Document 3NdqgJe314n5mpbLXpY4MMB3y

HEATINC VENTILATING AIR CONDITIONING GUIDE 1944 Table 5. Specific Enthalpy of Water Vapor at Zero Pressure3 Temp F i Specific Enthalpy Btu per Lb C Mean Specific Heat tec -96 -64 -32 0 1018.61 1032.76 1046.92 1061.09 0.4425 0.4427 0.4429 0.4431 Temp F t Specific Enthalpy Btu per Lb c Mean Specific Heat 32 1075.28 0.4435 64 1089.51 0.4440 96 1103.76 0.4444 128 1118.05 0.4450 Temp F t Specific Mean ' Enthalpy Specific Btu per Lb Heat c - KY 160 1132.38 0.4455 192 1146.76 0.4462 224 1161.20 0.4469 256 1175.70 0.4477 aPrepared by John A. Goff from published data computed from spectroscopic measurements. datum, best available information regarding- latent heat, saturation pressure and second virial coefficient at 32 F has been used. The values in Table 5 do not agree exactly with those in the steam tables, but do agree with later information from the National Bureau of Standards [8]. MOIST AIR Dalton's Law. Having accurate information regarding the thermo dynamic properties of dry air and water vapor separately, it is desired to predict the properties of moist air which is regarded as a mixture, of these two constitutents. Statistical mechanics furnishes' a starting point in the form of a prediction that, at not too high pressures, . Pv = RT ~ [,4aa** + 24aw * (1 - x) + Am (1 - *)*] P (9) where P = observed pressure, pounds per square foot, v = specific volume, cubic feet per mol. =Asti* second virial coefficient for the dry air expressing the effect of forces between air--air molecules, cubic feet per mol. Asfrw second virial coefficient for the water vapor, expressing the effect of forces between water--water molecules, cubic feet per mol. a. ^aw interaction constant expressing the effect of forces between air--water mole cules, cubic feet per mol. X -- mol-fraction of dry air in the mixture, mols dry air per mol mixture. .* . Equation 9 will be recognized as a generalization of Equation 2. Both- ^4aa and ylware known; but until recently no reliable information on the interaction constant has been available. Preliminary results of a cooperative investigation between the A.S.H.V.E. and the Towne Scientific School, University of Pennsylvania, have indicated that the. ratio 2i4aw/(^4aa + Aww) has an approximately constant value X = 0.075 [10]. However, before attempting to make use of this information it is advisable, in the interest of simplicity, to first ignore the complica tions arising from intermolecular forces. Now, in the absence of intermolecular forces, each constituent gas .in' a mixture such as moist air would behave exactly as if it alone occupied -the volume V at the temperature T of the mixture and: (1) the observed pressure P would be the sum of individual partial pressures p; (2) the total enthalpy H would be the sum of the individual enthalpies. This is the essence of Dalton's Law of Partial Pressures. 8 CHAPTER 1. THERMODYNAMICS OF AIR AND WATER MIXTURE Referring to dry air by the subscript a and, to water vapor by the subscript w, Dalton's Law would predict where naRT Pa nwRT Pvt (na + w) RT P P -- Pa + Pw (10a) (10b) From these equations are easily obtained, in which, fiw Pvt . Pvt _ %/na na P -- pvt r P 1+ w/a pa = partial pressure of the dry air. pw = partial pressure of the water vapor. P = observed pressure of the mixture. a = weight of dry air (mols). nw = weight of water vapor (mols). (10c) Humidity Ratio In Equation 10c the ratio by weight of water vapor to dry air, Kw/i, is expressed in mols per mol. Most engineers prefer to : express it in pounds per pound which can easily be done, since the molecular weights of both water vapor (18.0154 lb per mol) and of dry air (28.967 lb per mol) . are. known. Thus Equation 10c becomes W = 0 62193 p~pw or = 0.62193 + W; ^ There is little doubt but that the weight ratio W is the most convenient parameter in terms of whi^h to express the composition of moist air; but . to choose a suitable name and one that would have general acceptance has always been a perplexing problem. In previous issues of the Guide, specific humidity was adopted even though it was recognized that the, i adjective,specific should properly refer to weight of water vapor per ; pound of mixture, and not per pound of dry air. Various other- names have been proposed from time to time including: mixing ratio, propor tionate humidity, density ratio, absolute humidity. It is believed that j the name humidity ratio is most suggestive, of the meaning which it is desired to express, that it violates no well established usage as does the name specific humidity and that its adoption will avoid much confusion. To repeat: in the case of moist air, the ratio by weight (pounds) of water vapor to dry air is called humidity ratio and denoted by the letter W. Saturation It is often stated that moist air is saturated when the water vapor in it is itself in the dry saturated condition at the given temperature. This statement would imply that the humidity ratio of saturated moist air is, in accordance with Equation 11, Ws = 0.62193 ,, P -- Pa where pa is the saturation pressure of pure water vapor. 9, (12)