Document mqgBjvnkbEkmVy90Q2xY08vK0

HEATING VENTILATING AIR CONDITIONING GUIDE 1943 Table 5. Specific Enthalpy of Water Vapor at Zero Pressure3 Temp F / Specific Enthalpy Btu per Lb c Mean Specific Heat KU -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 4Btu per Lb Mean Specific Heat K]` 32 1075.28 0.4435 64 1089.51 0.4440 96 1103.76 0.4444 128 1118.05 0.4450 Temp F t Specific Enthalpy Btu per Lb 4 Mean Specific Heat ten 160 1132.38 0.4455 192 1146.76 0.4462 224 1161.20 . 0.4469 256 1175.70 0.4477 Prepared 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 - + 24aw * (1 - *) + Aww (1 - *)*] P (9) where P -- observed pressure, pounds per square foot. . v = specific volume, cubic feet per mol. j4aa = second virial coefficient for the dry air expressing the effect of forces between air--air molecules, cubic feet per mol. i4ww = second virial coefficient for the water vapor, expressing the effect of forces between water--water molecules, cubic feet per mol. /law = 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 ^4W are'kno\yn; but until recently no reliable information on the interaction constant 4aw has been available. Preliminary results of a cooperative investigation between the A.S.H.V.E. arid -the Towne- Scientific School, University of Pennsylvania, have, indicated that the ' ratio 2^4aw/(^4aa + A^,) has an approximately constant value X = 0.075 [10]. However, before attempting to make use of this informatiori it is advisable, in the interest of simplicity, to first ignore the complica-^ tioris 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. J 8 CHAPTER 1. THERMODYNAMICS OF AIR AND WATER MIXTURES Referring to dry air by the subscript a and, to water vapor by the subscript w, Dalton's Law would predict where y _ n^RT _ nwRT _ (ffa ~f~ Bw) RT Pa pw P P -- Pa A Pw From these equations are easily obtained, (10a) (10b) in which, Ww = Pw a P ~ Pw Pw _ Wff/na 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). w = weight of water vapor (mols). (10c) Humidity Ratio In Equation 10c the ratio by weight of water vapor to dry air, ww/a, 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---r~ or ^ A Pw P w 0.62193 + W (11) There is little doubt but that the weight ratio W is the most convenient parameter in terms of which to express the composition of moist air; but to choose a suitable name and orie 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 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 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 h p* P. -- pB where pt is.the saturation pressure of pure water vapor.' 9 (12) .P