. Thus, given the percentage humidity and the temperature, the humidity may be obtained from Figure 13.4, the enthalpy calculated from equations 13.16, 13.17 or 13.18 and plotted against the humidity, usually with enthalpy as the abscissa. Such a plot is shown in Figure 13.7 for the air-water system, which includes the curves for 100 per cent humidity and for some lower value, say Z per cent. 

In the cooling tower the temperature of the liquid falls and the temperature and humidity of the air rise, and its action is thus similar to that of an air humidifier. The limiting temperature to which the water can be cooled is the wet-bulb temperature corresponding to the condition of the air at inlet. The enthalpy of the air stream does not remain... 

If the Lewis relation (equation 13.11) is applied, it is possible to obtain workable equations in terms of enthalpy instead of temperature and humidity. Thus, writing h(, as hops, from equation 13.42 ... 

It is supposed that water is to be cooled at a mass rate L per unit area from a temperature 0L2 to Ql - The air will be assumed to have a temperature 6G, a humidity Jf ], and an enthalpy Hoi (which can be calculated from the temperature and humidity), at the inlet point at the bottom of the tower, and its mass flow per unit area will be taken as G. The change in the condition of the liquid and gas phases will now be followed on an enthalpy-temperature diagram (Figure 13.16). The enthalpy-temperature curve PQ for saturated air is plotted either using calculated data or from the humidity chart (Figure 13.4). The region below this line relates to unsaturated air and the region above it to supersaturated air. If it is assumed that the air in contact with the liquid surface... 

The change in the humidity and temperature of the air is now obtained. The enthalpy and temperature of the air are known only at the bottom of the tower, where fresh air is admitted. Here the condition of the air may be represented by a point E with coordinates (HGe %i)- Thus the line AE (Figure 13.16) is parallel to the temperature axis. 

The relative lengths of the environmental parameter vectors on the first and second axes (Fig. 7) can be used a measure of importance for the various climate parameters at constraining the directions of the axes. The mean annual temperature has the longest length, followed by enthalpy, specific humidity, and relative humidity. From these scores, we can identify the first axis with mean annual temperature while the second axis aligns with the mean specific or relative humidity. These associations also allow us to infer which character states are most important for estimating the climate parameters as discussed next. 

Define the dry-bulb temperature, wet-bulb temperature, and humid volume of humid air. Given values of any two of the variables plotted on the psychrometric chart (dry-buib and wet-bulb temperatures, absolute and relative humidity, dew point, humid volume), determine the remaining variable values and the specific enthalpy of the humid air. Use the psychrometric chart to carry out material and energy balance calculations on a heating, cooling, humidification, or dehumidification process involving air and water at 1 atm. 

The remaining curves on the psychrometric chart are almost vertical and convex to the left, with labeled values (on Figure 8.4-1) of -0.05, -0.1, -0.2, and so on. (The units of these numbers are kJ/kg DA). These curves are used to determine the enthalpy of humid air that is not saturated. The procedure is as follows (a) locate the point on the chart corresponding to air at its specified condition (b) interpolate to estimate the enthalpy deviation at this point ... 

Use the psychrometric chart to estimate (1) the absolute humidity, wet-bulb temperature, humid volume, dew point, and specific enthalpy of humid air at 41°C and 10% relative humidity, and (2) the amount of water in 150 m of air at these conditions. 

Enthalpy, humidity, and humid volume data for the air taken from the humidity chart are as follows (see Fig. ]. 50) ... 

Psychrometric charts are plots of humidity, temperature, enthalpy, and other useful parameters of a gas-vapor mixture. They are helpful for rapid estimates of conditions and for visuahzation of process operations such as humidification and drying. They apply to a given system at a given pressure, the most common of course being air-water at atmospheric pressure. There are four types, of which the Grosvenor and Mollier types are most widely used ... 

Equation (8-3) shows that the enthalpy of a gas-vapor mixture depends upon the temperature and humidity at a given pressure. If the mixture is saturated, the humidity is determined by the temperature therefore, the enthalpy of saturated gas-vapor mixtures depends only upon the temperature at a given pressure. ... 

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