Document 4aBEKXQBkLgn9ox8YY2GpoyGR

64 CHAPTER 3 1948-Guide WET-BULB TEMPERATURES BELOW 32F A condition in which the water evaporating from the wick of a wet-bulb thermometer remains liquid at 32 F or lower is one of metastable equi librium and should therefore not be expected to. occur in practice. The evidence that it does sometimes occur appears to be indirect and incon clusive. Stable equilibrium requires that the water freeze at 32 F or lower and is the condition to be expected in practice. On the Mollier Diagram the lines of constant thermodynamic wet-bulb temperature have been drawn for stable equilibrium only. In other words it has been assumed that the water evaporating from the wick of the wet-bulb thermometer freezes when its temperature falls to 32 F or lower. Example 15. Find the temperature at which dry air has a thermodynamic wet-bulb temperature of 32 F. Solution. If it is assumed that the water evaporating from the wick of the wet-bulb thermometer remains liquid, the specific enthalpy of the dry air must have the value = 11.758 - 0.04 X 0.003788 = 11.758 corresponding to which the temperature is 48.95 F. On the other hand if it is assumed^ that the water freezes, the specific enthalpy of the dry air must have the value, K = 11.758 + 143.36 X 0.003788 = 12.301 corresponding to which the temperature is 51.21 F. The second assumption is the. as sumption of stable equilibrium and should be expected to represent the actual situatioa The corresponding answer, namely 51.21 F, is the one given by the Mollier Diagram at intersection of 32. F thermodynamic wet-bulb and 0 per cent saturation. DALTON'S RULE As stated in the introduction the thermodynamic properties of moist air have hitherto been obtained from those of dry air and water vapor separately by application of Dalton's Rule. Actual departures from the rule are due principally, but not entirely, to intermolecular forces; therefore, in order to apply the rule with any measure of consistency it is necessary to idealize the situation by assuming that the effects of such intermolecular forces are negligible and that both the dry air mid the water vapor behave like perfect gases. Making this assumption, the volume t occupied by wa mols of dry air at temperature T and pressure Pa is VT = nzRT/pz while that occupied by w mols of water vapor at the same temperature but at pressure pwisvr = ru,,RT/pw. According to Dalton's Rule, if the dry air and water vapor'are mixed, each occupies the whole volume of the mixture at the temperature of the mixture and the pressure of the mixture is the sum of the individual pressures. Mathe matically, naRT n-wRT (a "4" nin)RT Pr = --P--a = --Prw = ----------Pr----------- /io^ It follows from these equations that the so-called partial pressure of each constituent is its mol-fraction times the observed pressure of the mixture; thus, for water vapor, w Pw ~ *ht "h nw (13) and similarly for dry air. Equation 13 may be regarded as the Dalton Rule definition of partial pressure in terms of the observable terms na, ttw, p- Thermodynamics 65 The humidity ratio W is the mol ratio Ww/Wa times the ratio of mole cular weights, namely, 18.016/28.966 = 0.6220; hence Equation 13 can be written . W = 0.6220 ---- P -- Pw (14) . Now, even if it is assumed that both the dry air and the water vapor behave like perfect gases, it does not follow that at saturation the partial pressure of the water vapor can be put equal to the saturation pressure . of pure water at the temperature of the mixture because:' (I) the coexisting liquid (or solid) phase, is not pure water but contains a small amount of dissolved air, and (2) the coexisting liquid (or solid) phase has to support the observed pressure p and not just the saturation pressure pB of pure water. These effects are calculable but are in general smaller than the effects of intermolecular forces which have already been ignored. Be sides, the only legitimate reason for retaining Dalton's Rule is to gain simplicity; hence these effects should be disregarded.also, and the humi dity ratio at saturation estimated as follows, Wa = 0.6220 --**-' P ~~ Ps (15) In this chapter the ratio W/WB has been called degree of saturation and denoted by the greek letter jjl. The ratio pw/ps has long been called relative humidity and will be denoted by the Greek letter 9. Equations 14 and 15 can be combined to give (* = which can be inverted to give 1 - Ps/P 1 -- 9ps/P (16) 9 1 - (1 - ript/p (17) Example 16. Find the relative humidity of moist air at 180 F, 20 per cent saturation. Solution.. Inserting numerical data from Table 1 into Equation 17, the answer is 0.20 1 - 0.80 X 15.294/29.921 = 0.3384 Example 17. Find the degree of saturation of moist air at 70 F, 50 per cent relative .humidity. Solution. Inserting numerical data from Table 1 into Equation 16, the answer is n r,, U t>U 1 1 - 0.73915/29.921 - 0.50 X 0.73915/29.921 = 0.4937 The foregoing examples show that there is a substantial difference between degree of saturation and relative humidity, particularly at higher temperatures. Of course, they both have the value zero for dry air and the value unity for saturated moist air regardless of the tem perature. A Dalton Rule expression for the volume of moist air per pound of dry air obtainable .directly from Equation 12 is '= where Ra ~ gas constant for dry air = 1545.31 -h 28.966 = 53.349 (ft/F). (W