Chapter 1: Psychrometrics PDF

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Related Commercial Resources CHAPTER 1 PSYCHROMETRICS Composition of Dry and Moist Air............................................ 1.1 Thermodynamic Wet-Bulb and Dew-Point Temperature........... 1.9 U.S. Standard Atmosphere......................................................... 1.1 Numerical Calculation of Moist Air Properties....................... 1.10 Thermodynamic Properties of Moist Air................................... 1.2 Psychrometric Charts............................................................... 1.10 Thermodynamic Properties of Water at Saturation................... 1.4 Typical Air-Conditioning Processes........................................ 1.12 Humidity Parameters................................................................. 1.8 Transport Properties of Moist Air............................................ 1.15 Perfect Gas Relationships for Dry and Moist Air...................... 1.8 Symbols.................................................................................... 1.15 P SYCHROMETRICS uses thermodynamic properties to ana- lyze conditions and processes involving moist air. This chapter discusses perfect gas relations and their use in common heating, water phase (liquid or solid); unless otherwise stated, it assumes a flat interface surface between moist air and the condensed phase. Saturation conditions change when the interface radius is very small cooling, and humidity control problems. Formulas developed by (e.g., with ultrafine water droplets). According to the Industrial For- Herrmann et al. (2009) may be used where greater precision is mulation IAPWS-IF97 (R7-97 2012), the relative molecular mass of required. water is 18.015 257. The gas constant for water vapor is Herrmann et al. (2009), Hyland and Wexler (1983a, 1983b), and Nelson and Sauer (2002) developed formulas for thermodynamic Rw = 8314.472/18.015 257 = 461.524 J/(kgw ·K) (2) properties of moist air and water modeled as real gases. However, perfect gas relations can be substituted in most air-conditioning 2. U.S. STANDARD ATMOSPHERE problems. Kuehn et al. (1998) showed that errors are less than 0.7% in calculating humidity ratio, enthalpy, and specific volume of satu- The temperature and barometric pressure of atmospheric air vary rated air at standard atmospheric pressure for a temperature range of considerably with altitude as well as with local geographic and –50 to 50°C. Furthermore, these errors decrease with decreasing weather conditions. The standard atmosphere gives a standard of ref- pressure. erence for estimating properties at various altitudes. At sea level, Hermann et al. (2020) prepared formulas for transport properties standard temperature is 15°C; standard barometric pressure is of moist air. 101.325 kPa. Temperature is assumed to decrease linearly with in- creasing altitude throughout the troposphere (lower atmosphere), and 1. COMPOSITION OF DRY AND MOIST AIR to be constant in the lower reaches of the stratosphere. The lower at- mosphere is assumed to consist of dry air that behaves as a perfect gas. Atmospheric air contains many gaseous components as well as Gravity is also assumed constant at the standard value, 9.806 65 m/s2. water vapor and miscellaneous contaminants (e.g., smoke, pollen, Table 1 summarizes property data for altitudes to 10 000 m. and gaseous pollutants not normally present in free air far from pol- Pressure values in Table 1 may be calculated from lution sources). Dry air is atmospheric air with all water vapor and contaminants p = 101.325(1 – 2.25577  10 –5Z) 5.2559 (3) removed. Its composition is relatively constant, but small variations in the amounts of individual components occur with time, geo- The equation for temperature as a function of altitude is graphic location, and altitude. Harrison (1965) lists the approximate percentage composition of dry air by volume as: nitrogen, 78.084; t =15 – 0.0065Z (4) oxygen, 20.9476; argon, 0.934; neon, 0.001818; helium, 0.000524; where methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; Z = altitude, m and minor components such as krypton, xenon, and ozone, 0.0002. p = barometric pressure, kPa Harrison (1965) and Hyland and Wexler (1983a) used a value 0.0314 t = temperature, °C (circa 1955) for carbon dioxide. Carbon dioxide reached 0.0379 in 2005, is currently increasing by 0.00019 percent per year and is pro- Equations (3) and (4) are accurate from –5000 m to 11 000 m. jected to reach 0.0438 in 2036 (Gatley et al. 2008; Keeling and For higher altitudes, comprehensive tables of barometric pressure Whorf 2005a, 2005b). Increases in carbon dioxide are offset by and other physical properties of the standard atmosphere, in both SI decreases in oxygen; consequently, the oxygen percentage in 2036 is and I-P units, can be found in NASA (1976). projected to be 20.9352. Using the projected changes, the relative molecular mass for dry air for at least the first half of the 21st century is 28.966, based on the carbon-12 scale. The gas constant for dry air 3. THERMODYNAMIC PROPERTIES OF MOIST using the Mohr and Taylor (2005) value for the universal gas con- AIR stant is Table 2, calculated using ASHRAE’s (2021) LibHuAirProp soft- Rda = 8314.472/28.966 = 287.042 J/(kgda ·K) (1) ware (based on ASHRAE RP-1485; Hermann et al. 2009, 2020), Moist air is a binary (two-component) mixture of dry air and shows values of thermodynamic properties of saturated moist air and water vapor. The amount of water vapor varies from zero (dry air) to dry air at 101.325 kPa and temperatures from –60 to 90°C. a maximum that depends on temperature and pressure. Saturation is The following properties are shown in Table 2: a state of neutral equilibrium between moist air and the condensed t = Celsius temperature, based on the ITS-90 and expressed relative The preparation of this chapter is assigned to TC 1.1, Thermodynamics and to absolute temperature T in kelvins (K) by the following relation: Psychrometrics. T = t + 273.15 1.1 1.2 2021 ASHRAE Handbook—Fundamentals (SI) Table 1 Standard Atmospheric Data for Altitudes to 10 000 m vas = vs – vda, difference between specific volume of moist air at saturation and that of dry air, m3/kgda, at same pressure and Altitude, m Temperature, °C Pressure, kPa temperature. –500 18.2 107.478 vs = specific volume of moist air at saturation, m3/kgda. 0 15.0 101.325 hda = specific enthalpy of dry air, kJ/kgda. In Table 2, hda is assigned a 500 11.8 95.461 value of 0 at 0°C and standard atmospheric pressure. has = hs – hda, difference between specific enthalpy of moist air at 1000 8.5 89.875 saturation and that of dry air, kJ/kgda, at same pressure and 1500 5.2 84.556 temperature. 2000 2.0 79.495 hs = specific enthalpy of moist air at saturation, kJ/kgda. 2500 –1.2 74.682 sda = specific entropy of dry air, kJ/(kgda ·K). In Table 2, sda is 3000 –4.5 70.108 assigned a value of 0 at 0°C and standard atmospheric pressure. 4000 –11.0 61.640 ss = specific entropy of moist air at saturation kJ/(kgda ·K). 5000 –17.5 54.020 6000 –24.0 47.181 4. THERMODYNAMIC PROPERTIES OF WATER 7000 –30.5 41.061 AT SATURATION 8000 –37.0 35.600 9000 –43.5 30.742 Table 3 shows thermodynamic properties of water at saturation 10 000 –50 26.436 for temperatures from –60 to 160°C, calculated using ASHRAE (2021) LibHuAirProp software, based on IAPWS formulations Source: Adapted from NASA (1976). described in IAPWS R7-97 (2012), R10-06 (2009), and R14-08 (2011). The internal energy and entropy of saturated liquid water are Ws = humidity ratio at saturation; gaseous phase (moist air) exists in equilibrium with condensed phase (liquid or solid) at given both assigned the value zero at the triple point, 0.01°C. Between the temperature and pressure (standard atmospheric pressure). At triple-point and critical-point temperatures of water, both saturated given values of temperature and pressure, humidity ratio W can liquid and saturated vapor may coexist in equilibrium; below the have any value from zero to Ws. triple-point temperature, both saturated ice and saturated vapor vda = specific volume of dry air, m3/kgda. may coexist in equilibrium. Table 2 Thermodynamic Properties of Saturated Moist and Dry Air at Standard Atmospheric Pressure, 101.325 kPa Specific Volume, Specific Enthalpy, Specific Heat Capacity, Specific Entropy, m3/kgda kJ/kgda kJ/(kg·K) kJ/(kgda·K) Humidity Ratio Ws, Temp. t, °C kgw/kgda vda vs hda hs t cp,s sda ss –60 0.0000067 0.6027 0.6027 –60.341 –60.325 1.0062 1.0062 –0.2494 –0.2494 –59 0.0000076 0.6055 0.6055 –59.335 –59.317 1.0062 1.0062 –0.2447 –0.2446 –58 0.0000087 0.6084 0.6084 –58.329 –58.308 1.0061 1.0061 –0.2400 –0.2399 –57 0.0000100 0.6112 0.6112 –57.323 –57.299 1.0061 1.0061 –0.2354 –0.2353 –56 0.0000114 0.6141 0.6141 –56.317 –56.289 1.0061 1.0061 –0.2307 –0.2306 –55 0.0000129 0.6169 0.6169 –55.311 –55.280 1.0060 1.0061 –0.2261 –0.2260 –54 0.0000147 0.6198 0.6198 –54.305 –54.269 1.0060 1.0060 –0.2215 –0.2213 –53 0.0000167 0.6226 0.6226 –53.299 –53.258 1.0060 1.0060 –0.2169 –0.2167 –52 0.0000190 0.6255 0.6255 –52.293 –52.247 1.0060 1.0060 –0.2124 –0.2121 –51 0.0000215 0.6283 0.6283 –51.287 –51.235 1.0059 1.0059 –0.2078 –0.2076 –50 0.0000243 0.6312 0.6312 –50.281 –50.222 1.0059 1.0059 –0.2033 –0.2030 –49 0.0000275 0.6340 0.6340 –49.275 –49.209 1.0059 1.0059 –0.1988 –0.1985 –48 0.0000311 0.6369 0.6369 –48.269 –48.194 1.0059 1.0059 –0.1943 –0.1940 –47 0.0000350 0.6397 0.6397 –47.263 –47.179 1.0058 1.0059 –0.1899 –0.1895 –46 0.0000395 0.6425 0.6426 –46.257 –46.162 1.0058 1.0058 –0.1854 –0.1850 –45 0.0000445 0.6454 0.6454 –45.252 –45.144 1.0058 1.0058 –0.1810 –0.1805 –44 0.0000500 0.6482 0.6483 –44.246 –44.125 1.0058 1.0058 –0.1766 –0.1761 –43 0.0000562 0.6511 0.6511 –43.240 –43.104 1.0057 1.0058 –0.1722 –0.1716 –42 0.0000631 0.6539 0.6540 –42.234 –42.081 1.0057 1.0058 –0.1679 –0.1672 –41 0.0000708 0.6568 0.6568 –41.229 –41.057 1.0057 1.0058 –0.1635 –0.1628 –40 0.0000793 0.6596 0.6597 –40.223 –40.031 1.0057 1.0058 –0.1592 –0.1583 –39 0.0000887 0.6625 0.6626 –39.217 –39.002 1.0057 1.0057 –0.1549 –0.1539 –38 0.0000992 0.6653 0.6654 –38.211 –37.970 1.0057 1.0057 –0.1506 –0.1495 –37 0.0001108 0.6682 0.6683 –37.206 –36.936 1.0056 1.0057 –0.1464 –0.1451 –36 0.0001237 0.6710 0.6711 –36.200 –35.899 1.0056 1.0057 –0.1421 –0.1408 –35 0.0001379 0.6738 0.6740 –35.195 –34.859 1.0056 1.0057 –0.1379 –0.1364 –34 0.0001536 0.6767 0.6769 –34.189 –33.815 1.0056 1.0057 –0.1337 –0.1320 –33 0.0001710 0.6795 0.6797 –33.183 –32.766 1.0056 1.0057 –0.1295 –0.1276 –32 0.0001902 0.6824 0.6826 –32.178 –31.714 1.0056 1.0057 –0.1253 –0.1232 –31 0.0002113 0.6852 0.6855 –31.172 –30.656 1.0056 1.0058 –0.1211 –0.1189 Psychrometrics 1.3 Table 2 Thermodynamic Properties of Saturated Moist and Dry Air at Standard Atmospheric Pressure, 101.325 kPa (Continued) Specific Volume, Specific Enthalpy, Specific Heat Capacity, Specific Entropy, m3/kgda kJ/kgda kJ/(kg·K) kJ/(kgda·K) Humidity Ratio Ws, Temp. t, °C kgw/kgda vda vs hda hs t cp,s sda ss –30 0.0002345 0.6881 0.6883 –30.167 –29.593 1.0056 1.0058 –0.1170 –0.1145 –29 0.0002602 0.6909 0.6912 –29.161 –28.525 1.0056 1.0058 –0.1129 –0.1101 –28 0.0002883 0.6938 0.6941 –28.156 –27.450 1.0055 1.0058 –0.1088 –0.1057 –27 0.0003193 0.6966 0.6970 –27.150 –26.368 1.0055 1.0058 –0.1047 –0.1013 –26 0.0003532 0.6994 0.6998 –26.144 –25.278 1.0055 1.0058 –0.1006 –0.0969 –25 0.0003905 0.7023 0.7027 –25.139 –24.181 1.0055 1.0059 –0.0965 –0.0924 –24 0.0004314 0.7051 0.7056 –24.133 –23.074 1.0055 1.0059 –0.0925 –0.0880 –23 0.0004761 0.7080 0.7085 –23.128 –21.958 1.0055 1.0059 –0.0884 –0.0835 –22 0.0005251 0.7108 0.7114 –22.122 –20.831 1.0055 1.0060 –0.0844 –0.0790 –21 0.0005787 0.7137 0.7143 –21.117 –19.693 1.0055 1.0060 –0.0804 –0.0745 –20 0.0006373 0.7165 0.7172 –20.111 –18.542 1.0055 1.0061 –0.0765 –0.0699 –19 0.0007013 0.7193 0.7201 –19.106 –17.377 1.0055 1.0061 –0.0725 –0.0653 –18 0.0007711 0.7222 0.7231 –18.100 –16.198 1.0055 1.0062 –0.0685 –0.0607 –17 0.0008473 0.7250 0.7260 –17.095 –15.003 1.0055 1.0063 –0.0646 –0.0560 –16 0.0009303 0.7279 0.7290 –16.089 –13.791 1.0055 1.0063 –0.0607 –0.0513 –15 0.0010207 0.7307 0.7319 –15.084 –12.560 1.0055 1.0064 –0.0568 –0.0465 –14 0.0011191 0.7336 0.7349 –14.078 –11.310 1.0055 1.0065 –0.0529 –0.0416 –13 0.0012261 0.7364 0.7378 –13.073 –10.037 1.0055 1.0066 –0.0490 –0.0367 –12 0.0013425 0.7392 0.7408 –12.067 –8.7408 1.0055 1.0067 –0.0452 –0.0317 –11 0.0014689 0.7421 0.7438 –11.062 –7.4193 1.0055 1.0068 –0.0413 –0.0267 –10 0.0016062 0.7449 0.7468 –10.056 –6.0705 1.0056 1.0069 –0.0375 –0.0215 –9 0.0017551 0.7478 0.7499 –9.0505 –4.6921 1.0056 1.0071 –0.0337 –0.0163 –8 0.0019166 0.7506 0.7529 –8.0449 –3.2820 1.0056 1.0072 –0.0299 –0.0110 –7 0.0020916 0.7534 0.7560 –7.0393 –1.8377 1.0056 1.0074 –0.0261 –0.0055 –6 0.0022812 0.7563 0.7591 –6.0337 –0.3565 1.0056 1.0076 –0.0223 0.0000 –5 0.0024863 0.7591 0.7622 –5.0282 1.1643 1.0056 1.0078 –0.0186 0.0057 –4 0.0027083 0.7620 0.7653 –4.0225 2.7276 1.0056 1.0080 –0.0148 0.0115 –3 0.0029482 0.7648 0.7684 –3.0169 4.3368 1.0056 1.0082 –0.0111 0.0175 –2 0.0032076 0.7677 0.7716 –2.0113 5.9952 1.0056 1.0084 –0.0074 0.0236 –1 0.0034877 0.7705 0.7748 –1.0057 7.7064 1.0057 1.0087 –0.0037 0.0299 0 0.0037900 0.7733 0.7780 0.0000 9.4744 1.0057 1.0090 0.00000 0.0364 1 0.0040763 0.7762 0.7813 1.0057 11.203 1.0057 1.0092 0.0037 0.0427 2 0.0043818 0.7790 0.7845 2.0114 12.981 1.0057 1.0095 0.0073 0.0492 3 0.0047075 0.7819 0.7878 3.0171 14.811 1.0057 1.0098 0.0110 0.0559 4 0.0050547 0.7847 0.7911 4.0228 16.696 1.0057 1.0101 0.0146 0.0627 5 0.0054247 0.7875 0.7944 5.0285 18.639 1.0058 1.0105 0.0182 0.0697 6 0.0058186 0.7904 0.7978 6.0343 20.644 1.0058 1.0108 0.0219 0.0769 7 0.0062379 0.7932 0.8012 7.0401 22.714 1.0058 1.0112 0.0254 0.0843 8 0.0066839 0.7961 0.8046 8.0459 24.853 1.0058 1.0116 0.0290 0.0919 9 0.0071584 0.7989 0.8081 9.0517 27.065 1.0058 1.0121 0.0326 0.0997 10 0.0076627 0.8017 0.8116 10.058 29.354 1.0059 1.0125 0.0362 0.1078 11 0.0081985 0.8046 0.8152 11.063 31.724 1.0059 1.0130 0.0397 0.1162 12 0.0087677 0.8074 0.8188 12.069 34.180 1.0059 1.0136 0.0432 0.1248 13 0.0093720 0.8103 0.8224 13.075 36.727 1.0059 1.0141 0.0468 0.1337 14 0.010013 0.8131 0.8262 14.081 39.370 1.0060 1.0147 0.0503 0.1430 15 0.010694 0.8159 0.8299 15.087 42.114 1.0060 1.0153 0.0538 0.1525 16 0.011415 0.8188 0.8338 16.093 44.965 1.0060 1.0160 0.0573 0.1624 17 0.012181 0.8216 0.8377 17.099 47.929 1.0060 1.0167 0.0607 0.1726 18 0.012991 0.8245 0.8416 18.105 51.011 1.0061 1.0174 0.0642 0.1832 19 0.013851 0.8273 0.8457 19.111 54.218 1.0061 1.0182 0.0676 0.1942 20 0.014761 0.8301 0.8498 20.117 57.558 1.0061 1.0191 0.0711 0.2057 21 0.015724 0.8330 0.8540 21.124 61.037 1.0062 1.0199 0.0745 0.2175 1.4 2021 ASHRAE Handbook—Fundamentals (SI) Table 2 Thermodynamic Properties of Saturated Moist and Dry Air at Standard Atmospheric Pressure, 101.325 kPa (Continued) Specific Volume, Specific Enthalpy, Specific Heat Capacity, Specific Entropy, m3/kgda kJ/kgda kJ/(kg·K) kJ/(kgda·K) Humidity Ratio Ws, Temp. t, °C kgw/kgda vda vs hda hs t cp,s sda ss 22 0.016744 0.8358 0.8583 22.130 64.662 1.0062 1.0209 0.0779 0.2298 23 0.017823 0.8387 0.8626 23.136 68.443 1.0062 1.0218 0.0813 0.2426 24 0.018965 0.8415 0.8671 24.142 72.387 1.0063 1.0229 0.0847 0.2559 25 0.020173 0.8443 0.8716 25.148 76.503 1.0063 1.0240 0.0881 0.2698 26 0.021451 0.8472 0.8763 26.155 80.800 1.0063 1.0251 0.0915 0.2842 27 0.022802 0.8500 0.8811 27.161 85.288 1.0064 1.0263 0.0948 0.2992 28 0.024229 0.8529 0.8860 28.167 89.978 1.0064 1.0276 0.0982 0.3148 29 0.025738 0.8557 0.8910 29.174 94.881 1.0064 1.0290 0.1015 0.3311 30 0.027333 0.8585 0.8961 30.180 100.01 1.0065 1.0304 0.1048 0.3481 31 0.029018 0.8614 0.9014 31.187 105.37 1.0065 1.0319 0.1081 0.3658 32 0.030797 0.8642 0.9069 32.193 110.98 1.0066 1.0335 0.1115 0.3843 33 0.032677 0.8671 0.9124 33.200 116.86 1.0066 1.0352 0.1147 0.4035 34 0.034663 0.8699 0.9182 34.207 123.01 1.0066 1.0370 0.1180 0.4236 35 0.036760 0.8727 0.9241 35.213 129.46 1.0067 1.0388 0.1213 0.4446 36 0.038975 0.8756 0.9302 36.220 136.21 1.0067 1.0408 0.1246 0.4666 37 0.041313 0.8784 0.9365 37.227 143.29 1.0068 1.0428 0.1278 0.4895 38 0.043783 0.8813 0.9430 38.233 150.72 1.0068 1.0450 0.1311 0.5135 39 0.046391 0.8841 0.9498 39.240 158.51 1.0069 1.0473 0.1343 0.5386 40 0.049145 0.8869 0.9567 40.247 166.68 1.0069 1.0497 0.1375 0.5649 41 0.052053 0.8898 0.9639 41.254 175.27 1.0069 1.0522 0.1407 0.5923 42 0.055124 0.8926 0.9714 42.261 184.28 1.0070 1.0549 0.1439 0.6211 43 0.058368 0.8955 0.9791 43.268 193.75 1.0070 1.0577 0.1471 0.6512 44 0.061795 0.8983 0.9871 44.275 203.70 1.0071 1.0606 0.1503 0.6828 45 0.065416 0.9011 0.9955 45.282 214.17 1.0071 1.0637 0.1535 0.7159 46 0.069242 0.9040 1.0041 46.289 225.17 1.0072 1.0669 0.1566 0.7506 47 0.073286 0.9068 1.0131 47.297 236.76 1.0073 1.0703 0.1598 0.7871 48 0.077561 0.9096 1.0225 48.304 248.96 1.0073 1.0739 0.1629 0.8253 49 0.082081 0.9125 1.0323 49.311 261.80 1.0074 1.0777 0.1660 0.8655 50 0.086863 0.9153 1.0425 50.319 275.34 1.0074 1.0817 0.1692 0.9077 51 0.091922 0.9182 1.0531 51.326 289.62 1.0075 1.0858 0.1723 0.9521 52 0.097278 0.9210 1.0643 52.334 304.69 1.0075 1.0902 0.1754 0.9989 53 0.10295 0.9238 1.0759 53.341 320.59 1.0076 1.0948 0.1785 1.0480 54 0.10896 0.9267 1.0881 54.349 337.38 1.0076 1.0996 0.1816 1.0998 55 0.11533 0.9295 1.1009 55.356 355.14 1.0077 1.1047 0.1846 1.1544 56 0.12208 0.9324 1.1143 56.364 373.92 1.0078 1.1100 0.1877 1.2120 57 0.12925 0.9352 1.1284 57.372 393.80 1.0078 1.1156 0.1908 1.2728 58 0.13686 0.9380 1.1432 58.380 414.86 1.0079 1.1215 0.1938 1.3371 59 0.14495 0.9409 1.1587 59.388 437.18 1.0079 1.1277 0.1968 1.4050 60 0.15354 0.9437 1.1752 60.396 460.87 1.0080 1.1342 0.1999 1.4768 61 0.16270 0.9465 1.1925 61.404 486.04 1.0081 1.1410 0.2029 1.5530 62 0.17245 0.9494 1.2108 62.412 512.79 1.0081 1.1482 0.2059 1.6337 63 0.18284 0.9522 1.2302 63.420 541.27 1.0082 1.1557 0.2089 1.7194 64 0.19394 0.9551 1.2508 64.428 571.61 1.0083 1.1636 0.2119 1.8105 65 0.20579 0.9579 1.2726 65.436 603.98 1.0083 1.1719 0.2149 1.9074 66 0.21848 0.9607 1.2957 66.445 638.57 1.0084 1.1807 0.2179 2.0107 67 0.23207 0.9636 1.3204 67.453 675.56 1.0085 1.1899 0.2208 2.1208 Psychrometrics 1.5 Table 2 Thermodynamic Properties of Saturated Moist and Dry Air at Standard Atmospheric Pressure, 101.325 kPa (Continued) Specific Volume, Specific Enthalpy, Specific Heat Capacity, Specific Entropy, m3/kgda kJ/kgda kJ/(kg·K) kJ/(kgda·K) Humidity Ratio Ws, Temp. t, °C kgw/kgda vda vs hda hs t cp,s sda ss 68 0.24665 0.9664 1.3467 68.462 715.20 1.0085 1.1995 0.2238 2.2386 69 0.26231 0.9692 1.3748 69.470 757.73 1.0086 1.2097 0.2268 2.3646 70 0.27917 0.9721 1.4049 70.479 803.45 1.0087 1.2204 0.2297 2.4997 71 0.29734 0.9749 1.4372 71.488 852.69 1.0088 1.2316 0.2326 2.6448 72 0.31698 0.9778 1.4719 72.496 905.84 1.0088 1.2435 0.2356 2.8011 73 0.33824 0.9806 1.5093 73.505 963.31 1.0089 1.2559 0.2385 2.9696 74 0.36130 0.9834 1.5497 74.514 1025.6 1.0090 1.2690 0.2414 3.1519 75 0.38640 0.9863 1.5935 75.523 1093.3 1.0090 1.2829 0.2443 3.3495 76 0.41377 0.9891 1.6411 76.532 1167.2 1.0091 1.2974 0.2472 3.5644 77 0.44373 0.9919 1.6930 77.542 1247.9 1.0092 1.3127 0.2501 3.7988 78 0.47661 0.9948 1.7497 78.551 1336.4 1.0093 1.3289 0.2529 4.0552 79 0.51284 0.9976 1.8121 79.560 1433.9 1.0094 1.3460 0.2558 4.3370 80 0.55293 1.0005 1.8809 80.570 1541.7 1.0094 1.3640 0.2587 4.6477 81 0.59747 1.0033 1.9572 81.579 1661.5 1.0095 1.3830 0.2615 4.9919 82 0.64722 1.0061 2.0421 82.589 1795.1 1.0096 1.4030 0.2644 5.3752 83 0.70309 1.0090 2.1373 83.598 1945.1 1.0097 1.4242 0.2672 5.8045 84 0.76623 1.0118 2.2446 84.608 2114.6 1.0098 1.4467 0.2701 6.2883 85 0.83811 1.0146 2.3665 85.618 2307.4 1.0099 1.4704 0.2729 6.8374 86 0.92058 1.0175 2.5062 86.628 2528.6 1.0099 1.4955 0.2757 7.4658 87 1.0161 1.0203 2.6676 87.638 2784.7 1.0100 1.5221 0.2785 8.1917 88 1.1280 1.0232 2.8564 88.648 3084.5 1.0101 1.5503 0.2813 9.0393 89 1.2606 1.0260 3.0799 89.658 3439.8 1.0102 1.5802 0.2841 10.042 90 1.4202 1.0288 3.3487 90.668 3867.5 1.0103 1.6120 0.2869 11.245 The following properties are shown in Table 3: ln pws = C1/T + C2 + C3T + C4T 2 + C5T 3 + C6T 4 + C7 ln T (5) t = temperature in degrees Celsius based on ITS-90 and expressed where relative to absolute temperature T in degrees Kelvin by the C1 = –5.674 535 9 E+03 following relation: C2 = 6.392 524 7 E+00 T = (°C + 273.15) C3 = –9.677 843 0 E–03 pws = absolute pressure of water (solid, liquid, or vapor) at saturation C4 = 6.221 570 1 E–07 or sublimation temperature t, kPa C5 = 2.074 782 5 E–09 vi = specific volume of saturated solid (ice), m3/kg C6 = –9.484 024 0 E–13 vf = specific volume of saturated liquid (water), m3/kg C7 = 4.163 501 9 E00 vg = specific volume of saturated vapor (steam), m3/kg The saturation pressure over liquid water for the temperature range hi = specific enthalpy of saturated solid (ice), kJ/kg of 0 to 200°C is given by hf = specific enthalpy of saturated liquid (water), hg = specific enthalpy of saturated vapor (steam), kJ/kg ln pws = C8/T + C9 + C10T + C11T 2 + C12T 3 + C13 ln T (6) cp,i = specific isobaric heat capacity of saturated solid (ice), kJ/(kg·K) where cp,f = specific isobaric heat capacity of saturated liquid (water), kJ/ C8 = –5.800 220 6 E+03 (kg·K) C9 = 1.391 499 3 E+00 cp,g = specific isobaric heat capacity of saturated vapor (steam), kJ/ C10 = –4.864 023 9 E–02 (kg·K) C11 = 4.176 476 8 E–05 C12 = –1.445 209 3 E–08 si = specific entropy of saturated solid (ice), kJ/(kg·K) C13 = 6.545 967 3 E+00 sf = specific entropy of saturated liquid (water), sg = specific entropy of saturated vapor (steam), kJ/(kg·K) In both Equations (5) and (6), The water vapor saturation pressure is required to determine pws = saturation pressure, Pa T = absolute temperature, K = °C + 273.15 a number of moist air properties, principally the saturation humid- ity ratio. Values may be obtained from Table 3 or calculated from The coefficients of Equations (5) and (6) were derived from the formulas given by IPAWS R7-97(2012) and R14-08 (2011). Hyland-Wexler equations. Because of rounding errors in the deriva- The saturation (sublimation) pressure over ice for the tem- tions and in some computers’ calculating precision, results from perature range of 100 to 0°C is given by Equations (5) and (6) may not agree precisely with Table 3 values. 1.6 2021 ASHRAE Handbook—Fundamentals (SI) Table 3 Thermodynamic Properties of Water at Saturation Specific Volume, m3/kgw Specific Enthalpy, kJ/kgw Specific Entropy, kJ/(kgw ·K) Temp., Absolute Temp., °C Pressure Sat. Solid Evap. Sat. Vapor Sat. Solid Evap. Sat. Vapor Sat. Solid Evap. Sat. Vapor °C t pws, kPa vi /vf vig /vfg vg hi /hf hig /hfg hg si /sf sig /sfg sg t –60 0.00108 0.001081 90971.58 90971.58 –446.12 2836.27 2390.14 –1.6842 13.3064 11.6222 –60 –59 0.00124 0.001082 79885.31 79885.31 –444.46 2836.45 2391.99 –1.6764 13.2452 11.5687 –59 –58 0.00141 0.001082 70235.77 70235.78 –442.79 2836.63 2393.85 –1.6687 13.1845 11.5158 –58 –57 0.00161 0.001082 61826.23 61826.24 –441.11 2836.81 2395.70 –1.6609 13.1243 11.4634 –57 –56 0.00184 0.001082 54488.28 54488.28 –439.42 2836.97 2397.55 –1.6531 13.0646 11.4115 –56 –55 0.00209 0.001082 48077.54 48077.54 –437.73 2837.13 2399.40 –1.6453 13.0054 11.3601 –55 –54 0.00238 0.001082 42470.11 42470.11 –436.03 2837.28 2401.25 –1.6375 12.9468 11.3092 –54 –53 0.00271 0.001082 37559.49 37559.50 –434.32 2837.42 2403.10 –1.6298 12.8886 11.2589 –53 –52 0.00307 0.001083 33254.07 33254.07 –432.61 2837.56 2404.95 –1.6220 12.8310 11.2090 –52 –51 0.00348 0.001083 29474.87 29474.87 –430.88 2837.69 2406.81 –1.6142 12.7738 11.1596 –51 –50 0.00394 0.001083 26153.80 26153.80 –429.16 2837.81 2408.66 –1.6065 12.7171 11.1106 –50 –49 0.00445 0.001083 23232.03 23232.04 –427.42 2837.93 2410.51 –1.5987 12.6609 11.0622 –49 –48 0.00503 0.001083 20658.70 20658.70 –425.68 2838.04 2412.36 –1.5909 12.6051 11.0142 –48 –47 0.00568 0.001083 18389.75 18389.75 –423.93 2838.14 2414.21 –1.5832 12.5498 10.9666 –47 –46 0.00640 0.001083 16387.03 16387.03 –422.17 2838.23 2416.06 –1.5754 12.4950 10.9196 –46 –45 0.00720 0.001084 14617.39 14617.39 –420.40 2838.32 2417.91 –1.5677 12.4406 10.8729 –45 –44 0.00810 0.001084 13052.07 13052.07 –418.63 2838.39 2419.76 –1.5599 12.3867 10.8267 –44 –43 0.00910 0.001084 11666.02 11666.02 –416.85 2838.47 2421.62 –1.5522 12.3331 10.7810 –43 –42 0.01022 0.001084 10437.46 10437.46 –415.06 2838.53 2423.47 –1.5444 12.2801 10.7356 –42 –41 0.01146 0.001084 9347.38 9347.38 –413.27 2838.59 2425.32 –1.5367 12.2274 10.6907 –41 –40 0.01284 0.001084 8379.20 8379.20 –411.47 2838.64 2427.17 –1.5289 12.1752 10.6462 –40 –39 0.01437 0.001085 7518.44 7518.44 –409.66 2838.68 2429.02 –1.5212 12.1234 10.6022 –39 –38 0.01607 0.001085 6752.43 6752.43 –407.85 2838.72 2430.87 –1.5135 12.0720 10.5585 –38 –37 0.01795 0.001085 6070.08 6070.08 –406.02 2838.74 2432.72 –1.5057 12.0210 10.5152 –37 –36 0.02004 0.001085 5461.68 5461.68 –404.19 2838.76 2434.57 –1.4980 11.9704 10.4724 –36 –35 0.02234 0.001085 4918.69 4918.69 –402.36 2838.78 2436.42 –1.4903 11.9202 10.4299 –35 –34 0.02489 0.001085 4433.64 4433.64 –400.51 2838.78 2438.27 –1.4825 11.8703 10.3878 –34 –33 0.02771 0.001085 3999.95 3999.95 –398.66 2838.78 2440.12 –1.4748 11.8209 10.3461 –33 –32 0.03081 0.001086 3611.82 3611.82 –396.80 2838.77 2441.97 –1.4671 11.7718 10.3047 –32 –31 0.03423 0.001086 3264.15 3264.16 –394.94 2838.75 2443.82 –1.4594 11.7231 10.2638 –31 –30 0.03801 0.001086 2952.46 2952.46 –393.06 2838.73 2445.67 –1.4516 11.6748 10.2232 –30 –29 0.04215 0.001086 2672.77 2672.77 –391.18 2838.70 2447.51 –1.4439 11.6269 10.1830 –29 –28 0.04672 0.001086 2421.58 2421.58 –389.29 2838.66 2449.36 –1.4362 11.5793 10.1431 –28 –27 0.05173 0.001086 2195.80 2195.80 –387.40 2838.61 2451.21 –1.4285 11.5321 10.1036 –27 –26 0.05724 0.001087 1992.68 1992.68 –385.50 2838.56 2453.06 –1.4208 11.4852 10.0644 –26 –25 0.06327 0.001087 1809.79 1809.79 –383.59 2838.49 2454.91 –1.4131 11.4386 10.0256 –25 –24 0.06989 0.001087 1644.99 1644.99 –381.67 2838.42 2456.75 –1.4054 11.3925 9.9871 –24 –23 0.07714 0.001087 1496.36 1496.36 –379.75 2838.35 2458.60 –1.3977 11.3466 9.9489 –23 –22 0.08508 0.001087 1362.21 1362.21 –377.81 2838.26 2460.45 –1.3899 11.3011 9.9111 –22 –21 0.09376 0.001087 1241.03 1241.03 –375.88 2838.17 2462.29 –1.3822 11.2559 9.8736 –21 –20 0.10324 0.001087 1131.49 1131.49 –373.93 2838.07 2464.14 –1.3745 11.2110 9.8365 –20 –19 0.11360 0.001088 1032.38 1032.38 –371.98 2837.96 2465.98 –1.3668 11.1665 9.7996 –19 –18 0.12490 0.001088 942.64 942.65 –370.01 2837.84 2467.83 –1.3591 11.1223 9.7631 –18 –17 0.13722 0.001088 861.34 861.34 –368.05 2837.72 2469.67 –1.3514 11.0784 9.7269 –17 –16 0.15065 0.001088 787.61 787.61 –366.07 2837.59 2471.51 –1.3437 11.0348 9.6910 –16 –15 0.16527 0.001088 720.70 720.70 –364.09 2837.45 2473.36 –1.3360 10.9915 9.6554 –15 –14 0.18119 0.001088 659.94 659.94 –362.10 2837.30 2475.20 –1.3284 10.9485 9.6201 –14 –13 0.19849 0.001089 604.72 604.73 –360.10 2837.14 2477.04 –1.3207 10.9058 9.5851 –13 –12 0.21729 0.001089 554.51 554.51 –358.10 2836.98 2478.88 –1.3130 10.8634 9.5504 –12 –11 0.23771 0.001089 508.81 508.81 –356.08 2836.80 2480.72 –1.3053 10.8213 9.5160 –11 –10 0.25987 0.001089 467.19 467.19 –354.06 2836.62 2482.56 –1.2976 10.7795 9.4819 –10 –9 0.28391 0.001089 429.25 429.26 –352.04 2836.44 2484.40 –1.2899 10.7380 9.4481 –9 –8 0.30995 0.001089 394.66 394.66 –350.00 2836.24 2486.23 –1.2822 10.6967 9.4145 –8 –7 0.33817 0.001090 363.09 363.09 –347.96 2836.03 2488.07 –1.2745 10.6558 9.3812 –7 –6 0.36871 0.001090 334.26 334.26 –345.91 2835.82 2489.91 –1.2668 10.6151 9.3482 –6 –5 0.40174 0.001090 307.92 307.92 –343.86 2835.60 2491.74 –1.2592 10.5747 9.3155 –5 –4 0.43745 0.001090 283.82 283.83 –341.79 2835.37 2493.57 –1.2515 10.5345 9.2830 –4 –3 0.47604 0.001090 261.78 261.78 –339.72 2835.13 2495.41 –1.2438 10.4946 9.2508 –3 –2 0.51770 0.001091 241.60 241.60 –337.64 2834.88 2497.24 –1.2361 10.4550 9.2189 –2 –1 0.56266 0.001091 223.10 223.11 –335.56 2834.63 2499.07 –1.2284 10.4157 9.1872 –1 0 0.61115 0.001091 206.15 206.15 –333.47 2834.36 2500.90 –1.2208 10.3766 9.1558 0 Transition from saturated solid to saturated liquid 0 0.6112 0.001000 206.139 206.140 –0.04 2500.93 2500.89 –0.0002 9.1559 9.1558 0 1 0.6571 0.001000 192.444 192.445 4.18 2498.55 2502.73 0.0153 9.1138 9.1291 1 Psychrometrics 1.7 Table 3 Thermodynamic Properties of Water at Saturation (Continued) Specific Volume, m3/kgw Specific Enthalpy, kJ/kgw Specific Entropy, kJ/(kgw ·K) Temp., Absolute Temp., °C Pressure Sat. Solid Evap. Sat. Vapor Sat. Solid Evap. Sat. Vapor Sat. Solid Evap. Sat. Vapor °C t pws, kPa vi /vf vig /vfg vg hi /hf hig /hfg hg si /sf sig /sfg sg t 2 0.7060 0.001000 179.763 179.764 8.39 2496.17 2504.57 0.0306 9.0721 9.1027 2 3 0.7581 0.001000 168.013 168.014 12.60 2493.80 2506.40 0.0459 9.0306 9.0765 3 4 0.8135 0.001000 157.120 157.121 16.81 2491.42 2508.24 0.0611 8.9895 9.0506 4 5 0.8726 0.001000 147.016 147.017 21.02 2489.05 2510.07 0.0763 8.9486 9.0249 5 6 0.9354 0.001000 137.637 137.638 25.22 2486.68 2511.91 0.0913 8.9081 8.9994 6 7 1.0021 0.001000 128.927 128.928 29.43 2484.31 2513.74 0.1064 8.8678 8.9742 7 8 1.0730 0.001000 120.833 120.834 33.63 2481.94 2515.57 0.1213 8.8278 8.9492 8 9 1.1483 0.001000 113.308 113.309 37.82 2479.58 2517.40 0.1362 8.7882 8.9244 9 10 1.2282 0.001000 106.308 106.309 42.02 2477.21 2519.23 0.1511 8.7488 8.8998 10 11 1.3129 0.001000 99.792 99.793 46.22 2474.84 2521.06 0.1659 8.7096 8.8755 11 12 1.4028 0.001001 93.723 93.724 50.41 2472.48 2522.89 0.1806 8.6708 8.8514 12 13 1.4981 0.001001 88.069 88.070 54.60 2470.11 2524.71 0.1953 8.6322 8.8275 13 14 1.5989 0.001001 82.797 82.798 58.79 2467.75 2526.54 0.2099 8.5939 8.8038 14 15 1.7057 0.001001 77.880 77.881 62.98 2465.38 2528.36 0.2245 8.5559 8.7804 15 16 1.8188 0.001001 73.290 73.291 67.17 2463.01 2530.19 0.2390 8.5181 8.7571 16 17 1.9383 0.001001 69.005 69.006 71.36 2460.65 2532.01 0.2534 8.4806 8.7341 17 18 2.0647 0.001001 65.002 65.003 75.55 2458.28 2533.83 0.2678 8.4434 8.7112 18 19 2.1982 0.001002 61.260 61.261 79.73 2455.92 2535.65 0.2822 8.4064 8.6886 19 20 2.3392 0.001002 57.760 57.761 83.92 2453.55 2537.47 0.2965 8.3696 8.6661 20 21 2.4881 0.001002 54.486 54.487 88.10 2451.18 2539.29 0.3108 8.3331 8.6439 21 22 2.6452 0.001002 51.421 51.422 92.29 2448.81 2541.10 0.3250 8.2969 8.6218 22 23 2.8109 0.001003 48.551 48.552 96.47 2446.45 2542.92 0.3391 8.2609 8.6000 23 24 2.9856 0.001003 45.862 45.863 100.66 2444.08 2544.73 0.3532 8.2251 8.5783 24 25 3.1697 0.001003 43.340 43.341 104.84 2441.71 2546.54 0.3673 8.1895 8.5568 25 26 3.3637 0.001003 40.976 40.977 109.02 2439.33 2548.35 0.3813 8.1542 8.5355 26 27 3.5679 0.001004 38.757 38.758 113.20 2436.96 2550.16 0.3952 8.1192 8.5144 27 28 3.7828 0.001004 36.674 36.675 117.38 2434.59 2551.97 0.4091 8.0843 8.4934 28 29 4.0089 0.001004 34.718 34.719 121.56 2432.21 2553.78 0.4230 8.0497 8.4727 29 30 4.2467 0.001004 32.881 32.882 125.75 2429.84 2555.58 0.4368 8.0153 8.4521 30 31 4.4966 0.001005 31.153 31.154 129.93 2427.46 2557.39 0.4506 7.9812 8.4317 31 32 4.7592 0.001005 29.528 29.529 134.11 2425.08 2559.19 0.4643 7.9472 8.4115 32 33 5.0351 0.001005 28.000 28.001 138.29 2422.70 2560.99 0.4780 7.9135 8.3914 33 34 5.3247 0.001006 26.561 26.562 142.47 2420.32 2562.79 0.4916 7.8800 8.3715 34 35 5.6286 0.001006 25.207 25.208 146.64 2417.94 2564.58 0.5052 7.8467 8.3518 35 36 5.9475 0.001006 23.931 23.932 150.82 2415.56 2566.38 0.5187 7.8136 8.3323 36 37 6.2818 0.001007 22.728 22.729 155.00 2413.17 2568.17 0.5322 7.7807 8.3129 37 38 6.6324 0.001007 21.594 21.595 159.18 2410.78 2569.96 0.5457 7.7480 8.2936 38 39 6.9997 0.001007 20.525 20.526 163.36 2408.39 2571.75 0.5591 7.7155 8.2746 39 40 7.3844 0.001008 19.516 19.517 167.54 2406.00 2573.54 0.5724 7.6832 8.2557 40 41 7.7873 0.001008 18.564 18.565 171.72 2403.61 2575.33 0.5858 7.6512 8.2369 41 42 8.2090 0.001009 17.664 17.665 175.90 2401.21 2577.11 0.5990 7.6193 8.2183 42 43 8.6503 0.001009 16.815 16.816 180.08 2398.82 2578.89 0.6123 7.5876 8.1999 43 44 9.1118 0.001009 16.012 16.013 184.26 2396.42 2580.67 0.6255 7.5561 8.1816 44 45 9.5944 0.001010 15.252 15.253 188.44 2394.02 2582.45 0.6386 7.5248 8.1634 45 46 10.0988 0.001010 14.534 14.535 192.62 2391.61 2584.23 0.6517 7.4937 8.1454 46 47 10.6259 0.001011 13.855 13.856 196.80 2389.21 2586.00 0.6648 7.4628 8.1276 47 48 11.1764 0.001011 13.212 13.213 200.98 2386.80 2587.77 0.6778 7.4320 8.1099 48 49 11.7512 0.001012 12.603 12.604 205.16 2384.39 2589.54 0.6908 7.4015 8.0923 49 50 12.3513 0.001012 12.027 12.028 209.34 2381.97 2591.31 0.7038 7.3711 8.0749 50 51 12.9774 0.001013 11.481 11.482 213.52 2379.56 2593.08 0.7167 7.3409 8.0576 51 52 13.6305 0.001013 10.963 10.964 217.70 2377.14 2594.84 0.7296 7.3109 8.0405 52 53 14.3116 0.001014 10.472 10.473 221.88 2374.72 2596.60 0.7424 7.2811 8.0235 53 54 15.0215 0.001014 10.006 10.007 226.06 2372.30 2598.35 0.7552 7.2514 8.0066 54 55 15.7614 0.001015 9.5639 9.5649 230.24 2369.87 2600.11 0.7680 7.2219 7.9899 55 56 16.5322 0.001015 9.1444 9.1454 234.42 2367.44 2601.86 0.7807 7.1926 7.9733 56 57 17.3350 0.001016 8.7461 8.7471 238.61 2365.01 2603.61 0.7934 7.1634 7.9568 57 58 18.1708 0.001016 8.3678 8.3688 242.79 2362.57 2605.36 0.8060 7.1344 7.9405 58 59 19.0407 0.001017 8.0083 8.0093 246.97 2360.13 2607.10 0.8186 7.1056 7.9243 59 60 19.9458 0.001017 7.6666 7.6677 251.15 2357.69 2608.85 0.8312 7.0770 7.9082 60 61 20.8873 0.001018 7.3418 7.3428 255.34 2355.25 2610.58 0.8438 7.0485 7.8922 61 62 21.8664 0.001018 7.0328 7.0338 259.52 2352.80 2612.32 0.8563 7.0201 7.8764 62 63 22.8842 0.001019 6.7389 6.7399 263.71 2350.35 2614.05 0.8687 6.9919 7.8607 63 64 23.9421 0.001019 6.4591 6.4601 267.89 2347.89 2615.78 0.8811 6.9639 7.8451 64 65 25.0411 0.001020 6.1928 6.1938 272.08 2345.43 2617.51 0.8935 6.9361 7.8296 65 66 26.1827 0.001020 5.9392 5.9402 276.27 2342.97 2619.23 0.9059 6.9083 7.8142 66 67 27.3680 0.001021 5.6976 5.6986 280.45 2340.50 2620.96 0.9182 6.8808 7.7990 67 68 28.5986 0.001022 5.4674 5.4684 284.64 2338.03 2622.67 0.9305 6.8534 7.7839 68 69 29.8756 0.001022 5.2479 5.2490 288.83 2335.56 2624.39 0.9428 6.8261 7.7689 69 70 31.2006 0.001023 5.0387 5.0397 293.02 2333.08 2626.10 0.9550 6.7990 7.7540 70 71 32.5750 0.001023 4.8392 4.8402 297.21 2330.60 2627.81 0.9672 6.7720 7.7392 71 72 34.0001 0.001024 4.6488 4.6498 301.40 2328.11 2629.51 0.9793 6.7452 7.7245 72 73 35.4775 0.001025 4.4671 4.4681 305.59 2325.62 2631.21 0.9915 6.7185 7.7100 73 1.8 2021 ASHRAE Handbook—Fundamentals (SI) Table 3 Thermodynamic Properties of Water at Saturation (Continued) Specific Volume, m3/kgw Specific Enthalpy, kJ/kgw Specific Entropy, kJ/(kgw ·K) Temp., Absolute Temp., °C Pressure Sat. Solid Evap. Sat. Vapor Sat. Solid Evap. Sat. Vapor Sat. Solid Evap. Sat. Vapor °C t pws, kPa vi /vf vig /vfg vg hi /hf hig /hfg hg si /sf sig /sfg sg t 74 37.0088 0.001025 4.2937 4.2947 309.78 2323.13 2632.91 1.0035 6.6920 7.6955 74 75 38.5954 0.001026 4.1281 4.1291 313.97 2320.63 2634.60 1.0156 6.6656 7.6812 75 76 40.2389 0.001026 3.9699 3.9709 318.17 2318.13 2636.29 1.0276 6.6393 7.6669 76 77 41.9409 0.001027 3.8188 3.8198 322.36 2315.62 2637.98 1.0396 6.6132 7.6528 77 78 43.7031 0.001028 3.6743 3.6754 326.56 2313.11 2639.66 1.0516 6.5872 7.6388 78 79 45.5271 0.001028 3.5363 3.5373 330.75 2310.59 2641.34 1.0635 6.5613 7.6248 79 80 47.4147 0.001029 3.4042 3.4053 334.95 2308.07 2643.01 1.0754 6.5356 7.6110 80 81 49.3676 0.001030 3.2780 3.2790 339.15 2305.54 2644.68 1.0873 6.5100 7.5973 81 82 51.3875 0.001030 3.1572 3.1582 343.34 2303.01 2646.35 1.0991 6.4846 7.5837 82 83 53.4762 0.001031 3.0415 3.0426 347.54 2300.47 2648.01 1.1109 6.4592 7.5701 83 84 55.6355 0.001032 2.9309 2.9319 351.74 2297.93 2649.67 1.1227 6.4340 7.5567 84 85 57.8675 0.001032 2.8249 2.8259 355.95 2295.38 2651.33 1.1344 6.4090 7.5434 85 86 60.1738 0.001033 2.7234 2.7244 360.15 2292.83 2652.98 1.1461 6.3840 7.5301 86 87 62.5565 0.001034 2.6262 2.6272 364.35 2290.27 2654.62 1.1578 6.3592 7.5170 87 88 65.0174 0.001035 2.5330 2.5341 368.56 2287.70 2656.26 1.1694 6.3345 7.5039 88 89 67.5587 0.001035 2.4437 2.4448 372.76 2285.14 2657.90 1.1811 6.3099 7.4909 89 90 70.1824 0.001036 2.3581 2.3591 376.97 2282.56 2659.53 1.1927 6.2854 7.4781 90 91 72.8904 0.001037 2.2760 2.2771 381.18 2279.98 2661.16 1.2042 6.2611 7.4653 91 92 75.6849 0.001037 2.1973 2.1983 385.38 2277.39 2662.78 1.2158 6.2368 7.4526 92 93 78.5681 0.001038 2.1217 2.1228 389.59 2274.80 2664.39 1.2273 6.2127 7.4400 93 94 81.5420 0.001039 2.0492 2.0502 393.81 2272.20 2666.01 1.2387 6.1887 7.4275 94 95 84.6089 0.001040 1.9796 1.9806 398.02 2269.60 2667.61 1.2502 6.1648 7.4150 95 96 87.7711 0.001040 1.9128 1.9138 402.23 2266.98 2669.22 1.2616 6.1411 7.4027 96 97 91.0308 0.001041 1.8486 1.8497 406.45 2264.37 2670.81 1.2730 6.1174 7.3904 97 98 94.3902 0.001042 1.7870 1.7880 410.66 2261.74 2672.40 1.2844 6.0938 7.3782 98 99 97.8518 0.001043 1.7277 1.7288 414.88 2259.11 2673.99 1.2957 6.0704 7.3661 99 100 101.4180 0.001043 1.6708 1.6719 419.10 2256.47 2675.57 1.3070 6.0471 7.3541 100 101 105.0910 0.001044 1.6161 1.6171 423.32 2253.83 2677.15 1.3183 6.0238 7.3421 101 102 108.8735 0.001045 1.5635 1.5645 427.54 2251.18 2678.72 1.3296 6.0007 7.3303 102 103 112.7678 0.001046 1.5129 1.5140 431.76 2248.52 2680.28 1.3408 5.9777 7.3185 103 104 116.7765 0.001047 1.4642 1.4653 435.99 2245.85 2681.84 1.3520 5.9548 7.3068 104 105 120.9021 0.001047 1.4174 1.4185 440.21 2243.18 2683.39 1.3632 5.9320 7.2951 105 106 125.1472 0.001048 1.3724 1.3734 444.44 2240.50 2684.94 1.3743 5.9092 7.2836 106 107 129.5145 0.001049 1.3290 1.3301 448.67 2237.81 2686.48 1.3854 5.8866 7.2721 107 108 134.0065 0.001050 1.2873 1.2883 452.90 2235.12 2688.02 1.3965 5.8641 7.2607 108 109 138.6261 0.001051 1.2471 1.2481 457.13 2232.41 2689.55 1.4076 5.8417 7.2493 109 110 143.3760 0.001052 1.2083 1.2094 461.36 2229.70 2691.07 1.4187 5.8194 7.2380 110 111 148.2588 0.001052 1.1710 1.1721 465.60 2226.99 2692.58 1.4297 5.7972 7.2268 111 112 153.2775 0.001053 1.1351 1.1362 469.83 2224.26 2694.09 1.4407 5.7750 7.2157 112 113 158.4348 0.001054 1.1005 1.1015 474.07 2221.53 2695.60 1.4517 5.7530 7.2047 113 114 163.7337 0.001055 1.0671 1.0681 478.31 2218.78 2697.09 1.4626 5.7310 7.1937 114 115 169.1770 0.001056 1.0349 1.0359 482.55 2216.03 2698.58 1.4735 5.7092 7.1827 115 116 174.7678 0.001057 1.0038 1.0049 486.80 2213.27 2700.07 1.4844 5.6874 7.1719 116 117 180.5090 0.001058 0.9739 0.9750 491.04 2210.51 2701.55 1.4953 5.6658 7.1611 117 118 186.4036 0.001059 0.9450 0.9461 495.29 2207.73 2703.02 1.5062 5.6442 7.1504 118 119 192.4547 0.001059 0.9171 0.9182 499.53 2204.94 2704.48 1.5170 5.6227 7.1397 119 120 198.6654 0.001060 0.8902 0.8913 503.78 2202.15 2705.93 1.5278 5.6013 7.1291 120 122 211.5782 0.001062 0.8392 0.8403 512.29 2196.53 2708.82 1.5494 5.5587 7.1081 122 124 225.1676 0.001064 0.7916 0.7927 520.80 2190.88 2711.69 1.5708 5.5165 7.0873 124 126 239.4597 0.001066 0.7472 0.7483 529.32 2185.19 2714.52 1.5922 5.4746 7.0668 126 128 254.4813 0.001068 0.7058 0.7068 537.85 2179.47 2717.32 1.6134 5.4330 7.0465 128 130 270.2596 0.001070 0.6670 0.6681 546.39 2173.70 2720.09 1.6346 5.3918 7.0264 130 132 286.8226 0.001072 0.6308 0.6318 554.93 2167.89 2722.83 1.6557 5.3508 7.0066 132 134 304.1989 0.001074 0.5969 0.5979 563.49 2162.04 2725.53 1.6767 5.3102 6.9869 134 136 322.4175 0.001076 0.5651 0.5662 572.05 2156.15 2728.20 1.6977 5.2698 6.9675 136 138 341.5081 0.001078 0.5353 0.5364 580.62 2150.22 2730.84 1.7185 5.2298 6.9483 138 140 361.5010 0.001080 0.5074 0.5085 589.20 2144.24 2733.44 1.7393 5.1900 6.9293 140 142 382.4271 0.001082 0.4813 0.4823 597.79 2138.22 2736.01 1.7600 5.1505 6.9105 142 144 404.3178 0.001084 0.4567 0.4577 606.39 2132.15 2738.54 1.7806 5.1112 6.8918 144 146 427.2053 0.001086 0.4336 0.4346 615.00 2126.04 2741.04 1.8011 5.0723 6.8734 146 148 451.1220 0.001088 0.4118 0.4129 623.62 2119.88 2743.50 1.8216 5.0335 6.8551 148 150 476.1014 0.001091 0.3914 0.3925 632.25 2113.67 2745.92 1.8420 4.9951 6.8370 150 152 502.1771 0.001093 0.3722 0.3733 640.89 2107.41 2748.30 1.8623 4.9569 6.8191 152 154 529.3834 0.001095 0.3541 0.3552 649.55 2101.10 2750.64 1.8825 4.9189 6.8014 154 156 557.7555 0.001097 0.3370 0.3381 658.21 2094.74 2752.95 1.9027 4.8811 6.7838 156 158 587.3287 0.001100 0.3209 0.3220 666.89 2088.32 2755.21 1.9228 4.8436 6.7664 158 160 618.1392 0.001102 0.3057 0.3068 675.57 2081.86 2757.43 1.9428 4.8063 6.7491 160 Psychrometrics 1.9 The vapor pressure ps of water in saturated moist air differs neg- Ws ( p, td) = W (13) ligibly from the saturation vapor pressure pws of pure water at the same temperature. Consequently, ps can be used in equations in Thermodynamic wet-bulb temperature t* is the temperature place of pws with very little error: at which water (liquid or solid), by evaporating into moist air at dry- bulb temperature t and humidity ratio W, can bring air to saturation ps = xws p adiabatically at the same temperature t* while total pressure p is where xws is the mole fraction of water vapor in saturated moist air constant. This parameter is considered separately in the section on at temperature t and pressure p, and p is the total barometric pressure Thermodynamic Wet-Bulb and Dew-Point Temperature. of moist air. 6. PERFECT GAS RELATIONSHIPS FOR 5. HUMIDITY PARAMETERS DRY AND MOIST AIR When moist air is considered a mixture of independent perfect Basic Parameters gases (i.e., dry air and water vapor), each is assumed to obey the per- Humidity ratio W (or mixing ratio) of a given moist air sample fect gas equation of state as follows: is defined as the ratio of the mass of water vapor to the mass of dry air in the sample: Dry air: pdaV = nda RT (14) W = Mw /Mda (7) Water vapor: pwV = nw RT (15) W equals the mole fraction ratio xw /xda multiplied by the ratio of molecular masses (18.015 268/28.966 = 0.621 945): where pda = partial pressure of dry air W = 0.621 945xw /xda (8) pw = partial pressure of water vapor V = total mixture volume Specific humidity  is the ratio of the mass of water vapor to nda = number of moles of dry air total mass of the moist air sample: nw = number of moles of water vapor  = Mw /(Mw + Mda) (9a) R = universal gas constant, 8314.472 J/(kmol·K) T = absolute temperature, K In terms of the humidity ratio, The mixture also obeys the perfect gas equation:  = W/(1 + W) (9b) pV = nRT (16) Absolute humidity (alternatively, water vapor density) dv is the or ratio of the mass of water vapor to total volume of the sample: ( pda + pw)V = (nda + nw)RT (17) dv = Mw /V (10) where p = pda + pw is the total mixture pressure and n = nda + nw is Density  of a moist air mixture is the ratio of total mass to total the total number of moles in the mixture. From Equations (14) volume: to (17), the mole fractions of dry air and water vapor are, respec- tively,  = (Mda + Mw)/V = (1/v)(1 + W) (11) xda = pda /( pda + pw) = pda /p (18) where v is the moist air specific volume, m3/kgda, as defined by Equation (24). and xw = pw /(pda + pw) = pw /p (19) Humidity Parameters Involving Saturation The following definitions of humidity parameters involve the From Equations (8), (18), and (19), the humidity ratio W is concept of moist air saturation: pw Saturation humidity ratio Ws(t, p) is the humidity ratio of W = 0.621 945 --------------- (20) moist air saturated with respect to water (or ice) at the same tem- p – pw perature t and pressure p. The saturation humidity ratio Ws is Relative humidity  is the ratio of the actual water vapor partial pressure in moist air at the dew-point pressure and temperature to p ws the reference saturation water vapor partial pressure at the dry-bulb Ws = 0.621 945 ----------------- (21) pressure and temperature: p – p ws  = (pwv _ enh /pwvs _ ref |p,t) = [f(p, tdp)e(tdp)]/[ f(p, tdb)e(tdb)] (12) The term pws represents the saturation pressure of water vapor in the absence of air at the given temperature t. This pressure pws is a Note that Equations (12) and (22) have been revised so that they function only of temperature and differs slightly from the vapor cover both the normal range of relative humidity where e(tdb)  p pressure of water in saturated moist air. and the extended range (e.g., atmospheric pressure drying kilns) The relative humidity  is defined in Equation (12). Using the where e(tdb)  p. The definitions in earlier editions applied only to second equality and eliminating the enhancement factors, which are the normal range. not applicable using the perfect gas assumption, gives Dew-point temperature td is the temperature of moist air satu- rated at pressure p, with the same humidity ratio W as that of the  = e(tdp)/e(tdb) (22) given sample of moist air. It is defined as the solution td ( p, W) of the following equation: Substituting Equation (21) for Ws into Equation (13), 1.10 2021 ASHRAE Handbook—Fundamentals (SI)  hw* denotes specific enthalpy in kJ/kgw of water added at tem-  = ----------------------------------------------- (23) perature t* 1 –  1 –    p ws  p  Therefore, if the process is strictly adiabatic, conservation of en- where  is degree of saturation W/Ws, dimensionless. thalpy at constant total pressure requires that Both  and  are zero for dry air and unity for saturated moist air. At intermediate states, their values differ, substantially at higher h + (Ws* – W)hw* = hs* (31) temperatures. Ws*, hw*, and hs* are functions only of temperature t* for a fixed The specific volume v of a moist air mixture is expressed in value of pressure. The value of t* that satisfies Equation (31) for terms of a unit mass of dry air: given values of h, W, and p is the thermodynamic wet-bulb v = V/Mda = V/(28.966nda) (24) temperature. A psychrometer consists of two thermometers; one thermome- where V is the total volume of the mixture, Mda is the total mass of ter’s bulb is covered by a wick that has been thoroughly wetted with dry air, and nda is the number of moles of dry air. By Equations (14) water. When the wet bulb is placed in an airstream, water evaporates and (24), with the relation p = pda + pw , from the wick, eventually reaching an equilibrium temperature called the wet-bulb temperature. This process is not one of adia- RT R da T batic saturation, which defines the thermodynamic wet-bulb tem- v = ------------------------------------- = -------------- - (25) 28.966  p – p w  p – pw perature, but one of simultaneous heat and mass transfer from the wet bulb. The fundamental mechanism of this process is described Using Equation (18), by the Lewis relation [Equation (40) in Chapter 6]. Fortunately, only small corrections must be applied to wet-bulb thermometer readings RT  1 +  1.607 858 W  R da T  1 +  1.607 858 W  to obtain the thermodynamic wet-bulb temperature. v = -------------------------------------------------------- = ------------------------------------------------------------- (26) 28.966p p As defined, thermodynamic wet-bulb temperature is a unique property of a given moist air sample independent of measurement In Equations (25) and (26), v is specific volume, T is absolute tem- techniques. perature, p is total pressure, pw is partial pressure of water vapor, and Equation (31) is exact because it defines the thermodynamic wet- W is humidity ratio. bulb temperature t*. Substituting the approximate perfect gas rela- In specific units, Equation (26) may be expressed as tion [Equation (30)] for h, the corresponding expression for hs*, and v = 0.287 042(t + 273.15)(1 + 1.607 858W )/p the approximate relation for saturated liquid water where h*w  4.186t* (32) v = specific volume, m3/kg da into Equation (31), and solving for the humidity ratio, t = dry-bulb temperature, °C W = humidity ratio, kgw /kgda  2501 – 2.326t* W*s – 1.006  t – t*  p = total pressure, kPa W = --------------------------------------------------------------------------------------- - (33) 2501 + 1.86t – 4.186t* The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the components. Therefore, the spe- where t and t* are in °C. Below freezing, the corresponding equa- cific enthalpy of moist air can be written as follows: tions are h = hda + Whg (27) h*w  –333.4 + 2.1t* (34) where hda is the specific enthalpy for dry air in kJ/kgda and hg is the specific enthalpy for saturated water vapor in kJ/kgw at the mixture’s  2830 – 0.24t* W*s – 1.006  t – t*  W = ------------------------------------------------------------------------------------ - (35) temperature. As an approximation, 2830 + 1.86t – 2.1t* hda  1.006t (28) A wet/ice-bulb thermometer is imprecise when determining hg  2501 + 1.86t (29) moisture content at 0°C. The dew-point temperature td of moist air with humidity ratio where t is the dry-bulb temperature in °C. The moist air specific W and pressure p was defined as the solution td ( p, W ) of Ws ( p, td). enthalpy in kJ/kg da then becomes For perfect gases, this reduces to h = 1.006t + W(2501 + 1.86t) (30) pws(td) = pw = ( pW )/(0.621 945 + W) (36) 7. THERMODYNAMIC WET-BULB AND where pw is the water vapor partial pressure for the moist air sam- DEW-POINT TEMPERATURE ple and pws(td) is the saturation vapor pressure at temperature td. The saturation vapor pressure is obtained from Table 3 or by using For any state of moist air, a temperature t* exists at which liquid Equation (5) or (6). Alternatively, the dew-point temperature can (or solid) water evaporates into the air to bring it to saturation at be calculated directly by one of the following equations (Peppers exactly this same temperature and total pressure (Harrison 1965). 1988): During adiabatic saturation, saturated air is expelled at a temper- Between dew points of 0 and 93°C, ature equal to that of the injected water. In this constant-pressure process, td = C14 + C15  + C162 + C173 + C18 ( pw )0.1984 (37) Humidity ratio increases from initial value W to Ws*, correspond- Below 0°C, ing to saturation at temperature t* td = 6.09 + 12.608 + 0.49592 (38) Enthalpy increases from initial value h to hs*, corresponding to saturation at temperature t* where Mass of water added per unit mass of dry air is (Ws* – W), which td = dew-point temperature, °C adds energy to the moist air of amount (Ws* – W)hw*, where  = ln pw Psychrometrics 1.11 pw = water vapor partial pressure, kPa Moist Air Property Tables for Standard Pressure C14 = 6.54 Table 2 shows thermodynamic properties for standard atmo- C15 = 14.526 spheric pressure at temperatures from –60 to 90°C calculated using C16 = 0.7389 the ASHRAE RP-1485 (Herrmann et al. 2009) research project C17 = 0.09486 numerical model. Properties of intermediate moist air states can be C18 = 0.4569 calculated using the degree of saturation : Volume v = vda + vas (39) 8. NUMERICAL CALCULATION OF MOIST AIR PROPERTIES Enthalpy h = hda + has (40) The following are outlines, citing equations and tables already These equations are accurate to about 350°C. At higher tempera- presented, for calculating moist air properties using perfect gas tures, errors can be significant. relations. These relations are accurate enough for most engineer- ing calculations in air-conditioning practice, and are readily 9. PSYCHROMETRIC CHARTS adapted to either hand or computer calculating methods. For more A psychrometric chart graphically represents the thermody- details, refer to Tables 15 through 18 in Chapter 1 of Olivieri namic properties of moist air. (1996). Graphical procedures are discussed in the section on Psy- The choice of coordinates for a psychrometric chart is arbitrary. chrometric Charts. A chart with coordinates of enthalpy and humidity ratio provides convenient graphical solutions of many moist air problems with a SITUATION 1. minimum of thermodynamic approximations. ASHRAE developed Given: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure p five such psychrometric charts. Chart 1 is shown as Figure 1; the To Obtain Use Comments others may be obtained through ASHRAE. Charts 1, 2, 3 and 4 are for sea-level pressure (101.325 kPa). pws (t*) Table 3 or Equation (5) or (6) Sat. press. for temp. t* Chart 5 is for 750 m altitude (92.634 kPa), Chart 6 is for 1500 m alti- W s* Equation (21) Using pws (t*) tude (84.54 kPa), and Chart 7 is for 2250 m altitude (77.058 kPa). W Equation (33) or (35) All charts use oblique-angle coordinates of enthalpy and humidity pws (t) Table 3 or Equation (5) or (6) Sat. press. for temp. t ratio, and are consistent with the data of Table 2 and the properties Ws Equation (21) Using pws (t) computation methods of Hyland and Wexler (1983a) and ASHRAE  Equation (23) Using pws (t) research project RP-1485. Palmatier (1963) describes the geometry v Equation (26) of chart construction applying specifically to Charts 1 and 4. The dry-bulb temperature ranges covered by the charts are h Equation (30) pw Equation (36) Charts 1, 5, 6, 7 Normal temperature 0 to 50°C td Table 3 with Equation (36), (37), or (38) Chart 2 Low temperature –40 to 10°C Chart 3 High temperature 10 to 120°C SITUATION 2. Chart 4 Very high temperature 100 to 200°C Given: Dry-bulb temperature t, Dew-point temperature td , Pressure p Charts 8 to 16 are for 200 to 320°C and cover the same pressures as 1, 5, 6, and 7 plus the additional pressures of 0.2, 0.5,1.0, 2.0, and To Obtain Use Comments 5.0 MPa. They were produced by Nelson and Sauer (2002) and are pw = pws (td) Table 3 or Equation (5) or (6) Sat. press. for temp. td available as a download with Gatley (2013). W Equation (20) Psychrometric properties or charts for other barometric pressures pws (t) Table 3 or Equation (5) or (6) Sat. press. for temp. t can be derived by interpolation. Sufficiently exact values for most Ws Equation (21) Using pws (t) purposes can be derived by methods described in the section on Per-  Equation (23) Using pws (t) fect Gas Relationships for Dry and Moist Air. Constructing charts v Equation (26) for altitude conditions has been discussed by Haines (1961), Karig h Equation (30) (1946), and Rohsenow (1946).