Document 6bj6gE49yMey8273ELpvz2XB6

66 CHAPTER 3' `1946 Guide The humidity ratio W is the mol ratio Ww/na iimes the ratio of mole cular weights, namely, 18.016/28.966 = 0.6220; hence (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; (1) 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 p, 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 --5 P -- Pa . (15) In this chapter the ratio W/We has been called degree of saturation and denoted by the greek letter p.. The ratio pa,/Pa has long been called relative humidity and will be denoted by the' Greek letter 9. Equations 14 and 15 can be combined to give = 9 1 ~ PalP 1 - 9Pa/P which can be inverted to give 1* 1 - (1 - v)pa/p (16) (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 (17), the answer is = 0-20 , -(p 1 -.0.80 X 15.294/29.921 ,, 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 1 - 0.73915/29.921' % p = 0.50 1 - 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 I. 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 . .. : (R*T\ , fWaRv,T\ / = {--) +(--p~)................., (I8) where ;-j Ra = gas constant for dry air = 1545.31 28.966 = 53.349 (ft/Fj. ' ' Thermodynamicsi____________________________ _________ ____________________ ___________ 67, = gas constant for water vapor = 1545.31 18.016 = 85.774-(ft/F).' This expression is of the form of Equation 4. According to Dalton's Rule the enthalpy of moist air is the sum of separate contributions from the dry air and the water vapor; thus,. . h = ha. 4- p(IFsiw) ' (19) where, to be consistent, the specific enthalpies ha and K, should be ' allowed to vary with`temperature only, riot with pressure or compo sition. This expression is of the form of Equation 5. 0 Within the accuracy of Dalton's Rule the following empirical equations give suitable values of ha and h,,: ' . .. . ha -- 0.2401 ha, = 0.444f + 1061 (20) Equation 7 defining thermodynamic wet-bulb temperature may be written in the form, h -V + tWs* - W)K* = ha* -- V If the quantify h! that has been subtracted from both sides is understood to be the enthalpy at the thermodynamic wet-bulb ternperature t* but at the humidity ratio W, then within the accuracy of Dalton's Rule ' h -- h' -- (0.240 + 0.444 IF) (1 - (*) As* - A1 = (1061 + 0.4441*) (IFs* - HO A,,* = 1* - 32 With these approximations Equation 7 becomes Wa* -W = 0.240 + 0.444 W 1093 - 0.5561* . ,. 1 (21) Carrier 6 has modified Equation 21 by introducing further approxh mations as, follows, . .. . Ws* = 0.6220ps*/(p - pa*)- ; .W = 0.6220pw/(p -- pa*) , 0.444 W -- 0 ' , the first of which is.part of Dalton's Rule. The result is Pw -- ps* 2830 - 1.441* (1 - 1*) (22) except that the numerical values of the constants in the denominator of the rightmost term are somewhat different than Carrier's; ':' Equation 22 permits direct calculation of the partial pressure pw from observed values of pressure p, temperature t, arid wet-bulb temperature t*, assuming that information is available regarding the . saturation pressure ps. . The ratio pa,/pa is the sorcalled relative humidity. ..- Example 18. Kind the relative humidity of moist air at 90 F dry-bulb; arid -63 F- (thermodynamic wet-bulb).. ' -i ... Solution. At 63 F the value of the saturation pressure is 0.58002 in. Hgi Therefore, at atmospheric pressure (29.921 in. Hg), pa, = 0.58002 - 29.341 X 27/2739 = 0.2908 in. Hg