Document aDVeNrrEMqvdBEJE25OEaGwQa

Heating Ventilating Air Conditioning Guide 1938 A'fg OF,. -- m = Cpa (/ -- t<) + C^W (t -. t') (9a) and using = 0.24 and Cpj -- 0.45 where A'fg (lVt. -- HO = (0.24 + 0.45HO (t - <0 (9b) h'iz = latent heat of vaporization at f, Btu per pound. (H^t. -- W) = increase in vapor associated with 1 lb of dry air when it is saturated adiabatically from an initial dry-bulb temperature, 1, and an initial vapor, content, W. pounds. Knowing any two of the three primary variables, t, f .- or, W, the. third may be found from this equation for any process of adiabatic saturation. TOTAL HEAT AND HEAT CONTENT The total heat of a mixture of dry air and water vapor was originallydefined by W. H. Carrier as S = c^(t - 0) + W [A'fg + cPs (t - /)] where S = total heat of the mixture, Btu per pound of dry air. Cpj, = mean specific heat at constant pressure of dry air. Cp, = mean specific heat at constant pressure of water vapor. t = dry-bulb temperature, degrees Fahrenheit. t' = wet-bulb temperature, degrees Fahrenheit. W --- weight of water vapor mixed with each pound of dry air, pounds. ft'fg = latent heat of vaporization at t', Btu per pound. (10) Since this definition holds for any mixture of dry air and water vapor, the total heat of a mixture with a relative humidity of 100 per cent and at a temperature equal to the wet-bulb temperature (/') is S' = Cfe ' - 0) + H^t. A'fg ' (11) By equating Equation 10 to Equation 11, the equation, for the adiabatic saturation process, Equation 9a, follows. This demonstrates that the adiabatic saturation process at constant wet-bulb temperature is also a process of constant total heat. . In short, the total heat of a mixture of dry air and water vapor is the same for any two states of the mixture at the same wet-bulb temperature. This fact Furnishes a convenient means of finding the-total heat of-an-air-vapor mixture in any state. Enthalpy ......................... This total heat of an air:vapor mixture"is not exactly equal to the true heat content-or (enthalpy of the mixture since the heat content of the liquid is not. included in Equation lO, ..With the meaning of heat content in agreement with present practise in other branches of thermodynamics, the true heat content of a mixture of dry air and water vapor (with 0 F as the datum for dry air, and the saturated liquid at 32 F as the datum for the water vapor) is 22 Chapter 1. Air, Water and Steam ' A = Cpa (t - 0) + W A, = 0.24 (1 -- 0) + W ft, where h = the heat content of the mixture, Btu per pound of dry air. t -- the dry-bulb temperature, degrees Fahrenheit. W = the weight of vapor per pound of dry air, pounds. hs -- the heat content of the vapor in .the mixture, Btu per pound. (12) The heat content of the water vapor in the mixture may be found in steam charts or tables when the dry-bulb temperature and the partial pressure of the vapor are known. Or, since the heat content of steam at low partial pressures, whether super-heated or saturated, depends only upon temperature, the following empirical equation, derived from Proper ties of Saturated Steam by J'. H. Keenan, Table 8, may be used: Aa = 1059.2 + 0.45 <' (13) Substituting this value of ha.in Equation 12, the heat content of the mixture is h = 0.24 (I -- 0) + W (1059.2 + 0.45 1') (14) Example 5. Find the total heat of an air-vapor mixture having a dry-bulb tem perature of 85 F and a wet-bulb temperature of 70 F. Solution. From Table 6, for saturation at the wet-bulb temperature, HV = 0.01574, and from Equation 14, A = 0.24 (70 -0) + 0.01574 [1059.2 + (0.45 X 70)1 = 33.96 Btu per pound dry air. By considering the temperatures in Table 6 to be wet-bulb readings, the enthalpy of any air-vapor mixture may be obtained from the last column in the table. An energy equation can be written that applies, in general, to various air conditioning processes, and this equation can be used to determine the quantity of heat transferred during such processes. In the most general form, this equation may be explained with the aid of Fig. 1 as follows: The rectangle may represent any. apparatus, t.g., a drier, humidifier, dehumidifier, cooling tower, or the like, by proper choice of the direction of the arrows. In general, a mixture of air and water vapor, such as atmospheric air, enters the apparatus at 1 and leaves at 3. Water is supplied at some temperature, tr- For the flow of 1 lb of dry air (with accompanying vapor) through the apparatus, provided there is no appreciable change in the elevation or velocity of the fluids and no mechanical energy delivered to or by the apparatus, A. + h + OF, - W,) hr = h, + flc Eh -- Rc = h, -- ft, -- (IF, - Wt) h, 1 (15) where Eh = the quantity of heat supplied per pound of dry air, Btu................... Rc = the quantity of heat lost externally by heat transfer from the. apparatus. Btu per pound of dry air. H'i = the weight of water vapor entering, per pound of. dry air.. H^i = the weight of water vapor leaving, per pound of dry air. Ai = the heat content of the water supplied at It, Btu per pound. ' 23