Document pBypeqYEzB6oQp3Bzje0YwOy6

16 CHAPTER 3 1959 Guide Equations 18 and 19 and solving for the ratio of mol frac tions. Thus, using perfect gas relationships, - Pm (2Q) P. The humidity ratio W may be obtained-from Equation 17: W 18.016 p, . 0.622 --&-- 28461 p. " P - Pm ' (21) where .18.016 and 28.9G6. are the molecular weights of water and dry air, respectively. . Equation 16 may be rewritten as. where h =. ft; + WK (22) h = enthalpy, Btu per pound of dry air. In relating the enthalpy to. the state of the moist air, the fact that in all applications only differences in enthalpy are involved, allows the arbitrary selection of a datum or zero enthalpy point. Accordingly, from perfect gas relationships, it is possible to write for any temperature t (Fahrenheit) greater than OF A. - 0.24 t (23) where it is assumed that the same arbitrary datum of 0 F is used as in determining the properties of moist air in Table 2. Tables of Thermodynamic Properties--of Moist Air Research' -work, conducted at the University o! Pennsyl vania and at other institutions has shown that the GibboDalton Rule is inaccurate in varying degrees,' depending on temperature, pressure, and the amount of water vapor pres ent. This inaccuracy is probably due to the effect of: 1. Chemical solution of gas molecules in the water vapor. 2. The finite site of the molecules causing interference with the free passage of other molecules toward the boundaries of the system. . . 3. Intermolecular forces of attraction and repulsion. Many attempts have been made to develop an equation of state which would predict the true states of real gases and vapors. The Van der Waal, Maxwell, and Beattie-Bridgman equations are probably the best known. Unfortunately, these expressions rapidly become much too complicated to be used in everyday calculations and, therefore, engineers find it more convenient to use tables of thermodynamic properties for specific working substances, as these can be prepared by physicists using the best laboratory .equipment and all the refinements of mathematics. . Mechanical engineers have long' been familiar' with such tables for the.properties of steams Tables of the properties of moist-air, as prepared by Goodenough and others, have been available for some time, but the latest and most precise of such tables are those which have resulted from a coopera tive research agreement between the American Society op Heating and As-Conditioning Engineers and the Towne Scientific School of the University of Pennsylvania. These properties are published herein as Table 2, and are taken from a research report by Goff and Gratch.f Table 2, which ex perimentally and mathematically takes into account devia tions from perfect gas behavior, such as those' listed above, makes the application of the Gibbs-Oalton Rule a less fre quent necessity. In Table 2 there are 15 columns of figures, each, column being headed by a suitable symbol. In the following subparagraphs brief explanations are given of the data in Table 2 under the appropriate column headings. /(F) Fahrenheit temperature defined in terms of absolute temperature T by the relation, T *= I + 469-67 (24) W, = humidity ratio at saturation. Saturation is the condi tion at which the vapor phase (moist air) may exist in equi librium with a condensed phase (liquid or solid) at the given temperature and pressure (standard atmospheric pressure m the case of Table 2). At given values of temperature and pres sure, the humidity ratio iv can have any value from zero to W,.. v, = specific volume of dry air, cubic feet per pound. a v, -- b , the difference between the volume of moist air at saturation, per pound of dry air, and the specific volume of the dry air itself, cubic feet per pound of dry air. v, ~ specific volume of moist air at saturation per pound of dry air, cubic feet peT pound of dry aiT. ft. specific enthalpy of dry air, Btu per pound of dry air. The specific enthalpy of dry air has been assigned the value zero at 0 F, standard atmospheric pressure. The energy unit Btu is related to the foot-pound by definition, as follows: 1 Btu = 778,3 ft-lb. -- A. -- ft. , the difference between the enthalpy of moist air'd/ saturation, per pound of dry air, and the specific enthalpy of.the dry air itself, Btu per pound of dry air. ft, = enthalpy of moist air at saturation per pound of dry air, Btu per pound of dry air. * specific entropy of dry air, Btu per (pound) (Fahren heit degree). It will be noticed that the specific entropy of dry air has been assigned the value tero at 0 F and standard atmos pheric pressure. 8m = the difference between the entropy of moist air at saturation, per pound of dry air, and the specific entropy of the dry air itself, Btu per (pound of dry air) (Fahrenheit degree). s, " entropy of moist air at saturation per pound of dry air, Btu per (pound of dry air) (Fahrenheit degree). A. -- specific enthalpy of condensed water (liquid or solid) at standard atmospheric pressure, Btu per pound of water. The specific enthalpy of liquid water has been assigned the value zero at 32 F, saturation pressure (0.0SS5S6 psia). a* = specific entropy of condensed water (liquid or solid) at standard atmospheric pressure, Btu per (pound of water) (Fahrenheit degree). The specific entropy of liquid water has been' assigned the value zero at 32 F, saturation pressure (0.088586 psia). ' ' p, -- saturation pressure of pure water vapor, pounds per square inch or inches of mercury (absolute pressure). At a given pressure, moist air can be saturated at any temperature, though this requires that it have a definite humidity ratio W, and that the coexisting condensed phase contain a definite, but very small, quantity of dissolved air. On the other hand, Eure water vapor (steam) below the critical temperature, can e saturated at only one temperature for a given pressure. The values of saturation pressure listed in Table 2 have been com puted from the formulas of Goff and Gratch. THERMODYNAMIC PROPERTIES OF WATER AT SATURATION Since water vapor at low pressures acta almost as a perfect gas, the enthalpy of water vapor should also be a function only of the temperature within these limits. Therefore, the enthalpy of the water vapor may be expressed as approxi mately equal to the enthalpy of saturated vapor at the dry- Thermodynamics 17 bulb temperature of the mixture. Substituting these values in Equation 22, the enthalpy of the mixture becomes . . ,,,, n - 0.a4 t -r k*o) where ft, is the value of the enthalpy of saturated vapor at ~ the-temperature /, and is obtained from Table 3. Table 3 offers revisions to existing steam table date with extensions downward to --160 F. These revisions and ex tensions were a- necessary preliminary to the construction of Table 2. A detailed explanation of,the methods employed in -, the construction of Table 3 is given in a paper by John A. - Goff and S. Gratch.* As in Table 2, the temperature scale used as argument in Table 3 is the Fahrenheit scale defined in terms of absolute temperature T by Equation 24. The symbolsused as column headings in;.Table 3 are the same as those used in; steam tables, and 'have the same meanings. Properties of water above'212 F from Keenan and Keyes* are given in Table 4. DEGREE OF SATURATION Degree of saturation has previously been defined as the', ratio of the actual humidity ratio to the humidity ratio of-' saturated air at the same dry-bulb temperature and baro metric pressure. This may be stated mathematically as cient A for several higher temperatures, the value of p at which the correction term 6 attains its maximum value, and the maximum value of 5 term there attained. - The correction term for the enthalpy is m(1 ~ g)B 1 + aW* (31) Table 5 gives the values of the coefficient B and maximum values of ft, the maximum values occurring at the same degree of saturation as S. Corrections for the entropy consist of two terms: S which is defined as ail - M)C 1 -f- afViM (32) and s, the'BO-caUcd-.-imxvn$ entropy, which contributes the larger part of the error. The mixing entropy is defined as - 0.1579 ((1 + paW.) log(l + paW. - paW. log1#te> (33) - ail + aW.) log,,(l + aW,)] Table 5 lists the values of the coefficient C, the maximum values of i and I and-the values of p at which they occur. The maximum i occurs at the same degree of saturation as the maximum values of v and ft. Obviously the degree of saturation p can have any. value from aero (dry air) to unity (moist air at saturation). The degree of saturation is conveniently used to interpolate values for the enthalpy, specific volume, and entropy- of moist air from the date of Table 2. Within the estimated precision of the date of Table 2, at temperatures below 150 F, the volume's, enthalpy ft, and entropy s, of moist air per pound of dry air at any degree of saturation p may be computed from the simple relations: (27) ft = A 4- nft (28) 8 = 8 + p8m (29) Thus, the degree of saturation is used in conjunction with Table 2 in the same manner^as the quality is used with tables of the thermodynamic properties o! steam. THE ASHAE; PSYCHROMETRIC CHART A psychrometric chart is a graphical representation of the thermodynamic properties of moist air. To be of real value in the solution of engineering problems, it must have distinc tive features which aid in problem analysis. An examination of psychrometric maCT and energy balances shows that no properties other than enthalpy and humidity ratio are required for the solution of problems. It is logical, then, to use these properties as the coordinates of a psychro metric chart. This was initially done by Mollier in 1923,7- * and is the arrangement followed in the chart included with The Guide. The ASHAE Psychrometric Chart is based on the best thermodynamic date available today, namely, those of Goff and Gratch, as given in Table 2. The chart is plotted on oblique coordinates of enthalpy and humidity ratio; tiie enthalpy axis making an angle of approximately 40 deg with the humidity ratio axis. This is shown in Fig. 3. For practical use; the inclusion of dry-bulb and wet-bulb temperatures, volumes, and indexes of the condition of the Correction of Table 2 for Temperatures Above 150 F The simple relations expressed in Equations 27, 28, and 29 . give the properties of unsaturated air with satisfactory pre cision for most engineering design problems. Above 150 F, when greater precision than that obtained by Table 2 is required, these simple relations can be adjusted by the addi tion of supplementary terms. To correct the volume, it is necessary to add a correction term d which is defined as _ ,, - MA 1 + aWjx where a denotes the ratio of the apparent molecular weight of dry air (28.966) to the molecular weight of water (18.016). and is equal to 1.6078. Table 5 gives the valuesof the coeffi- fig. 3____Basic Coordinates of ASHAE Psychrometric Chart