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HEATING VENTILATING AIR CONDITIONING GUIDE 1941 Table 5. Specific Enthalpy of Water Vapor at Zero Pressure3 Temp F t Specific Enthalpy Btu per Lb hw Mean Specific Heat tei: -96 -64 -32 0 1018.49 1032.64 1046.80 1060.97 0.4425 0.4427 0.4429 0.4431 Temp F / Specific Enthalpy Btu per Lb c Mean Specific Heat K]i I Temp F t Specific Enthalpy Btu per Lb kw Mean Specific Heat kj: 32 1075.16 0.4435 64 1089.39 0.4440 96 1103.64 0.4444 128 1117.93 0.4450 160 1132.26 0.4455 192 1146.64 0.4462 224 1161.08 0.4469 256 1175.58 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. 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 - [a*a*5 + 2.4aw * (1 - *) + A,,w (1 - *)>] P (9) where P = observed pressure, pounds, per square foot. v = specific volume, cubic feet per mol. 4aa = second virial coefficient for the dry air expressing the effect of forces between air--air molecules, Gubic feet per mol. Aypff = second virial coefficient for the water-vapor, expressing the effect of forces between water--water molecules, cubic feet per mol. Aaw -- 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 j4aa and Aaw are known; but there is no reliable information at present available on the interaction constant Aaw though experiments are in progress3 to measure it. Pending the results of these experiments, an accurate and thermodynamically consistent treatment is impossible arid the simplest thing to do is to ignore the effect of intermolecular forces entirely. But, 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. *At the Towne Scientific School, University of Pennsylvania, in cooperation .with the A.S.H.V.E. through the Research Technical Advisory Committee on Psychrometry. 8 - CHAPTER T. 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 naRT _ nwRT _ (wa + w) RT pa Pw P P = Pa + Pw (10a) (10b) From these equations are easily obtained, Bw_ par Pw_ nyr/ng no. P -- pw F P 1 + w/a (10c) in which, pa -- partial pressure of the dry air. pv, = partial pressure of the water vapor. P = observed pressure of the mixture. a = weight of dry air (mols). nw = weight of water vapor (mols). 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 ^or ~p~ = 0.62193 + W ^ 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 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 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, Wa = 0.62193 p ft - * " Ps where ps is the saturation pressure of pure water vapor. 9 (12)