Psychrometrics: Thermodynamics of Moist Air

CHAPTER 6 PSYCHROMETRICS Composition of Dry and Moist Air ........................................... 6.1 United States Standard Atmosphere ......................................... 6.1 Thermodynamic Properties of Moist Air ................................. 6.2 Thermodynamic Properties of Water at Saturation .............................................................................. 6.2 Humidity Parameters ................................................................ 6.8 Perfect Gas Relationships for Dry and Moist Air ................................................................................ 6.8 Thermodynamic Wet-Bulb Temperature and Dew-Point Temperature ........................................................ 6.9 Numerical Calculation of Moist Air Properties ...................... 6.10 Psychrometric Charts ............................................................. 6.12 Typical Air-Conditioning Processes ....................................... 6.12 Transport Properties of Moist Air .......................................... 6.16 References for Air, Water, and Steam Properties ................... 6.16 References for Air, Water, and Steam Properties ................... 6.17 P small such as with ultrafine water droplets. The relative molecular mass of water is 18.01528 on the carbon-12 scale. The gas constant for water vapor is SYCHROMETRICS deals with the thermodynamic properties of moist air and uses these properties to analyze conditions and processes involving moist air. Hyland and Wexler (1983a,b) developed formulas for thermodynamic properties of moist air and water. However, perfect gas relations can be used instead of these formulas in most air-conditioning problems. Kuehn et al. (1998) showed that errors are less than 0.7% in calculating humidity ratio, enthalpy, and specific volume of saturated air at standard atmospheric pressure for a temperature range of −50 to 50°C. Furthermore, these errors decrease with decreasing pressure. This chapter discusses perfect gas relations and describes their use in common air-conditioning problems. The formulas developed by Hyland and Wexler (1983a) and discussed by Olivieri (1996) may be used where greater precision is required. Rw = 8314.41/18.01528 = 461.520 J/(kg·K) UNITED STATES STANDARD ATMOSPHERE The temperature and barometric pressure of atmospheric air vary considerably with altitude as well as with local geographic and weather conditions. The standard atmosphere gives a standard of reference for estimating properties at various altitudes. At sea level, standard temperature is 15°C; standard barometric pressure is 101.325 kPa. The temperature is assumed to decrease linearly with increasing altitude throughout the troposphere (lower atmosphere), and to be constant in the lower reaches of the stratosphere. The lower atmosphere is assumed to consist of dry air that behaves as a perfect gas. Gravity is also assumed constant at the standard value, 9.806 65 m/s2. Table 1 summarizes property data for altitudes to 10 000 m. COMPOSITION OF DRY AND MOIST AIR Atmospheric air contains many gaseous components as well as water vapor and miscellaneous contaminants (e.g., smoke, pollen, and gaseous pollutants not normally present in free air far from pollution sources). Dry air exists when all water vapor and contaminants have been removed from atmospheric air. The composition of dry air is relatively constant, but small variations in the amounts of individual components occur with time, geographic location, and altitude. Harrison (1965) lists the approximate percentage composition of dry air by volume as: nitrogen, 78.084; oxygen, 20.9476; argon, 0.934; carbon dioxide, 0.0314; neon, 0.001818; helium, 0.000524; methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; and minor components such as krypton, xenon, and ozone, 0.0002. The relative molecular mass of all components for dry air is 28.9645, based on the carbon-12 scale (Harrison 1965). The gas constant for dry air, based on the carbon-12 scale, is Rda = 8314.41/28.9645 = 287.055 J/(kg·K) Table 1 Standard Atmospheric Data for Altitudes to 10 000 m (1) Moist air is a binary (two-component) mixture of dry air and water vapor. The amount of water vapor in moist air varies from zero (dry air) to a maximum that depends on temperature and pressure. The latter condition refers to saturation, a state of neutral equilibrium between moist air and the condensed water phase (liquid or solid). Unless otherwise stated, saturation refers to a flat interface surface between the moist air and the condensed phase. Saturation conditions will change when the interface radius is very The preparation of this chapter is assigned to TC 1.1, Thermodynamics and Psychrometrics. Copyright © 2002 ASHRAE (2) 6.1 Altitude, m Temperature, °C Pressure, kPa −RMM M NUKO NRKM NMTKQTU NMNKPOR RMM N MMM NNKU UKR VRKQSN UVKUTR N RMM O MMM RKO OKM UQKRRS TVKQVR O RMM P MMM −NKO −QKR TQKSUO TMKNMU Q MMM R MMM −NNKM −NTKR SNKSQM RQKMOM S MMM T MMM −OQKM −PMKR QTKNUN QNKMSN U MMM V MMM −PTKM −QPKR PRKSMM PMKTQO NM MMM NO MMM −RM −SP OSKQPS NVKOUQ NQ MMM −TS NPKTUS NS MMM −UV VKSPO NU MMM OM MMM −NMO −NNR SKRRS QKPOU 6.2 2001 ASHRAE Fundamentals Handbook (SI) The pressure values in Table 1 may be calculated from Ó5 p Z 101.325 ( 1 Ó 2.25577 × 10 Z ) 5.2559 (3) The equation for temperature as a function of altitude is given as t Z 15 Ó 0.0065Z (4) where Z = altitude, m p = barometric pressure, kPa t = temperature, °C Equations (3) and (4) are accurate from −5000 m to 11 000 m. For higher altitudes, comprehensive tables of barometric pressure and other physical properties of the standard atmosphere can be found in NASA (1976). THERMODYNAMIC PROPERTIES OF MOIST AIR Table 2, developed from formulas by Hyland and Wexler (1983a,b), shows values of thermodynamic properties of moist air based on the thermodynamic temperature scale. This ideal scale differs slightly from practical temperature scales used for physical measurements. For example, the standard boiling point for water (at 101.325 kPa) occurs at 99.97°C on this scale rather than at the traditional value of 100°C. Most measurements are currently based on the International Temperature Scale of 1990 (ITS-90) (PrestonThomas 1990). The following paragraphs briefly describe each column of Table 2: t = Celsius temperature, based on thermodynamic temperature scale and expressed relative to absolute temperature T in kelvins (K) by the following relation: T Z t H 273.15 Ws = humidity ratio at saturation, condition at which gaseous phase (moist air) exists in equilibrium with condensed phase (liquid or solid) at given temperature and pressure (standard atmospheric pressure). At given values of temperature and pressure, humidity ratio W can have any value from zero to Ws . vda = specific volume of dry air, m3/kg (dry air). vas = vs − vda , difference between specific volume of moist air at saturation and that of dry air itself, m3/kg (dry air), at same pressure and temperature. vs = specific volume of moist air at saturation, m3/kg (dry air). hda = specific enthalpy of dry air, kJ/kg (dry air). In Table 2, hda has been assigned a value of 0 at 0°C and standard atmospheric pressure. has = hs − hda , difference between specific enthalpy of moist air at saturation and that of dry air itself, kJ/kg (dry air), at same pressure and temperature. hs = specific enthalpy of moist air at saturation, kJ/kg (dry air). sda = specific entropy of dry air, kJ/(kg·K) (dry air). In Table 2, sda has been assigned a value of 0 at 0°C and standard atmospheric pressure. sas = ss − sda , difference between specific entropy of moist air at saturation and that of dry air itself, kJ/(kg·K) (dry air), at same pressure and temperature. ss = specific entropy of moist air at saturation kJ/(kg·K) (dry air). hw = specific enthalpy of condensed water (liquid or solid) in equilibrium with saturated moist air at specified temperature and pressure, kJ/kg (water). In Table 2, hw is assigned a value of 0 at its triple point (0.01°C) and saturation pressure. Note that hw is greater than the steam-table enthalpy of saturated pure condensed phase by the amount of enthalpy increase governed by the pressure increase from saturation pressure to 101.325 kPa, plus influences from presence of air. sw = specific entropy of condensed water (liquid or solid) in equilibrium with saturated air, kJ/(kg·K) (water); sw differs from entropy of pure water at saturation pressure, similar to hw. ps = vapor pressure of water in saturated moist air, kPa. Pressure ps differs negligibly from saturation vapor pressure of pure water pws for conditions shown. Consequently, values of ps can be used at same pressure and temperature in equations where pws appears. Pressure ps is defined as ps = xws p, where xws is mole fraction of water vapor in moist air saturated with water at temperature t and pressure p, and where p is total barometric pressure of moist air. THERMODYNAMIC PROPERTIES OF WATER AT SATURATION THERMODYNAMIC PROPERTIES OF WATER AT SATURATION Table 3 shows thermodynamic properties of water at saturation for temperatures from −60 to 160°C, calculated by the formulations described by Hyland and Wexler (1983b). Symbols in the table follow standard steam table nomenclature. These properties are based on the thermodynamic temperature scale. The enthalpy and entropy of saturated liquid water are both assigned the value zero at the triple point, 0.01°C. Between the triple-point and critical-point temperatures of water, two states—liquid and vapor—may coexist in equilibrium. These states are called saturated liquid and saturated vapor. The water vapor saturation pressure is required to determine a number of moist air properties, principally the saturation humidity ratio. Values may be obtained from Table 3 or calculated from the following formulas (Hyland and Wexler 1983b). The saturation pressure over ice for the temperature range of −100 to 0°C is given by 2 ln p ws Z C 1 ⁄ T H C 2 H C 3 T H C 4 T H C 5 T 4 H C 6 T H C 7 ln T 3 (5) where C1 = −5.674 535 9 E+03 C2 = 6.392 524 7 E+00 C3 = −9.677 843 0 E–03 C4 = 6.221 570 1 E−07 C5 = 2.074 782 5 E−09 C6 = −9.484 024 0 E−13 C7 = 4.163 501 9 E+00 The saturation pressure over liquid water for the temperature range of 0 to 200°C is given by ln p ws Z C 8 ⁄ T H C 9 H C 10 T H C 11 T 3 H C 12 T H C 13 ln T 2 (6) where C8 = −5.800 220 6 E+03 C9 = 1.391 499 3 E+00 C10 = −4.864 023 9 E−02 C11 = 4.176 476 8 E−05 C12 = −1.445 209 3 E−08 C13 = 6.545 967 3 E+00 In both Equations (5) and (6), ln = natural logarithm pws = saturation pressure, Pa T = absolute temperature, K = °C + 273.15 The coefficients of Equations (5) and (6) have been derived from the Hyland-Wexler equations. Due to rounding errors in the derivations and in some computers’ calculating precision, the results obtained from Equations (5) and (6) may not agree precisely with Table 3 values. Psychrometrics 6.3 Table 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 101.325 kPa Condensed Water Humidity Temp., Ratio, °C kg(w)/kg(da) í të Specific Volume, m3/kg (dry air) Specific Enthalpy, kJ/kg (dry air) Ü~ë Specific Entropy, kJ/(kg · K) (dry air) Specific Specific Vapor Enthalpy, Entropy, Pressure, Temp., °C kJ/kg kJ/(kg·K) kPa í ëï éë Üï îÇ~ î~ë îë ÜÇ~ Üë ëÇ~ ë~ë ëë −SM −RV −RU −RT −RS −RR −RQ −RP −RO −RN MKMMMMMST MKMMMMMTS MKMMMMMUT MKMMMMNMM MKMMMMNNQ MKMMMMNOV MKMMMMNQT MKMMMMNST MKMMMMNVM MKMMMMONR MKSMOT MKSMRS MKSMUQ MKSNNP MKSNQN MKSNTM MKSNVU MKSOOS MKSORR MKSOUP MKMMMM MKMMMM MKMMMM MKMMMM MKMMMM MKMMMM MKMMMM MKMMMM MKMMMM MKMMMM MKSMOT MKSMRS MKSMUQ MKSNNP MKSNQN MKSNTM MKSNVU MKSOOT MKSORR MKSOUQ −SMKPRN −RVKPQQ −RUKPPU −RTKPPO −RSKPOS −RRKPNV −RQKPNP −RPKPMT −ROKPMN −RNKOVR MKMNT MKMNU MKMON MKMOQ MKMOU MKMPN MKMPS MKMQN MKMQS MKMRO −SMKPPQ −RVKPOS −RUKPNT −RTKPMU −RSKOVU −RRKOUU −RQKOTU −RPKOST −ROKORR −RNKOQP −MKOQVR −MKOQQU −MKOQMN 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MKMMUTSS MKUMTR MKMNNP MKUNUU NOKMTN OOKNMU NP MKMMVPTM MKUNMP MKMNOO MKUOOR NPKMTT OPKSQV Gbñíê~éçä~íÉÇ=íç=êÉéêÉëÉåí=ãÉí~ëí~ÄäÉ=ÉèìáäáÄêáìã=ïáíÜ=ìåÇÉêÅççäÉÇ=äáèìáÇK OVKPRO PNKTOQ PQKNTV PSKTOS MKMPSO MKMPVT MKMQPP MKMQSU MKMTNT MKMTSR MKMUNS MKMUTM MKNMTU MKNNSO MKNOQU MKNPPT QOKNN QSKPN RMKRM RQKSV NKOOUM NKPNOU NKQMOS NKQVTV NM NN NO NP MKNRNN MKNSRV MKNUMS MKNVRP 6.4 2001 ASHRAE Fundamentals Handbook (SI) Table 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 101.325 kPa (Continued) Condensed Water Humidity Temp., Ratio, °C kg(w)/kg(da) í të NQ NR NS NT NU NV OM ON OO OP OQ OR OS OT OU OV PM PN PO PP PQ PR PS PT PU PV QM QN QO QP QQ QR QS QT QU QV RM RN RO RP RQ RR RS RT RU RV SM SN SO SP SQ SR SS ST SU SV TM TN TO TP TQ TR TS TT TU TV UM UN UO UP UQ UR US UT UU UV VM MKMNMMNO MKMNMSVO MKMNNQNP MKMNONTU MKMNOVUV MKMNPUQU MKMNQTRU MKMNRTON MKMNSTQN MKMNTUON MKMNUVSP MKMOMNTM MKMONQQU MKMOOTVU MKMOQOOS MKMORTPR MKMOTPOV MKMOVMNQ MKMPMTVP MKMPOSTQ MKMPQSSM MKMPSTRS MKMPUVTN MKMQNPMV MKMQPTTU MKMQSPUS MKMQVNQN MKMROMQV MKMRRNNV MKMRUPSR MKMSNTVN MKMSRQNN MKMSVOPV MKMTPOUO MKMTTRRS MKMUOMTT MKMUSURU MKMVNVNU MKMVTOTO MKNMOVQU MKNMUVRQ MKNNRPON MKNOOMTT MKNOVOQP MKNPSURN MKNQQVQO MKNRPRQ MKNSOSV MKNTOQQ MKNUOUQ MKNVPVP MKOMRTV MKONUQU MKOPOMT MKOQSSQ MKOSOPN MKOTVNS MKOVTPQ MKPNSVU MKPPUOQ MKPSNPM MKPUSQN MKQNPTT MKQQPTO MKQTSSP MKRNOUQ MKRROVR MKRVTRN MKSQTOQ MKTMPNN MKTSSOQ MKUPUNO MKVOMSO NKMNSNN NKNOUMM NKOSMSQ NKQOMPN Specific Volume, m3/kg (dry air) Specific Enthalpy, kJ/kg (dry air) îÇ~ î~ë îë ÜÇ~ MKUNPO MKUNSM MKUNUU MKUONT MKUOQR MKUOTQ MKUPMO MKUPPM MKUPRV MKUPUT MKUQNS MKUQQQ MKUQTO MKURMN MKUROV MKURRU MKURUS MKUSNQ MKUSQP MKUSTN MKUTMM MKUTOU MKUTRS MKUTUR MKUUNP MKUUQO MKUUTM MKUUVU MKUVOT MKUVRR MKUVUP MKVMNO MKVMQM MKVMSV MKVMVT MKVNOR MKVNRQ MKVNUO MKVONN MKVOPV MKVOST MKVOVS MKVPOQ MKVPRP MKVPUN MKVQMV MKVQPU MKVQSS MKVQVQ MKVROP MKVRRN MKVRUM MKVSMU MKVSPS MKVSSR MKVSVP MKVTON MKVTRM MKVTTU MKVUMT MKVUPR MKVUSP MKVUVO MKVVOM MKVVQU MKVVTT NKMMMR NKMMPQ NKMMSO NKMMVM NKMNNV NKMNQT NKMNTR NKMOMQ NKMOPO NKMOSN NKMOUV MKMNPN MKMNQM MKMNRM MKMNSM MKMNTO MKMNUQ MKMNVS MKMONM MKMOOQ MKMOQM MKMORS MKMOTP MKMOVN MKMPNN MKMPPN MKMPRP MKMPTS MKMQMM MKMQOS MKMQRQ MKMQUP MKMRNQ MKMRQS MKMRUN MKMSNU MKMSRT MKMSVU MKMTQN MKMTUU MKMUPT MKMUUU MKMVQP MKNMMO MKNMSP MKNNOV MKNNVU MKNOTO MKNPRM MKNQPP MKNRON MKNSNQ MKNTNP MKNUNV MKNVPO MKOMRN MKONTV MKOPNR MKOQSM MKOSNQ MKOTUM MKOVRT MKPNQT MKPPRM MKPRSU MKPUMP MKQMRR MKQPOU MKQSOO MKQVQN MKROUT MKRSSO MKSMTO MKSRNV MKTMNM MKTRRM MKUNQR MKUUMR MKVRPV NKMPSM NKNOUP NKOPOU NKPRNU NKQUUT NKSQTP NKUPPP OKMRQM OKPNVV MKUOSO MKUPMM MKUPPU MKUPTT MKUQNT MKUQRT MKUQVU MKURQM MKURUP MKUSOT MKUSTN MKUTNT MKUTSQ MKUUNN MKUUSM MKUVNM MKUVSO MKVMNR MKVMSV MKVNOR MKVNUP MKVOQO MKVPMP MKVPSS MKVQPN MKVQVU MKVRSU MKVSQM MKVTNQ MKVTVO MKVUTO MKVVRR NKMMQO NKMNPO NKMOOS NKMPOP NKMQOR NKMRPO NKMSQP NKMTSM NKMUUO NKNMMV NKNNQP NKNOUQ NKNQPO NKNRUU NKNTRO NKNVOS NKONMV NKOPMP NKORMU NKOTOS NKOVRU NKPOMQ NKPQST NKPTQV NKQMQV NKQPTO NKQTNV NKRMVP NKRQVT NKRVPR NKSQNN NKSVPM NKTQVU NKUNON NKUUNM NKVRTO OKMQOO OKNPTP OKOQQS OKPSSS OKRMSO OKSSTS OKURSR PKMUMM PKPQUU NQKMUQ NRKMVM NSKMVS NTKNMO NUKNMU NVKNNQ OMKNON ONKNOT OOKNPP OPKNQM OQKNQS ORKNRP OSKNRV OTKNSR OUKNTO OVKNTV PMKNUR PNKNVO POKNVU PPKOMR PQKONO PRKONV PSKOOS PTKOPP PUKOPV PVKOQS QMKORP QNKOSN QOKOSU QPKOTR QQKOUO QRKOUV QSKOVS QTKPMQ QUKPNN QVKPNV RMKPOS RNKPPQ ROKPQN RPKPQV RQKPRT RRKPSR RSKPTP RTKPUN RUKPUV RVKPVT SMKQMR SNKQNP SOKQON SPKQOV SQKQPU SRKQQS SSKQRR STKQSP SUKQTO SVKQUN TMKQUV TNKQVU TOKRMT TPKRNS TQKROR TRKRPR TSKRQP TTKRRP TUKRSO TVKRTO UMKRUN UNKRVN UOKSMM UPKSNM UQKSOM URKSPM USKSQM UTKSRM UUKSSN UVKSTN VMKSUN Ü~ë Üë ORKOUS PVKPTM OTKMOP QOKNNP OUKUST QQKVSP PMKUOQ QTKVOS POKVMM RNKMMU PRKNMN RQKONS PTKQPQ RTKRRR PVKVMU SNKMPR QOKROT SQKSSM QRKPMN SUKQQM QUKOPV TOKPUR RNKPQT TSKRMM RQKSPU UMKTVU RUKNOM URKOUR SNKUMQ UVKVTS SRKSVV VQKUTU SVKUOM NMMKMMS TQKNTT NMRKPSV TUKTUM NNMKVTV UPKSRO NNSKURT UUKTVV NOPKMNN VQKOPS NOVKQRR VVKVUP NPSKOMV NMSKMRU NQPKOVM NNOKQTQ NRMKTNP NNVKORU NRUKRMQ NOSKQPM NSSKSUP NPQKMMR NTRKOSR NQOKMMT NUQKOTR NRMKQTR NVPKTQV NRVKQNT OMPKSVV NSUKUTQ ONQKNSQ NTUKUUO OORKNTV NUVKQRR OPSKTRV OMMKSQQ OQUKVRR ONOKQUR OSNKUMP OORKMNV OTRKPQR OPUKOVM OUVKSOQ OROKPQM PMQKSUO OSTKOQT POMKRVS OUPKMPN PPTKPUU OVVKTTO PRRKNPT PNTKRQV PTPKVOO PPSKQNT PVPKTVU PRSKQSN QNQKURM PTTKTUU QPTKNUR QMMKQRU QSMKUSP QOQKSOQ QUSKMPS QRMKPTT RNOKTVU QTTKUPT RQNKOSS RMTKNTT RTNKSNR RPUKRQU SMPKVVR RTOKNNS SPUKRTN SMUKNMP STRKRSS SQSKTOQ TNRKNVS SUUKOSN TRTKTQO TPOKVRV UMPKQQU TUNKOMU UROKTMS UPPKPPR VMRKUQO UUVKUMT VSPKPOP VRNKMTT NMORKSMP NMNTKUQN NMVPKPTR NMVMKSOU NNSTKNTO NNTMKPOU NOQTKUUN NORTKVON NPPSKQUP NPRQKPQT NQPPKVNU NQSNKOMM NRQNKTUN NRTVKVSN NSSNKRRO NTNOKRQT NTVRKNQU NUSNKRQU NVQRKNRU OMOVKVUP ONNQKSMP OOONKUMS OPMTKQPS OQQOKMPS OROUKSTT OSVTKMNS OTUQKSSS OVVRKUVM PMUQKRRN PPRMKORQ PQPVKVOR PTTSKVNU PUSTKRVV Specific Entropy, kJ/(kg · K) (dry air) ëÇ~ ë~ë MKMRMP MKMVOT MKMRPU MKMVUT MKMRTP MKNMRN MKMSMT MKNNNV MKMSQO MKNNVM MKMSTT MKNOSS MKMTNN MKNPQS MKMTQR MKNQPM MKMTTV MKNRNV MKMUNP MKNSNP MKMUQT MKNTNO MKMUUN MKNUNT MKMVNR MKNVOT MKMVQU MKOMQQ MKMVUO MKONSS MKNMNR MKOOVS MKNMQU MKOQPO MKNMUO MKORTS MKNNNR MKOTOU MKNNQU MKOUUT MKNNUM MKPMRS MKNONP MKPOPP MKNOQS MKPQOM MKNOTU MKPSNT MKNPNN MKPUOQ MKNPQP MKQMQP MKNPTR MKQOTP MKNQMT MKQRNS MKNQPV MKQTTN MKNQTN MKRMQN MKNRMP MKRPOR MKNRPR MKRSOQ MKNRSS MKRVQM MKNRVU MKSOTP MKNSOV MKSSOQ MKNSSN MKSVVQ MKNSVO MKTPUR MKNTOP MKTTVU MKNTRQ MKUOPQ MKNTUR MKUSVR MKNUNS MKVNUO MKNUQT MKVSVU MKNUTT NKMOQP MKNVMU NKMUOM MKNVPU NKNQPO MKNVSV NKOMUN MKNVVV NKOTSV MKOMOV NKPRMM MKOMRV NKQOTU MKOMUV NKRNMQ MKONNV NKRVUR MKONQV NKSVOR MKONTV NKTVOT MKOOMV NKUVVV MKOOPU OKMNQT MKOOSU OKNPTU MKOOVT OKOSVV MKOPOT OKQNOO MKOPRS OKRSRR MKOPUR OKTPNN MKOQNQ OKVNMQ MKOQQP PKNMRO MKOQTO PKPNTN MKORMN PKRQUS MKORPM PKUMOP MKORRV QKMUNM MKORUT QKPUVM MKOSNS QKTPMR MKOSQQ RKNNMU MKOSTP RKRPTO MKOTMN SKMNUN MKOTOV SKRSQQ MKOTRT TKNVMN MKOTUR TKVNOU MKOUNP UKTRUM MKOUQN VKTRTT MKOUSV NMKVRUS ëë MKNQPM MKNROR MKNSOQ MKNTOS MKNUPO MKNVQO MKOMRT MKONTR MKOOVU MKOQOS MKORRV MKOSVU MKOUQO MKOVVO MKPNQU MKPPNN MKPQUN MKPSRU MKPUQO MKQMPR MKQOPS MKQQQS MKQSSS MKQUVR MKRNPR MKRPUS MKRSQV MKRVOP MKSONN MKSRNO MKSUOU MKTNRV MKTRMT MKTUTN MKUORP MKUSRR MKVMTT MKVRON MKVVUU NKMQUM NKMVVU NKNRQQ NKONOM NKOTOU NKPPTM NKQMRM NKQTSU NKRRPM NKSPPT NKTNVQ NKUNMR NKVMTQ OKMNMS OKNOMU OKOPUR OKPSQS OKQVVS OKSQQU OKUMNM OKVSVS PKNRNU PKPQVS PKRSQQ PKTVUT QKMRRP QKPPSU QKSQTT QKVVON RKPTRP RKUMQR SKOUUO SKUPTP TKQSRU UKNVNQ VKMPVP NMKMQNV NNKOQRR Specific Specific Vapor Enthalpy, Entropy, Pressure, Temp., °C kJ/kg kJ/(kg·K) kPa í ëï éë Üï RUKUU SPKMT STKOS TNKQQ TRKSP TVKUN UQKMM UUKNU VOKPS VSKRR NMMKTP NMQKVN NMVKMV NNPKOT NNTKQR NONKSP NORKUN NOVKVV NPQKNT NPUKPR NQOKRP NQSKTN NRMKUV NRRKMT NRVKOR NSPKQP NSTKSN NTNKTV NTRKVT NUMKNR NUQKPP NUUKRN NVOKSV NVSKUU OMNKMS OMRKOQ OMVKQO ONPKSM ONTKTU OONKVT OOSKNR OPMKPP OPQKRO OPUKTM OQOKUU OQTKMT ORNKOR ORRKQQ ORVKSO OSPKUN OSUKMM OTOKNU OTSKPT OUMKRS OUQKTR OUUKVQ OVPKNP OVTKPO PMNKRN PMRKTM PMVKUV PNQKMU PNUKOU POOKQT POSKST PPMKUS PPRKMS PPVKOR PQPKQR PQTKSR PRNKUR PRSKMR PSMKOR PSQKQR PSUKSR PTOKUS PTTKMS MKOMVV MKOOQQ MKOPUV MKORPQ MKOSTU MKOUON MKOVSR MKPNMT MKPOQV MKPPVM MKPRPN MKPSTO MKPUNO MKPVRN MKQMVM MKQOOV MKQPST MKQRMR MKQSQO MKQTTV MKQVNR MKRMRN MKRNUS MKRPON MKRQRS MKRRVM MKRTOQ MKRURT MKRVVM MKSNOO MKSORQ MKSPUS MKSRNT MKSSQU MKSTTU MKSVMU MKTMPU MKTNST MKTOVS MKTQOQ MKTRRO MKTSUM MKTUMT MKTVPQ MKUMSN MKUNUT MKUPNP MKUQPU MKURSP MKUSUU MKUUNO MKUVPS MKVMSM MKVNUP MKVPMS MKVQOV MKVRRN MKVSTP MKVTVQ MKVVNS NKMMPT NKMNRT NKMOTU NKMPVU NKMRNT NKMSPS NKMTRR NKMUTQ NKMVVP NKNNNN NKNOOU NKNPQS NKNQSP NKNRUM NKNSVS NKNUNO NKNVOU NKRVUT NKTMRR NKUNUR NKVPUM OKMSQP OKNVTV OKPPUV OKQUTU OKSQQU OKUNMR OKVURO PKNSVP PKPSPP PKRSTQ PKTUOP QKMMUQ QKOQSO QKQVSN QKTRUS RKMPQR RKPOQO RKSOUM RKVQSU SKOUNO SKSPNR SKVVUU TKPUPU TKTUSS UKOMUN UKSQVR VKNNNM VKRVPR NMKMVUO NMKSORM NNKNTRQ NNKTRMO NOKPRMP NOKVTSQ NPKSOVP NQKPNMU NRKMOMR NRKTSMN NSKRPNN NTKPPPT NUKNSVN NVKMPVP NVKVQPV OMKUURU ONKUSRN OOKUUOS OPKVQMR ORKMPVT OSKNUNM OTKPSSQ OUKRVST OVKUTQN PNKNVUS POKRTPQ PPKVVUP PRKQTRV PTKMMSP PUKRVQM QMKOPSV QNKVPUU QPKTMOM QRKROQU QTKQNPR QVKPSTM RNKPUSM RPKQTQS RRKSPPT RTKUSRU SMKNTOT SOKRRQQ SRKMNSS STKRRUN TMKNUNT NQ NR NS NT NU NV OM ON OO OP OQ OR OS OT OU OV PM PN PO PP PQ PR PS PT PU PV QM QN QO QP QQ QR QS QT QU QV RM RN RO RP RQ RR RS RT RU RV SM SN SO SP SQ SR SS ST SU SV TM TN TO TP TQ TR TS TT TU TV UM UN UO UP UQ UR US UT UU UV VM Psychrometrics 6.5 Table 3 Thermodynamic Properties of Water at Saturation Specific Enthalpy, kJ/kg (water) Specific Volume, m3/kg (water) Specific Entropy, kJ/(kg ·K) (water) Temp., °C t Absolute Pressure, kPa p Sat. Solid vi Evap. vig Sat. Vapor vg Sat. Solid hi Evap. hig Sat. Vapor hg Sat. Solid si Evap. sig Sat. Vapor sg Temp., °C t −SM −RV −RU −RT −RS −RR −RQ −RP −RO −RN MKMMNMU MKMMNOQ MKMMNQN MKMMNSN MKMMNUQ MKMMOMV MKMMOPU MKMMOTN MKMMPMT MKMMPQU MKMMNMUO MKMMNMUO MKMMNMUO MKMMNMUO MKMMNMUO MKMMNMUO MKMMNMUO MKMMNMUP MKMMNMUP MKMMNMUP VMVQOKMM TVURUKSV TMONOKPT SNUMRKPR RQQSVKPV QUMSNKMR QOQRRKRT PTRQSKMV PPOQOKNQ OVQSQKST VMVQOKMM TVURUKSV TMONOKPT SNUMRKPR RQQSVKPV QUMSNKMR QOQRRKRT PTRQSKMV PPOQOKNQ OVQSQKST −QQSKQM −QQQKTQ −QQPKMS −QQNKPU −QPVKSV −QPUKMM −QPSKOV −QPQKRV −QPOKUT −QPNKNQ OUPSKOT OUPSKQS OUPSKSQ OUPSKUN OUPSKVT OUPTKNP OUPTKOT OUPTKQO OUPTKRR OUPTKSU OPUVKUT OPVNKTO OPVPKRT OPVRKQP OPVTKOU OPVVKNO OQMMKVU OQMOKUP OQMQKSU OQMSKRP −NKSURQ −NKTSST −NKSSVU −NKSSOM −NKSRQO −NKSQSQ −NKSPUS −NKSPMU −NKSOPM −NKSNRP NPKPMSR NPKOQRO NPKUNQR NPKNOQP NPKMSQS NPKMMRQ NOKVQSU NOKUUUS NOKUPMV NOKTTPU NNKSONN NNKRSTT NNKRNQT NNKQSOP NNKQNMQ NNKPRVM NNKPMUO NNKORTU NNKOMTV NNKNRUR −SM −RV −RU −RT −RS −RR −RQ −RP −RO −RN −RM −QV −QU −QT −QS −QR −QQ −QP −QO −QN MKMMPVQ MKMMQQR MKMMRMP MKMMRSU MKMMSQM MKMMTON MKMMUNN MKMMVNN MKMNMOO MKMNNQT MKMMNMUP MKMMNMUP MKMMNMUP MKMMNMUP MKMMNMUP MKMMNVUQ MKMMNMUQ MKMMNMUQ MKMMNMUQ MKMMNMUQ OSNQRKMN OPOOPKSV OMSRNKSU NUPUPKRM NSPUNKPR NQSNOKPR NPMQTKSR NNSSNKUR NMQPPKUR =VPQQKOR OSNQRKMN OPOOPKTM OMSRNKSV NUPUPKRN NSPUNKPS NQRNOKPS NPMQTKSS NNSSNKUR NMQPPKUR =VPQQKOR −QOVKQN −QOTKST −QORKVP −QOQKOT −QOOKQN −QOMKSR −QNUKUT −QNTKMV −QNRKPM −QNPKRM OUPTKUM OUPTKVN OUPUKMO OUPUKNO OUPUKON OUPUKOV OUPUKPT OUPUKQQ OUPUKRM OUPUKRR OQMUKPV OQNMKOQ OQNOKMV OQNPKVQ OQNRKTV OQNTKSR OQNVKRM OQONKPR OQOPKOM OQORKMR −NKSMTR −NKRVVT −NKRVNV −NKRUQO −NKRTSQ −NKRSUS −NKRSMV −NKRRPN −NKRQRP −NKRPTS NOKTNTM NOKSSMU NOKSMRN NOKRQVU NOKQVQV NOKQQMR NOKPUSS NOKPPPM NOKOTVV NOKOOTP NNKNMVS NNKMSNN NNKMNPN NMKVSRS NMKVNUR NMKUTNV NMKUORT NMKTTVV NMKTPQS NMKSUVT −RM −QV −QU −QT −QS −QR −QQ −QP −QO −QN −QM −PV −PU −PT −PS −PR −PQ −PP −PO −PN MKMNOUR MKMNQPU MKMNSMU MKMNTVS MKMOMMQ MKMOOPR MKMOQVM MKMOTTN MKMPMUO MKMPQOQ MKMMNMUQ MKMMNMUR MKMMNMUR MKMMNMUR MKMMNMUR MKMMNMUR MKMMNMUR MKMMNMUR MKMMNMUS MKMMNMUS =UPTSKPP =TRNRKUS =STRMKPS =SMSUKNS =RQRVKUO =QVNTKMV =QQPOKPS =PVVUKTN =PSNMKTN =POSPKOM =UPTSKPP =TRNRKUT =STRMKPS =SMSUKNT =RQRVKUO =QVNTKNM =QQPOKPT =PVVUKTN =PSNMKTN =POSPKOM −QNNKTM −QMVKUU −RMUKMT −QMSKOQ −QMQKQM −QMOKRS −QMMKTO −PVUKUS −PVTKMM −PVRKNO OUPUKSM OUPUKSQ OUPUKST OUPUKTM OUPUKTN OUPUKTP OUPUKTP OUPUKTO OUPUKTN OUPUKSV OQOSKVM OQOUKTS NQPMKSN OQPOKQS OQPQKPN OQPSKNS OQPUKMN OQPVKUS OQQNKTO OQQPKRT −NKROVU −NKROON −NKRNQP −NKRMSS −NKQVUU −NKQVNN −NKQUPP −NKQTRS −NKQSTU −NKQSMN NOKNTRM NOKNOPO NOKMTNU NOKMOMU NNKVTMO NNKVNVV NNKUTMN NNKUOMT NNKTTNS NNKTOOV NMKSQRO NMKSMNN NMKRRTR NMKRNQO NMKQTNP NMKQOUV NMKPUSU NMKPQRN NMKPMPT NMKOSOU −QM −PV −PU −PT −PS −PR −PQ −PP −PO −PN −PM −OV −OU −OT −OS −OR −OQ −OP −OO −ON MKMPUMO MKMQONT MKMQSTP MKMRNTQ MKMRTOR MKMSPOV MKMSVVN MKMTTNS MKMURNM MKMVPTU MKMMNMUS MKMMNMUS MKMMNMUS MKMMNMUS MKMMNMUT MKMMNMUT MKMMNMUT MKMMNMUT MKMMNMUT MKMMNMUT =OVRNKSQ =OSTOKMP = OQOMKUV =ONVRKOP =NVVOKNR =NUMVKPR =NSQQKRV =NQVRKVU =NPSNKVQ =NOQMKTT =OVRNKSQ =OSTOKMP = OQOMKUV =ONVRKOP =NVVOKNR =NUMVKPR =NSQQKRV =NQVRKVU =NPSNKVQ =NOQMKTT −PVPKOR −PVNKPS −PUVKQT −PUTKRT −PURKSS −PUPKTQ −PUNKPQ −PTVKUV −PTTKVR −PTSKMN OUPUKSS OUPUKSP OUPUKRV OUPUKRP OUPUKQU OUPUKQN OUPUKPQ OUPUKOS OUPUKNT OUPUKMT OQQRKQO OQQTKOT OQQVKNO OQRMKVT OQROKUO OQRQKST OQRSKRO OQRUKPT OQSMKOO OQSOKMS −NKQROQ −NKQQQS −NKQPSV −NKQOVN −NKQONQ −NKQNPT −NKQMRV −NKPVUO −NKPVMR −NKPUOU NNKSTQS NNKSOSS NNKQTVM NNKRPNU NNKQUQV NNKQPUP NNKPVON NNKPQSO NNKPMMT NNKORRR NMKOOOO NMKNUOM NMKNQON NMKNMOS NMKMSPQ NMKMOQS VKVUSO VKVQUM VKVNMO VKUTOU −PM −OV −OU −OT −OS −OR −OQ −OP −OO −ON −OM −NV −NU −NT −NS −NR −NQ −NP −NO −NN MKNMPOS MKNNPSO MKNOQVO MKNPTOR MKNRMSU MKNSRPM MKNUNOO MKNVURO MKONTPO MKOPTTQ MKMMNMUT MKMMNMUU MKMMNMUU MKMMNMUU MKMMNMUU MKMMNMUU MKMMNMUU MKMMNMUV MKMMNMUV MKMMNMUV =NNPNKOT =NMPOKNU VQOKQS USNKNT TUTKQU TOMKRV SRVKUS SMQKSR RRQKQR RMUKTR =NNPNKOT =NMPOKNU VQOKQT USNKNU TUTKQV TOMKRV SRVKUS SMQKSR RRQKQR RMUKTR −PTQKMS −PTOKNM −PTMKNP −PSUKNR −PSSKNT −PSQKNU −PSOKNU −PSMKNU −PRUKNT −PRSKNR OUPTKVT OUPTKUS OUPTKTQ OUPTKSN OUPTKQT OUPTKPP OUPTKNU OUPTKMO OUPSKUR OUPSKSU OQSPKVN OQSRKTS OQSTKSN OQSVKQS OQTNKPM OQTPKNR OQTQKVV OQTSKUQ OQTUKSU OQUMKRP −NKPTRM −NKPSTP −NKPRVS −NKPRNU −NKPQQN −NKPPSQ −NKPOUT −NKPONM −NKPOPO −NKPMRR NNKONMS NNKNSSN NNKNONU NNKMTTV NNKMPQP NMKVVNM NMKVQUM NMKVMRP NMKUSOV NMKUOMU VKUPRS VKTVUU VKTSOP VKTOSN VKSVMO VKSRQS VKSNVP VKRUQQ VKRQVT VKRNRP −OM −NV −NU −NT −NS −NR −NQ −NP −NO −NN −NM −V −U −T −S −R −Q −P −O −N M MKORVVM MKOUPVP MKPMVVU MKPPUNV MKPSUTQ MKQMNTS MKQPTQT MKQTSMS MKRNTTO MKRSOST MKSNNNR MKMMNMUV MKMMNMUV MKMMNMVM MKMMNMVM MKMMNMVM MKMMNMVM MKMMNMVM MKMMNMVM MKMMNMVN MKMMNMVN MKMMNMVN QSTKNQ QOVKON PVQKSQ PSPKMT PPQKOR PMTKVN OUPKUP OSNKTV OQNKSM OOPKNN OMSKNS QSTKNQ QOVKON PVQKSQ PSPKMT PPQKOR PMTKVN OUPKUP OSNKTV OQNKSM OOPKNN OMSKNS −PRQKNO −PROKMU −PRMKMQ −PQTKVV −PQRKVP −PQPKUT −PQNKUM −PPVKTO −PPTKSP −PPRKRP −PPPKQP OUPSKQV OUPSKPM OUPSKNM OUPRKUV OUPRKSU OUPRKQR OUPRKOO OUPQKVU OUPQKTO OUPQKQT OUPQKOM OQUOKPT OQUQKOO OQUSKMS OQUTKVM OQUVKTQ OQVNKRU OQVPKQO OQVRKOS OQVTKNM OQVUKVP ORMMKTT −NKOVTU −NKOVMN −NKOUOQ −NKOTQS −NKOSSV −OKORVO −NKORNR −NKOQPU −NKOPSN −NKOOUQ −NKOOMS NMKTTVM NMKTPTR NMKSVSO NMKSRRO NMKSNQR NMKQTQN NMKRPQM NMKQVQN NMKQRQQ NMKQNRN NMKPTSM VKQUNO VKQQTQ VKQNPV VKPUMS VKPQTS VKPNQV VKOUOR VKORMP VKONUQ VKNUST VKNRRP −NM −V −U −T −S −R −Q −P −O −N M 6.6 2001 ASHRAE Fundamentals Handbook (SI) Table 3 Thermodynamic Properties of Water at Saturation (Continued) Specific Enthalpy, kJ/kg (water) Specific Volume, m3/kg (water) Specific Entropy, kJ/(kg ·K) (water) Temp., °C t Absolute Pressure, kPa p Sat. Liquid vf Evap. vfg Sat. Vapor vg Sat. Liquid hf Evap. hfg Sat. Vapor hg Sat. Liquid sf Evap. sfg Sat. Vapor sg Temp., °C t M N O P Q R S T U V NM NN NO NP NQ NR NS NT NU NV OM ON OO OP OQ OR OS OT OU OV PM PN PO PP PQ PR PS PT PU PV QM QN QO QP QQ QR QS QT QU QV RM RN RO RP RQ RR RS RT RU RV SM SN SO SP SQ SR SS ST SU SV MKSNNO MKSRTN MKTMSM MKTRUM MKUNPR MKUTOR MKVPRP NKMMOM NKMTOU NKNQUN NKOOUM NKPNOT NKQMOS NKQVTU NKRVUT NKTMRR NKUNUQ NKVPUM OKMSQP OKNVTU OKPPUU OKQUTT OKSQQU OKUNMQ OKVURN PKNSVO PKPSPN PKRSTP PKTUOO QKMMUP QKOQSM QKQVRV QKTRUR RKMPQP RKPOPV RKSOTU RKVQSS SKOUNM SKSPNR SKVVUT TKPUPR TKTUSP UKOMUM UKSQVO VKNNMT VKRVPO NMKMVTS NMKSOQS NNKNTRN NNKTRMM NOKPQVV NOKVTRV NPKSOVM NQKPNMM NRKMOMM NRKTRVT NSKRPMQ NTKPPPN NUKNSVM NVKMPUT NVKVQQ OMKUUR ONKUSQ OOKUUO OPKVQM ORKMQM OSKNUM OTKPSS OUKRVS OVKUTP MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMM MKMMNMMN MKMMNMMN MKMMNMMN MKMMNMMN MKMMNMMN MKMMNMMN MKMMNMMO MKMMNMMO MKMMNMMO MKMMNMMO MKMMNMMO MKMMNMMP MKMMNMMP MKMMNMMP MKMMNMMP MKMMNMMQ MKMMNMMQ MKMMNMMQ MKMMNMMQ MKMMNMMR MKMMNMMR MKMMNMMR MKMMNMMS MKMMNMMS MKMMNMMS MKMMNMMT MKMMNMMT MKMMNMMU MKMMNMMU MKMMNMMU MKMMNMMV MKMMNMMV MKMMNMNM MKMMNMNM MKMMNMNM MKMMNMNN MKMMNMNN MKMMNMNO MKMMNMNO MKMMNMNP MKMMNMNP MKMMNMNQ MKMMNMNQ MKMMNMNR MKMMNMNR MKMMNMNS MKMMNMNS MKMMNMNT MKMMNMNT MKMMNMNU MKMMNMNU MKMMNMNV MKMMNMNV MKMMNMOM MKMMNMOM MKMMNMON MKMMNMOO MKMMNMOO OMSKNQN NVOKQRR NTVKTSV NSUKMOS NRTKNPT NQTKMPO NPTKSRP NOUKVQT NOMKURM NNPKPOS NMSKPOU =VVKUNO =VPKTQP =UUKMUU =UOKUNR TTKUVT TPKPMT SVKMON SRKMNT SRKOTQ RTKTTQ RQKQRM RNKQPP QUKRSO QRKUTO QPKPRM QMKVUR PUKTSS PSKSUO PQKTOS POKUUV PNKNSM OVKRPR OUKMMS OSKRST ORKONO OPKVPR OOKTPP ONKRVV OMKROV NVKROM NUKRST NTKSST NSKUNU NSKMNQ NRKORR NQKRPT NPKURU NPKONQ NOKSMS NOKMOV NNKQUO NMKVSQ NMKQTP NMKMMN VKRSP VKNQT UKTQQ UKPSVM UKMMVQ TKSSTT TKPQOU TKMPPT SKTPVT SKQRVV SKNVPR RKVPVT RKSVUO RKQSUM RKOQUR OMSKNQP NVOKQRS NTVKTTM NSUKMOT NRTKNPU NQTKMPP NPTKSRQ NOUKVQU NOMKURN NNPKPOT NMSKPOV =VVKUNP =VPKTQQ =UUKMUV =UOKUNS TTKUVU TPKPMU SVKMOO SRKMNU SNKOTP RTKTTP RQKRMM RNKQPQ QUKRSP QRKUTP QPKPRN QMKVUS PUKTST PSKSUP PQKTOT POKUUV PNKNSN OVKRPS OUKMMT OSKRSU ORKONP OPKVPS OOKTPQ ONKSMM OMKRPM NVKRON NUKRSU NTKSSU NSKUNV NSKMNR NRKORS NQKRPU NPKURV NPKONR NOKSMT NOKMOV NNKQUP NMKVSR NMKQTQ NMKMMU VKRSSP VKNQSU UKTQUV UKPTMM UKMNNQ TKSSVT TKPQPU TKMPQT SKTQMT SKQSMV SKNVQS RKVQMV RKSVVO RKQSVM RKOQVR −MKMQ QKNU UKPV NOKSM NSKUN ONKMO ORKOO OVKQO PPKSO PTKUO QOKMN QSKON RMKQM RQKRV RUKTU SOKVT STKNS TNKPQ TRKRP TVKTO UPKVM UUKMU VOKOT VSKQR NMMKSP NMQKUN NMUKVV NNPKNU NNTKPS NONKRQ NORKTO NOVKVM NPQKMU NPUKOS NQOKQQ NQSKSO NRMKUM NRQKVU NRVKNS NSPKPQ NSTKRO NTNKTM NTRKUU NUMKMS NUQKOQ NUUKQO NVOKSM NVSKTU OMMKVT OMRKNR OMVKPP ONPKRN ONTKTM OONKUU OOSKMS OPMKOR OPQKQP OPUKSN OQOKUM OQSKVV ORNKNT ORRKPS ORVKRQ OSPKTP OSTKVO OTOKNN OTSKPM OUMKQV OUQKSU OUUKUT ORMMKUN OQVUKQP OQVSKMR OQVPKSU OQVNKPN OQUUKVQ OQUSKRT OQUQKOM OQUNKUQ OQTVKQT OQTTKNN OQTQKTQ OQTOKPU OQTMKMO OQSTKSS OQSRKPM OQSOKVP OQSMKRT OQRUKON OQRRKUR OQRPKQU OQRNKNO OQQUKTR OQQSKPV OQQQKMO OQQNKSS OQPVKOV OQPSKVO OQPQKRR OQPOKNT OQOVKUM OQOTKQP OQORKMR OQOOKST OQNMKOV OQNTKVN OQNRKRP OQNPKNQ OQNMKTS OQMUKPT OQMRKVU OQMPKRU OQMNKNV OPVUKTV OPVSKPV OPVPKVV OPVNKRV OPUVKNU OPUSKTT OPUQKPS OPUNKVQ OPTVKRP OPTTKNM OPTQKSU OPTOKOS OPSVKUP OPSTKPV OPSQKVS OPSOKRO OPSMKMU OPRTKSP OPRRKNV OPROKTP OPRMKOU OPQTKUO OPQRKPS OPQOKUV OPQMKQO OPPTKVR OPPRKQT ORMMKTT ORMOKSN ORMQKQR ORMSKOU ORMUKNO ORMVKVS ORNNKTV ORNPKSO ORNRKQS ORNTKOV ORNVKNO OROMKVR OROOKTU OROQKSN OROSKQQ OROUKOS ORPMKMV ORPNKVO ORPPKTQ ORPRKRS ORPTKPU ORPVKOM ORQNKMO ORQOKUQ ORQQKSR ORQSKQT ORQUKOU ORRMKMV ORRNKVM ORRPKTN ORRRKRO ORRTKPO ORRVKNP ORSMKVP ORSOKTP ORSQKRP ORSSKPP ORSUKNO ORSVKVN ORTNKTN ORTPKRM ORTRKOU ORTTKMT ORTUKUR ORUMKSP ORUOKQN ORUQKNV ORURKVS ORUTKTQ ORUVKRN ORVNKOT ORVPKMQ ORVQKUM ORVSKRS ORVUKPO OSMMKMT OSMNKUO OSMPKRT OSMRKPO OSMTKMS OSMUKUM OSNMKRQ OSNOKOU OSNQKMN OSNRKTQ OSNTKQS OSNVKNV OSOMKVM OSOOKSO OSOQKPP −MKMMMO MKMNRP MKMPMS MKMQRV MKMSNN MKMTSP MKMVNP MKNMSQ MKNONP MKNPSO MKNRNN MKNSRV MKNUMS MKNVRP MKOMVV MKOOQQ MKOPUV MKORPQ MKOSTU MKOUON MKOVSQ MKPNMT MKPOQV MKPPVM MKPRPN MKPSTO MKPUNO MKPVRN MKQMVM MKQOOV MKQPST MKQRMR MKQSQO MKQTTV MKQVNR MKRMRN MKRNUS MKRPON MKRQRS MKRRVM MKRTOQ MKRURT MKRVVM MKSNOO MKSORQ MKSPUS MKSRNT MKSSQU MKSTTU MKSVMU MKTMPU MKTNST MKTOVS MKTQOQ MKTRRO MKTSUM MKTUMT MKTVPQ MKUMSN MKUNUT MKUPNP MKUQPU MKURSP MKUSUU MKUUNO MKUVPS MKVMSM MKVNUP MKVPMS MKVQOV VKNRRR VKNNPQ VKMTNS VKMPMO UKVUVM UKVQUO UKVMTT UKUSTQ UKUOTP UKTUTU UKTQUQ UKTMVP UKSTMR UKSPNV UKRVPS UKRRRS UKRNTU UKQUMQ UKQQPN UKQMSN UKPSVQ UKPPOV UKOVST UKOSMT UKOOQV UKNUVQ UKNRQN UKNNVM UKMUQO UKMQVS UKMNRO TKVUNM TKVQTN TKVNPP TKUTVM TKUQSR TKUNPQ TKTUMR TKTQTV TKTNRQ TKSUPN TKSRNM TKSNVN TKRUTR TKPRSM TKROQT TKQVPS TKQSOS TKQPNV TKQMNP TKPTMV TKPQMT TKPNMT TKOUMV TKORNO TKOONT TKNVOQ TKNSPO TKNPQO TKNMRQ TKMTST TKMQUO TKMNVU SKVVNS SKVSPS SKVPRT SKVMUM SKUUMQ OKURPM SKUORT VKNRRP VKNOUS VKNMOO VKMTSN VKMRMN VKMOQQ UKVVVM UKVTPU UKVQUU UKVOQR UKUVVR UKUTRO UKURNN UKUOTO PKUMPR UKTUMN UKTRSU UKTPPU UKTNMV UKSUUP UKSSRU UKSQPS UKSONR UKRVVS UKRTUM UKRRSR UKRPRO UKRNQN UKQVPO UKQTOQ UKQRNV UKQPNR UKQNNO UKPVNO UKPTNP UKPRNS UKPPOM UKPNOT UKOVPQ UKOTQQ UKORRR UKOPST UKONUN UKNVVT UKNUNQ UKNSPO UKNQRO UKNOTQ UKNMVT UKMVON UKMTQT UKMRTQ UKMQMP UKMOPP UKMMSQ TKVUVT TKVTPN TKVRSS TKVQMP TKVOQM TKVMTV TKUVOM TKUTSN TKUSMQ TKUQQU TKUOVP TKUNQM TKTVUT TKTUPS TKTSUS M N O P Q R S T U V NM NN NO NP NQ NR NS NT NU NV OM ON OO OP OQ OR OS OT OU OV PM PN PO PP PQ PR PS PT PU PV QM QN QO QP QQ QR QS QT QU QV RM RN RO RP RQ RR RS RT RU RV SM SN SO SP SQ SR SS ST SU SV Psychrometrics 6.7 Table 3 Thermodynamic Properties of Water at Saturation (Continued) Specific Enthalpy, kJ/kg (water) Specific Volume, m3/kg (water) Temp., °C t Absolute Pressure, kPa p Sat. Liquid vf TM TN TO TP TQ TR TS TT TU TV UM UN UO UP UQ UR US UT UU UV VM VN VO VP VQ VR VS VT VU VV NMM NMN NMO NMP NMQ NMR NMS NMT NMU NMV NNM NNN NNO NNP NNQ NNR NNS NNT NNU NNV NOM NOO NOQ NOS NOU NPM NPO NPQ NPS NPU NQM NQO NQQ NQS NQU NRM NRO NRQ NRS NRU NSM PNKNVU POKRTO PPKVVT PRKQTR PTKMMS PUKRVO QMKOPS QNKVPU QPKTMM QRKROQ QTKQNO QVKPSQ RNKPUQ RPKQTP RRKSPP RTKUSR SMKNTN SOKRRQ SRKMNR STKRRS TMKNUM TOKUUU TRKSUP TUKRSS UNKRQN UQKSMU UTKTTM VNKMPM VQKPVM VTKURO NMNKQNV NMRKMVO NMUKUTR NNOKTTM NNSKTTV NOMKVMS NORKNRO NOVKROM NPQKMNO NPUKSPP NQPKPUQ NQUKOST NRPKOUT NRUKQQR NSPKTQR NSVKNVM NTQKTUO NUMKROR NUSKQOM NVOKQTP NVUKSUR ONNKSMN OORKNVQ OPVKQVM ORQKRNR OTMKOVU OUSKUSS PMQKOQT POOKQTM PQNKRSS PSNKRSR PUOKQVT QMQKPVQ QOTKOUU QRNKONN QTSKNVU RMOKOUN ROVKQVR RRTKUTR RUTKQRS SNUKOTR MKMMNMOP MKMMNMOP MKMMNMOQ MKMMNMOR MKMMNMOR MKMMNMOS MKMMNMOS MKMMNMOT MKMMNMOU MKMMNMOU MKMMNMOV MKMMNMPM MKMMNMPM MKMMNMPN MKMMNMPO MKMMNMPO MKMMNMPP MKMMNMPQ MKMMNMPR MKMMNMPR MKMMNMPS MKMMNMPT MKMMNMPT MKMMNMPU MKMMNMPV MKMMNMQM MKMMNMQM MKMMNMQN MKMMNMQO MKMMNMQQ MKMMNMQQ MKMMNMQQ MKMMNMQR MKMMNMQS MKMMNMQT MKMMNMQT MKMMNMQU MKMMNMQV MKMMNMRM MKMMNMRN MKMMNMRO MKMMNMRO MKMMNMRP MKMMNMRQ MKMMNMRR MKMMNMRS MKMMNMRT MKMMNMRU MKMMNMRV MKMMNMRV MKMMNMSM MKMMNMSO MKMMNMSQ MKMMNMSS MKMMNMSU MKMMNMTM MKMMNMTO MKMMNMTQ MKMMNMTS MKMMNMTU MKMMNMUM MKMMNMUO MKMMNMUQ MKMMNMUS MKMMNMUU MKMMNMVN MKMMNMVP MKMMNMVR MKMMNMVT MKMMNNMM MKMMNNMO Evap. vfg RKMPVO QKUPVS QKSQVO QKQSTR QKOVQM QKNOUQ PKVTMO PKUNVM PKSTQS PKRPSR PKQMQQ PKOTUN PKNRTP PKMQNT OKVPNM OKUORM OKTOPR OKSOSP OKRPPN OKQQPU OKPRUO OKOTSM OKNVTP OKNONT OKMQVO NKVTVS NKVNOU NKUQUS NKTUSV NKTOTT NKSTMU NKSNSN NKRSPR NKRNOV NKQSQO NKQNTQ NKPTOP NKPOVM NKOUTO NKOQTM NKOMUP NKNTNM NKNPRM NKNMMQ NKMSTM NKMPQU NKMMPU MKVTPV MKVQRM MKVNTN MKUVMO MKUPVN MKTVNS MKTQTO MKTMRT MKSSTM MKSPMU MKRVSV MKRSRN MKRPRQ MKRMTR MKQUNP MKQRST MKQPPS MKQNNV MKPVNQ MKPTOO MKPRQN MKPPTM MKPOMV MKPMRU Specific Entropy, kJ/(kg ·K) (water) Sat. Vapor vg Sat. Liquid hf Evap. hfg Sat. Vapor hg Sat. Liquid sf Evap. sfg Sat. Vapor sg Temp., °C t RKMQMO QKUQMT QKSRMO QKQSUR QKOVRN QKNOVQ PKVTNO PKUOMN PKSTRS PKRPTR PKQMRR PKOTVO PKNRUP PKMQOT OKVPOM OKUOSM OKTOQR OKSOTP OKRPQN OKQQQU OKPRVO OKOTTN OKNVUP OKNOOU OKMRMO NKVUMS NKVNPU NKUQVS NKTUUM NKTOUT NKSTNU NKSNTN NKRSQR NKRNPV NKQSRO NKQNUQ NKPTPQ NKPPMM NKOUUP NKOQUN NKOMVP NKNTOM NKNPSN NKNMNR NKMSUN NKMPRV NKMMQU MKVTQV MKVQSM MKVNUO MKUVNP MKUQMO MKTVOT MKTQUP MKTMSU MKSSUN MKSPNU MKRVTV MKRSSO MKRPSQ MKRMUR MKQUOQ MKQRTU MKQPQT MKQNPM MKPVOR MKPTPP MKPRRO MKPPUN MKPOOM MKPMSV OVPKMS OVTKOR PMNKQQ PMRKSP PMVKUP PNQKMO PNUKOO POOKQN POSKSN PPMKUN PPRKMM PPVKOM PQPKQM PQTKSM PRNKUM PRSKMN PRMKON PSQKQN PSUKSO PTOKUO PTTKMP PUNKOQ PURKQR PUVKSS PVPKUT PVUKMU QMOKOV QMSKRN QNMKTO QNQKVQ QNVKNS QOPKPU QOTKSM QPNKUO QPSKMQ QQMKOT QQQKQV QQUKTO QROKVR QRTKNU QSNKQN QSRKSQ QSVKUU QTQKNN QTUKPR QUOKRV QUSKUP QVNKMT QVRKPO QVVKRS RMPKUN RNOKPN ROMKUO ROVKPP RPTKUS RQSKPV RRQKVP RSPKQU RTOKMQ RUMKSM RUVKNU RVTKTS SMSKPS SNQKVT SOPKRU SPOKON SQMKUR SQVKRM SRUKNS SSSKUP STRKRO OPPOKVV OPPMKRM OPOUKMN OPORKRN OPOPKMO OPOMKRN OPNUKMN OPNRKQV OPNOKVU OPNMKQS OPMTKVP OPMRKQM OVMOKUS OPMMKPO OOVTKTU OOVRKOO OOVOKST OOVMKNN OOUTKRQ OOUQKVT OOUOKPV OOTVKUN OOTTKOO OOTQKSO OOTOKMO OOSVKQN OOSSKUM OOSQKNU OOSNKRR OORUKVO OORSKOU OORPKSQ OORMKVV OOQUKPP OOQRKSS OOQOKVV OOQMKPN OOPTKSP OOPQKVP OOPOKOP OOOVKRO OOOSKUN OOOQKMV OOONKPR OONUKSO OONRKUT OONPKNO OONMKPR OOMTKRU OOMQKUM OOMOKMO ONVSKQO ONVMKTU ONURKNN ONTVKQM ONTPKSS ONSTKUT ONSOKMR ONRSKNU ONRMKOU ONQQKPP ONPUKPQ ONPOKPN ONOSKOP ONOMKNM ONNPKVO ONMTKTM ONMNKQP OMVRKNN OMUUKTP OMUOKPN OSOSKMQ OSOTKTR OSOVKQR OSPNKNR OSPOKUQ OSPQKRP OSPSKOO OSPTKVM OSPVKRU OSQNKOS OSQOKVP OSQQKSM OSQSKOS OSQTKVO OSQVKRU OSRNKOP OSROKUU OSRQKRO OSRSKNS OSRTKTV OSRVKQO OSSNKMQ OSSOKSS OSSQKOU OSSRKUV OSSTKQV OSSVKMV OSTMKSV OSTOKOU OSTPKUS OSTRKQQ OSTTKMO OSTUKRU OSUMKNR OSUNKTN OSUPKOS OSUQKUM OSUSKPR OSUTKUU OSUVKQN OSVMKVP OSVOKQR OSVPKVS OSVRKQT OSVSKVT OSVUKQS OSVVKVR OTMNKQP OTMOKVM OTMQKPT OTMRKUP OTMSKTP OTNNKSM OTNQKQQ OTNTKOS OTOMKMR OTOOKUM OTORKRP OTOUKOO OTPMKUU OTPPKRN OTPSKNN OTPUKST OTQNKNV OTQPKSU OTQSKNP OTQUKRR OTRMKVP OTRPKOT OTRRKRT OTRTKUO MKVRRN MKVSTP MKVTVR MKVVNS NKMMPT NKMNRT NKMOTU NKMPVU NKMRNT NKMSPS NKMTRR NKMUTQ NKMVVP NKNNNN NKNOOU NKNPQS NKNQSP NKNRUM NKNSVS NKNUNO NKNVOU NKOMQQ NKONRV NKOOTQ NKOPUV NKORMQ NKOSNU NKOTPO NKOUQR NKOVRV NKPMTO NKPNUR NKPOVT NKPQNM NKPROO NKPSPQ NKPTQR NKPURS NKPVST NKQMTU NKQNUU NKQOVU NKQQMU NKQRNU NKQSOT NKQTPT NKQUQS NKQVRQ NKRMSP NKRNTN NKROTV NKRQVQ NKRTMV NKRVOO NKSNPR NKSPQT NKSRRT NKSTST NKSVTT NKTNUR NKTPVP NKTRVV NKTUMR NKUMNN NKUONR NKUQNV NKUSOO NKUUOQ NKVMOS NKVOOS NKVQOT SKTVUS SKTTNS SKTQQU SKTNUN SKSVNR SKSSRN SKSPUV SKSNOT SKRUST SKRSMV SKRPRN SKRMVR SKQUQN SKQRUT SKQPPR SKQMUQ SKPUPQ SKPRUS SKPPPV SKPMVP SKOUQU SKOSMR SKOPSO SKONON SKNUUN SKNSQO SKNQMQ SKNNSU SKMVPO SKMSVT SKMQSQ SKMOPO SKMMMM RKVTTM RKVRQN RKVPNP RKVMUS RKUUSM RKUSPR RKUQNM RKUNUT RKTVSR RKTTQQ RKTROQ RKTPMQ RKTMUS RKSUSU RKSSRO RKSQPS RKSOON RKSMMT RKRRUO RKRNSM RKQTQO RKQPOS RKPVNQ RKPRMR RKPMVV RKOSVT RKOOVS RKNUVV RKNRMR RKNNNP RKMTOQ RKMPPU QKVVRQ QKVRTP QKVNVQ QKUUNT QKUQQP QKUMTM TKTRPT TKTPUV TKTOQO TKTMVT TKSVRO TKSUMV TKSSSS TKSROR TKSPUQ TKSOQR TKSNMT TKRVSV TKRUPP TKRSVU TKRRSP TKRQPM TKROVT TKRNSS TKRMPR TKQVMR TKQTTS TKQSQU TKQRON TKQPVR TKQOTM TKQNQS TKQMOO TKPUVV TKPTTT TKPSRS TKPRPS TKPQNS TKPOVU TKPNUM TKPMSO TKOVQS TKOUPM TKOTNS TKOSMN TKOQUU TKOPTR TKOOSP TKONRO TKOQMO TKNVPN TKNUOO TKNTNQ TKNSMS TKNQVV TKNPVO TKNOUS TKNMTS TKMUSV TKMSSQ TKMQSN TKMOSN TKMMSP SKVUST SKVSTP SKVQUN SKVOVO SKVNMQ SKUVNU SKUTPR SKURRP SKUPTP SKUNVQ SKUMNT SKTUQO SKTSSV SKTQVT TM TN TO TP TQ TR TS TT TU TV UM UN UO UP UQ UR US UT UU UV VM VN VO VP VQ VR VS VT VU VV NMM NMN NMO NMP NMQ NMR NMS NMT NMU NMV NNM NNN NNO NNP NNQ NNR NNS NNT NNU NNV NOM NOO NOQ NOS NOU NPM NPO NPQ NPS NPU NQM NQO NQQ NQS NQU NRM NRO NRQ NRS NRU NSM 6.8 2001 ASHRAE Fundamentals Handbook (SI) W s ( p, t d ) Z W HUMIDITY PARAMETERS Basic Parameters Humidity ratio (alternatively, the moisture content or mixing ratio) W of a given moist air sample is defined as the ratio of the mass of water vapor to the mass of dry air contained in the sample: W Z M w ⁄ M da (7) The humidity ratio W is equal to the mole fraction ratio xw /xda multiplied by the ratio of molecular masses, namely, 18.01528/28.9645 = 0.62198: W Z 0.62198x w ⁄ x da (8) Specific humidity γ is the ratio of the mass of water vapor to the total mass of the moist air sample: γ Z M w ⁄ ( M w H M da ) Thermodynamic wet-bulb temperature t* is the temperature at which water (liquid or solid), by evaporating into moist air at a given dry-bulb temperature t and humidity ratio W, can bring air to saturation adiabatically at the same temperature t* while the total pressure p is maintained constant. This parameter is considered separately in the section on Thermodynamic Wet-Bulb Temperature and Dew-Point Temperature. PERFECT GAS RELATIONSHIPS FOR DRY AND MOIST AIR PERFECT GAS RELATIONSHIPS FOR DRY AND MOIST AIR When moist air is considered a mixture of independent perfect gases (i.e., dry air and water vapor), each is assumed to obey the perfect gas equation of state as follows: Dry air: (9a) (9b) dv Z Mw ⁄ V (10) The mixture also obeys the perfect gas equation: (11) where v is the moist air specific volume, m3/kg (dry air), as defined by Equation (27). Saturation humidity ratio Ws (t, p) is the humidity ratio of moist air saturated with respect to water (or ice) at the same temperature t and pressure p. Degree of saturation µ is the ratio of the air humidity ratio W to the humidity ratio Ws of saturated moist air at the same temperature and pressure: xw φ Z -------x ws ( p da H p w )V Z ( n da H n w )RT (19) x da Z p da ⁄ ( p da H p w ) Z p da ⁄ p (20) x w Z p w ⁄ ( p da H p w ) Z p w ⁄ p (21) and (12) From Equations (8), (20), and (21), the humidity ratio W is given by pw W Z 0.62198 --------------p Ó pw (13) (22) The degree of saturation µ is, by definition, Equation (12): t, p Combining Equations (8), (12), and (13), φ µ Z --------------------------------------------------------1 H ( 1 Ó φ )W s ⁄ 0.62198 (18) where p = pda + pw is the total mixture pressure and n = nda + nw is the total number of moles in the mixture. From Equations (16) through (19), the mole fractions of dry air and water vapor are, respectively, t, p Relative humidity φ is the ratio of the mole fraction of water vapor xw in a given moist air sample to the mole fraction xws in an air sample saturated at the same temperature and pressure: pV Z nRT or Humidity Parameters Involving Saturation The following definitions of humidity parameters involve the concept of moist air saturation: (17) pda = partial pressure of dry air pw = partial pressure of water vapor V = total mixture volume nda = number of moles of dry air nw = number of moles of water vapor R = universal gas constant, 8314.41 J/(kg mol·K) T = absolute temperature, K The density ρ of a moist air mixture is the ratio of the total mass to the total volume: ρ Z ( M da H M w ) ⁄ V Z ( 1 ⁄ v ) ( 1 H W ) (16) where Absolute humidity (alternatively, water vapor density) dv is the ratio of the mass of water vapor to the total volume of the sample: W µ Z ------Ws p da V Z n da RT Water vapor: p w V Z n w RT In terms of the humidity ratio, γ Z W ⁄ (1 H W) (15) W µ Z ------Ws (14) Dew-point temperature td is the temperature of moist air saturated at the same pressure p, with the same humidity ratio W as that of the given sample of moist air. It is defined as the solution td (p, W) of the following equation: t, p where p ws W s Z 0.62198 ----------------p Ó p ws (23) Psychrometrics 6.9 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 function only of temperature and differs slightly from the vapor pressure of water in saturated moist air. The relative humidity φ is, by definition, Equation (13): xw φ Z -------x ws t, p (24) t, p Substituting Equation (21) for xws into Equation (14), µ φ Z ----------------------------------------------1 Ó ( 1 Ó µ ) ( p ws ⁄ p ) (25) Both φ and µ are zero for dry air and unity for saturated moist air. At intermediate states their values differ, substantially so at higher temperatures. The specific volume v of a moist air mixture is expressed in terms of a unit mass of dry air: v Z V ⁄ M da Z V ⁄ ( 28.9645n da ) (26) where V is the total volume of the mixture, Mda is the total mass of dry air, and nda is the number of moles of dry air. By Equations (16) and (26), with the relation p = pda + pw, R da T RT v Z ---------------------------------------- Z --------------28.9645 ( p Ó p w ) p Ó pw (27) Using Equation (22), R da T ( 1 H 1.6078W ) RT ( 1 H 1.6078W ) v Z ------------------------------------------- Z ------------------------------------------------28.964p p (28) In Equations (27) and (28), v is specific volume, T is absolute temperature, p is total pressure, pw is the partial pressure of water vapor, and W is the humidity ratio. In specific units, Equation (28) may be expressed as v Z 0.2871 ( t H 273.15 ) ( 1 H 1.6078W ) ⁄ p where v = specific volume, m3/kg (dry air) t = dry-bulb temperature, °C W = humidity ratio, kg (water)/kg (dry air) p = total pressure, kPa THERMODYNAMIC WET-BULB TEMPERATURE DEW-POINT TEMPERATURE THERMODYNAMIC AND WET-BULB TEMPERATURE AND DEW-POINT TEMPERATURE • Humidity ratio is increased from a given initial value W to the value Ws* corresponding to saturation at the temperature t* • Enthalpy is increased from a given initial value h to the value hs* corresponding to saturation at the temperature t* • Mass of water added per unit mass of dry air is (Ws* − W), which adds energy to the moist air of amount (Ws* − W)hw*, where hw* denotes the specific enthalpy in kJ/kg (water) of the water added at the temperature t* Therefore, if the process is strictly adiabatic, conservation of enthalpy at constant total pressure requires that h H ( W s* Ó W ) h w* Z h s* (29) where hda is the specific enthalpy for dry air in kJ/kg (dry air) and hg is the specific enthalpy for saturated water vapor in kJ/kg (water) at the temperature of the mixture. As an approximation, h da ≈ 1.006t (30) h g ≈ 2501 H 1.805t (31) where t is the dry-bulb temperature in °C. The moist air specific enthalpy in kJ/kg (dry air) then becomes (33) The properties Ws*, hw*, and hs* are functions only of the temperature t* for a fixed value of pressure. The value of t*, which satisfies Equation (33) for given values of h, W, and p, is the thermodynamic wet-bulb temperature. The psychrometer consists of two thermometers; one thermometer’s bulb is covered by a wick that has been thoroughly wetted with water. When the wet bulb is placed in an airstream, water evaporates from the wick, eventually reaching an equilibrium temperature called the wet-bulb temperature. This process is not one of adiabatic saturation, which defines the thermodynamic wet-bulb temperature, but one of simultaneous heat and mass transfer from the wet bulb. The fundamental mechanism of this process is described by the Lewis relation [Equation (39) in Chapter 5]. Fortunately, only small corrections must be applied to wet-bulb thermometer readings to obtain the thermodynamic wetbulb temperature. As defined, thermodynamic wet-bulb temperature is a unique property of a given moist air sample independent of measurement techniques. Equation (33) is exact since it defines the thermodynamic wetbulb temperature t*. Substituting the approximate perfect gas relation [Equation (32)] for h, the corresponding expression for hs*, and the approximate relation h w* ≈ 4.186t* The enthalpy of a mixture of perfect gases equals the sum of the individual partial enthalpies of the components. Therefore, the specific enthalpy of moist air can be written as follows: h Z h da H Wh g (32) For any state of moist air, a temperature t* exists at which liquid (or solid) water evaporates into the air to bring it to saturation at exactly this same temperature and total pressure (Harrison 1965). During the adiabatic saturation process, the saturated air is expelled at a temperature equal to that of the injected water. In this constant pressure process, Substituting Equation (21) for xw and xws , pw φ Z -------p ws h Z 1.006t H W ( 2501 H 1.805t ) (34) into Equation (33), and solving for the humidity ratio, ( 2501 Ó 2.381t* )W s* Ó 1.006 ( t Ó t* ) W Z --------------------------------------------------------------------------------------2501 H 1.805t Ó 4.186t* (35) where t and t* are in °C. The dew-point temperature td of moist air with humidity ratio W and pressure p was defined earlier as the solution td (p, w) of Ws(p, td ). For perfect gases, this reduces to p ws ( t d ) Z p w Z ( pW ) ⁄ ( 0.62198 H W ) (36) where pw is the water vapor partial pressure for the moist air sample and pws (td) is the saturation vapor pressure at temperature td . The saturation vapor pressure is derived from Table 3 or from Equation 6.10 2001 ASHRAE Fundamentals Handbook (SI) (5) or (6). Alternatively, the dew-point temperature can be calculated directly by one of the following equations (Peppers 1988): For the dew-point temperature range of 0 to 93°C, 2 3 t d Z C 14 H C 15 α H C 16 α H C 17 α H C 18 ( p w ) 0.1984 2 Given: Dry-bulb temperature t, Relative humidity φ, Pressure p To Obtain (37) For temperatures below 0°C, t d Z 6.09 H 12.608α H 0.4959α SITUATION 3. (38) where pws(t) pw W Ws µ v h td t* td = dew-point temperature, °C α = ln pw pw = water vapor partial pressure, kPa C14 = 6.54 C15 = 14.526 C16 = 0.7389 C17 = 0.09486 C18 = 0.4569 Use Comments Table 3 or Equation (5) or (6) Equation (24) Equation (22) Equation (23) Equation (12) Equation (28) Equation (32) Table 3 with Equation (36), (37), or (38) Equation (23) and (35) with Table 3 or with Equation (5) or (6) Sat. press. for temp. t Requires trial-and-error or numerical solution method Exact Relations for Computing Ws and φ NUMERICAL CALCULATION OF MOIST AIR PROPERTIES Corrections that account for (1) the effect of dissolved gases on properties of condensed phase; (2) the effect of pressure on properties of condensed phase; and (3) the effect of intermolecular force on properties of moisture itself, can be applied to Equations (23) and (25): The following are outlines, citing equations and tables already presented, for calculating moist air properties using perfect gas relations. These relations are sufficiently accurate for most engineering calculations in air-conditioning practice, and are readily adapted to either hand or computer calculating methods. For more details, refer to Tables 15 through 18 in Chapter 1 of Olivieri (1996). Graphical procedures are discussed in the section on Psychrometric Charts. SITUATION 1. Given: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure p To Obtain Using pws(t) Using Ws f p ws W s Z 0.62198 -------------------p Ó f p ws (23a) µ φ Z --------------------------------------------------1 Ó ( 1 Ó µ ) ( f p ws ⁄ p ) (25a) Table 4 lists f values for a number of pressure and temperature combinations. Hyland and Wexler (1983a) give additional values. Use Comments pws(t*) Ws * Table 3 or Equation (5) or (6) Equation (23) Sat. press. for temp. t* Using pws(t*) W pws(t) Equation (35) Table 3 or Equation (5) or (6) Sat. press. for temp. t Ws Using pws(t) Using Ws q, K Ñ EMU E+04 Ñ EMU E+04 Ñ EMU E+04 µ Equation (23) Equation (12) NTPKNR NKMNMR NPQ NKMRQM SS NKNNPM NPS φ v Equation (25) Equation (28) Using pws(t) OTPKNR NKMMPV O= NKMNTT NM NKMPRP NV h pw PTPKNR NKMMPV MKN NKMNUM Q NKMOUQ NN Equation (32) td Table 3 with Equation (36), (37), or (38) Equation (36) Use Values of f and Estimated Maximum Uncertainties (EMUs) 0.1 MPa 0.5 MPa 1 MPa Moist Air Property Tables for Standard Pressure SITUATION 2. Given: Dry-bulb temperature t, Dew-point temperature td, Pressure p To Obtain Table 4 Comments pw = pws(td) Table 3 or Equation (5) or (6) W Equation (22) Sat. press. for temp. td pws (t) Table 3 or Equation (5) or (6) Sat. press. for temp. td Ws Equation (23) Using pws (t) µ Equation (12) Using Ws φ Equation (25) Using pws (t) v h Equation (28) Equation (32) t* Equation (23) and (35) with Table 3 or with Equation (5) or (6) Requires trial-and-error or numerical solution method Table 2 shows values of thermodynamic properties for standard atmospheric pressure at temperatures from −60 to 90°C. The properties of intermediate moist air states can be calculated using the degree of saturation µ: Volume v Z v da H µv as (39) Enthalpy h Z h da H µh as (40) Entropy s Z s da H µ sas (41) These equations are accurate to about 70°C. At higher temperatures, the errors can be significant. Hyland and Wexler (1983a) include charts that can be used to estimate errors for v, h, and s for standard barometric pressure. Licensing Information ASHRAE Psychrometric Chart No. 1 Psychrometrics Fig. 1 Fig. 1 ASHRAE Psychrometric Chart No. 1 6.11 6.12 2001 ASHRAE Fundamentals Handbook (SI) PSYCHROMETRIC CHARTS A psychrometric chart graphically represents the thermodynamic properties of moist air. The choice of coordinates for a psychrometric chart is arbitrary. A chart with coordinates of enthalpy and humidity ratio provides convenient graphical solutions of many moist air problems with a minimum of thermodynamic approximations. ASHRAE developed seven such psychrometric charts. Chart No. 1 is shown as Figure 1; the others may be obtained through ASHRAE. Charts 1 through 4 are for sea level pressure (101.325 kPa). Chart 5 is for 750 m altitude (92.66 kPa), Chart 6 is for 1500 m altitude (84.54 kPa), and Chart 7 is for 2250 m altitude (77.04 kPa). All charts use oblique-angle coordinates of enthalpy and humidity ratio, and are consistent with the data of Table 2 and the properties computation methods of Goff and Gratch (1945), and Goff (1949) as well as Hyland and Wexler (1983a). Palmatier (1963) describes the geometry of chart construction applying specifically to Charts 1 and 4. The dry-bulb temperature ranges covered by the charts are Charts 1, 5, 6, 7 Chart 2 Chart 3 Chart 4 Normal temperature Low temperature High temperature Very high temperature 0 to 50°C −40 to 10°C 10 to 120°C 100 to 200°C Psychrometric properties or charts for other barometric pressures can be derived by interpolation. Sufficiently exact values for most purposes can be derived by methods described in the section on Perfect Gas Relationships for Dry and Moist Air. The construction of charts for altitude conditions has been treated by Haines (1961), Rohsenow (1946), and Karig (1946). Comparison of Charts 1 and 6 by overlay reveals the following: 1. The dry-bulb lines coincide. 2. Wet-bulb lines for a given temperature originate at the intersections of the corresponding dry-bulb line and the two saturation curves, and they have the same slope. 3. Humidity ratio and enthalpy for a given dry- and wet-bulb temperature increase with altitude, but there is little change in relative humidity. 4. Volume changes rapidly; for a given dry-bulb and humidity ratio, it is practically inversely proportional to barometric pressure. region coincide with extensions of thermodynamic wet-bulb temperature lines. If required, the fog region can be further expanded by extension of humidity ratio, enthalpy, and thermodynamic wet-bulb temperature lines. The protractor to the left of the chart shows two scales—one for sensible-total heat ratio, and one for the ratio of enthalpy difference to humidity ratio difference. The protractor is used to establish the direction of a condition line on the psychrometric chart. Example 1 illustrates use of the ASHRAE Psychrometric Chart to determine moist air properties. Example 1. Moist air exists at 40°C dry-bulb temperature, 20°C thermodynamic wet-bulb temperature, and 101.325 kPa pressure. Determine the humidity ratio, enthalpy, dew-point temperature, relative humidity, and specific volume. Solution: Locate state point on Chart 1 (Figure 1) at the intersection of 40°C dry-bulb temperature and 20°C thermodynamic wet-bulb temperature lines. Read humidity ratio W = 6.5 g (water)/kg (dry air). The enthalpy can be found by using two triangles to draw a line parallel to the nearest enthalpy line [60 kJ/kg (dry air)] through the state point to the nearest edge scale. Read h = 56.7 kJ/kg (dry air). Dew-point temperature can be read at the intersection of W = 6.5 g (water)/kg (dry air) with the saturation curve. Thus, td = 7°C. Relative humidity φ can be estimated directly. Thus, φ = 14%. Specific volume can be found by linear interpolation between the volume lines for 0.88 and 0.90 m3/kg (dry air). Thus, v = 0.896 m3/kg (dry air). TYPICAL AIR-CONDITIONING PROCESSES The ASHRAE psychrometric chart can be used to solve numerous process problems with moist air. Its use is best explained through illustrative examples. In each of the following examples, the process takes place at a constant total pressure of 101.325 kPa. Moist Air Sensible Heating or Cooling The process of adding heat alone to or removing heat alone from moist air is represented by a horizontal line on the ASHRAE chart, since the humidity ratio remains unchanged. Figure 2 shows a device that adds heat to a stream of moist air. For steady flow conditions, the required rate of heat addition is The following table compares properties at sea level (Chart 1) and 1500 m (Chart 6): Chart No. db wb h W rh v 1 40 30 99.5 23.0 49 0.920 6 40 30 114.1 28.6 50 1.111 Figure 1, which is ASHRAE Psychrometric Chart No. 1, shows humidity ratio lines (horizontal) for the range from 0 (dry air) to 30 g (water)/kg (dry air). Enthalpy lines are oblique lines drawn across the chart precisely parallel to each other. Dry-bulb temperature lines are drawn straight, not precisely parallel to each other, and inclined slightly from the vertical position. Thermodynamic wet-bulb temperature lines are oblique lines that differ slightly in direction from that of enthalpy lines. They are straight but are not precisely parallel to each other. Relative humidity lines are shown in intervals of 10%. The saturation curve is the line of 100% rh, while the horizontal line for W = 0 (dry air) is the line for 0% rh. Specific volume lines are straight but are not precisely parallel to each other. A narrow region above the saturation curve has been developed for fog conditions of moist air. This two-phase region represents a mechanical mixture of saturated moist air and liquid water, with the two components in thermal equilibrium. Isothermal lines in the fog 1q2 Z m da ( h 2 Ó h 1 ) · (42) Example 2. Moist air, saturated at 2°C, enters a heating coil at a rate of 10 m3/s. Air leaves the coil at 40°C. Find the required rate of heat addition. Fig. 2 Schematic of Device for Heating Moist Air Fig. 2 Schematic of Device for Heating Moist Air Psychrometrics Fig. 3 6.13 Fig. 5 Schematic Solution for Example 3 Schematic Solution for Example 2 Fig. 3 Schematic Solution for Example 2 Fig. 4 Schematic of Device for Cooling Moist Air Fig. 5 Schematic Solution for Example 3 Fig. 6 Adiabatic Mixing of Two Moist Airstreams Fig. 4 Schematic of Device for Cooling Moist Air Solution: Figure 3 schematically shows the solution. State 1 is located on the saturation curve at 2°C. Thus, h1 = 13.0 kJ/kg (dry air), W1 = 4.3 g (water)/kg (dry air), and v1 = 0.784 m3/kg (dry air). State 2 is located at the intersection of t = 40°C and W2 = W1 = 4.3 g (water)/kg (dry air). Thus, h2 = 51.6 kJ/kg (dry air). The mass flow of dry air is Fig. 6 Adiabatic Mixing of Two Moist Airstreams m· da Z 10 ⁄ 0.784 Z 12.76 kg ⁄ s (dry air) From Equation (42), · 1q2 Z m da [ ( h 1 Ó h 2 ) Ó ( W 1 Ó W 2 ) h w2 ] 1q2 Z 12.76 ( 51.6 Ó 13.0 ) Z 492 kW (44) Example 3. Moist air at 30°C dry-bulb temperature and 50% rh enters a cooling coil at 5 m3/s and is processed to a final saturation condition at 10°C. Find the kW of refrigeration required. Moist Air Cooling and Dehumidification Moisture condensation occurs when moist air is cooled to a temperature below its initial dew point. Figure 4 shows a schematic cooling coil where moist air is assumed to be uniformly processed. Although water can be removed at various temperatures ranging from the initial dew point to the final saturation temperature, it is assumed that condensed water is cooled to the final air temperature t2 before it drains from the system. For the system of Figure 4, the steady flow energy and material balance equations are m· da h 1 Z m· da h 2 H 1q2 H m· w h w2 Solution: Figure 5 shows the schematic solution. State 1 is located at the intersection of t = 30°C and φ = 50%. Thus, h1 = 64.3 kJ/kg (dry air), W1 = 13.3 g (water)/kg (dry air), and v1 = 0.877 m3/kg (dry air). State 2 is located on the saturation curve at 10°C. Thus, h2 = 29.5 kJ/kg (dry air) and W2 = 7.66 g (water)/kg (dry air). From Table 2, hw2 = 42.11 kJ/kg (water). The mass flow of dry air is m· da Z 5 ⁄ 0.877 Z 5.70 kg ⁄ s (dry air) From Equation (44), 1q2 Z 5.70 [ ( 64.3 Ó 29.5 ) Ó ( 0.0133 Ó 0.00766 )42.11 ] Z 197 kW m· da W 1 Z m· da W 2 H m· w Adiabatic Mixing of Two Moist Airstreams Thus, m· w Z m· da ( W 1 Ó W 2 ) (43) A common process in air-conditioning systems is the adiabatic mixing of two moist airstreams. Figure 6 schematically shows the problem. Adiabatic mixing is governed by three equations: 6.14 2001 ASHRAE Fundamentals Handbook (SI) Fig. 7 Schematic Solution for Example 4 Fig. 8 Schematic Showing Injection of Water into Moist Air Fig. 8 Schematic Showing Injection of Water into Moist Air Fig. 9 Schematic Solution for Example 5 Fig. 7 Schematic Solution for Example 4 m· da1 h 1 H m· da2 h 2 Z m· da3 h 3 m· H m· Z m· da1 da2 da3 m· da1 W 1 H m· da2 W 2 Z m· da3 W 3 Eliminating m· da3 gives W2 Ó W3 m· da1 h2 Ó h3 ----------------- Z -------------------- Z ----------m· da2 h3 Ó h1 W3 Ó W1 (45) according to which, on the ASHRAE chart, the state point of the resulting mixture lies on the straight line connecting the state points of the two streams being mixed, and divides the line into two segments, in the same ratio as the masses of dry air in the two streams. Example 4. A stream of 2 m3/s of outdoor air at 4°C dry-bulb temperature and 2°C thermodynamic wet-bulb temperature is adiabatically mixed with 6.25 m3/s of recirculated air at 25°C dry-bulb temperature and 50% rh. Find the dry-bulb temperature and thermodynamic wet-bulb temperature of the resulting mixture. Solution: Figure 7 shows the schematic solution. States 1 and 2 are located on the ASHRAE chart, revealing that v1 = 0.789 m3/kg (dry air), and v2 = 0.858 m3/kg (dry air). Therefore, m· da1 Z 2 ⁄ 0.789 Z 2.535 kg ⁄ s (dry air) m· Z 6.25 ⁄ 0.858 Z 7.284 kg ⁄ s (dry air) da2 According to Equation (45), m· da2 m· da1 Line 3–2Line 1–3 -------------------- Z 7.284 ------------- Z 0.742 - or --------------------- Z ----------Z ----------m· da3 Line 1–3 9.819 Line 1–2 m· da2 Consequently, the length of line segment 1–3 is 0.742 times the length of entire line 1–2. Using a ruler, State 3 is located, and the values t3 = 19.5°C and t3* = 14.6°C found. Adiabatic Mixing of Water Injected into Moist Air Steam or liquid water can be injected into a moist airstream to raise its humidity. Figure 8 represents a diagram of this common airconditioning process. If the mixing is adiabatic, the following equations apply: Fig. 9 Schematic Solution for Example 5 m· da h 1 H m· w h w Z m· da h 2 m· da W 1 H m· w Z m· da W 2 Therefore, h2 Ó h1 ∆h-------------------- Z ------Z hw ∆W W2 Ó W1 (46) according to which, on the ASHRAE chart, the final state point of the moist air lies on a straight line whose direction is fixed by the specific enthalpy of the injected water, drawn through the initial state point of the moist air. Example 5. Moist air at 20°C dry-bulb and 8°C thermodynamic wet-bulb temperature is to be processed to a final dew-point temperature of 13°C by adiabatic injection of saturated steam at 110°C. The rate of dry airflow is 2 kg/s (dry air). Find the final dry-bulb temperature of the moist air and the rate of steam flow. Solution: Figure 9 shows the schematic solution. By Table 3, the enthalpy of the steam hg = 2691 kJ/kg (water). Therefore, according to Equation (46), the condition line on the ASHRAE chart connecting States 1 and 2 must have a direction: ∆h ⁄ ∆W Z 2.691 kJ/g (water) Psychrometrics 6.15 The condition line can be drawn with the ∆h/∆W protractor. First, establish the reference line on the protractor by connecting the origin with the value ∆h/∆W = 2.691 kJ/g (water). Draw a second line parallel to the reference line and through the initial state point of the moist air. This second line is the condition line. State 2 is established at the intersection of the condition line with the horizontal line extended from the saturation curve at 13°C (td2 = 13°C). Thus, t2 = 21°C. Values of W2 and W1 can be read from the chart. The required steam flow is, m· w Z m· da ( W 2 Ó W 1 ) Z 2 × 1000 ( 0.0093 Ó 0.0018 ) Z 15.0 kg/s (steam) Space Heat Absorption and Moist Air Moisture Gains Air conditioning a space is usually determined by (1) the quantity of moist air to be supplied, and (2) the supply air condition necessary to remove given amounts of energy and water from the space at the exhaust condition specified. Figure 10 schematically shows a space with incident rates of energy and moisture gains. The quantity qs denotes the net sum of all rates of heat gain in the space, arising from transfers through boundaries and from sources within the space. This heat gain involves addition of energy alone and does not include energy contributions due to addition of water (or water vapor). It is usually called the sensible heat gain. The quantity Σ m· w denotes the net sum of all rates of moisture gain on the space arising from transfers through boundaries and from sources within the space. Each kilogram of water vapor added to the space adds an amount of energy equal to its specific enthalpy. Assuming steady-state conditions, governing equations are m· da h 1 H q s H ∑ ( m· w h w ) Z m· da h 2 or q s H ∑ ( m· w h w ) Z m· da ( h 2 Ó h 1 ) (47) ∑ m· w Z m· da ( W2 Ó W1 ) (48) The left side of Equation (47) represents the total rate of energy addition to the space from all sources. By Equations (47) and (48), ∑ w Fig. 10 Example 6. Moist air is withdrawn from a room at 25°C dry-bulb temperature and 19°C thermodynamic wet-bulb temperature. The sensible rate of heat gain for the space is 9 kW. A rate of moisture gain of 0.0015 kg/s (water) occurs from the space occupants. This moisture is assumed as saturated water vapor at 30°C. Moist air is introduced into the room at a dry-bulb temperature of 15°C. Find the required thermodynamic wet-bulb temperature and volume flow rate of the supply air. Solution: Figure 11 shows the schematic solution. State 2 is located on the ASHRAE chart. From Table 3, the specific enthalpy of the added water vapor is hg = 2555.52 kJ/kg (water). From Equation (49), ∆h H ( 0.0015 × 2555.52 -) ------- Z 9------------------------------------------------------Z 8555 kJ/kg (water) 0.0015 ∆W With the ∆h/∆W protractor, establish a reference line of direction ∆h/∆W = 8.555 kJ/g (water). Parallel to this reference line, draw a straight line on the chart through State 2. The intersection of this line with the 15°C dry-bulb temperature line is State 1. Thus, t1* = 13.8°C. An alternate (and approximately correct) procedure in establishing the condition line is to use the protractor’s sensible-total heat ratio scale instead of the ∆h/∆W scale. The quantity ∆Hs /∆Ht is the ratio of the rate of sensible heat gain for the space to the rate of total energy gain for the space. Therefore, ∆H s qs 9 --------- Z --------------------------------- Z -------------------------------------------------------- Z 0.701 ∆H t q s H Σ ( m· w h w ) 9 H ( 0.0015 × 2555.52 ) Note that ∆Hs /∆Ht = 0.701 on the protractor coincides closely with ∆h/∆W = 8.555 kJ/g (water). The flow of dry air can be calculated from either Equation (47) or (48). From Equation (47), m· da W 1 H ∑ m· w Z m· da W 2 q s H ∑ ( m· w h w ) h2 Ó h1 ∆h-------------------- Z ------Z -----------------------------------∆W W2 Ó W1 m· according to which, on the ASHRAE chart and for a given state of the withdrawn air, all possible states (conditions) for the supply air must lie on a straight line drawn through the state point of the withdrawn air, that has a direction specified by the numerical value of [ q s H Σ ( m· w h w ) ] ⁄ Σm· w . This line is the condition line for the given problem. q s H Σ ( m· w h w ) 9 H ( 0.0015 × 2555.52 ) m· da Z ---------------------------------- Z -------------------------------------------------------h2 Ó h1 54.0 Ó 39.0 Z 0.856 kg ⁄ s (dry air) 3 At State 1, v 1 Z 0.859 m /kg (dry air) Therefore, supply volume = m· da v 1 = 0.856 × 0.859 = 0.735 m3/s Fig. 11 Schematic Solution for Example 6 (49) Schematic of Air Conditioned Space Fig. 10 Schematic of Air Conditioned Space Fig. 11 Schematic Solution for Example 6 6.16 2001 ASHRAE Fundamentals Handbook (SI) TRANSPORT PROPERTIES OF MOIST AIR For certain scientific and experimental work, particularly in the heat transfer field, many other moist air properties are important. Generally classified as transport properties, these include diffusion coefficient, viscosity, thermal conductivity, and thermal diffusion factor. Mason and Monchick (1965) derive these properties by calculation. Table 5 and Figures 12 and 13 summarize the authors’ results on the first three properties listed. Note that, within the boundaries of ASHRAE Psychrometric Charts 1, 2, and 3, the viscosity varies little from that of dry air at normal atmospheric presTable 5 Calculated Diffusion Coefficients for Water−Air at=101.325 kPa Temp., °C mm2/s Temp., °C mm2/s Temp., °C mm2/s −TM −RM −QM −PR −PM −OR −OM −NR −NM −R NPKO NRKS NSKV NTKR NUKO NUKU NVKR OMKO OMKU ONKR M R NM NR OM OR PM PR QM QR OOKO OOKV OPKS OQKP ORKN ORKU OSKR OTKP OUKM OUKU RM RR SM TM NMM NPM NSM NVM OOM ORM OVKR PMKP PNKN POKT PTKS QOKU QUKP RQKM SMKM SSKP Fig. 12 Viscosity of Moist Air Fig. 12 Viscosity of Moist Air Fig. 13 Thermal Conductivity of Moist Air sure, and the thermal conductivity is essentially independent of moisture content. REFERENCES FOR AIR, WATER, AND STEAM PROPERTIES Coefficient fw (over water) at pressures from 0.5 to 110 kPa for temperatures from −50 to 60°C (Smithsonian Institution). Coefficient fi (over ice) at pressures from 0.5 to 110 kPa for temperatures from 0 to 100°C (Smithsonian Institution). Compressibility factor of dry air at pressures from 1 kPa to 10 MPa and at temperatures from 50 to 3000 K (Hilsenrath et al. 1960). Compressibility factor of moist air at pressures from 0 to 10 MPa, at values of degree of saturation from 0 to 100, and for temperatures from 0 to 60°C (Smithsonian Institution). [Note: At the time the Smithsonian Meteorological Tables were published, the value µ = W/Ws was known as relative humidity, in terms of a percentage. Since that time, there has been general agreement to designate the value µ as degree of saturation, usually expressed as a decimal and sometimes as a percentage. See Goff (1949) for more recent data and formulations.] Compressibility factor for steam at pressures from 100 kPa to 30 MPa and at temperatures from 380 to 850 K (Hilsenrath et al. 1960). Density, enthalpy, entropy, Prandtl number, specific heat, specific heat ratio, and viscosity of dry air (Hilsenrath et al. 1960). Density, enthalpy, entropy, specific heat, viscosity, thermal conductivity, and free energy of steam (Hilsenrath et al. 1960). Dry air. Thermodynamic properties over a wide range of temperature (Keenan and Kaye 1945). Enthalpy of saturated steam (Osborne et al. 1939). Ideal-gas thermodynamic functions of dry air at temperatures from 10 to 3000 K (Hilsenrath et al. 1960). Ideal-gas thermodynamic functions of steam at temperatures from 50 to 5000 K. Functions included are specific heat, enthalpy, free energy, and entropy (Hilsenrath et al. 1960). Moist air properties from tabulated virial coefficients (Chaddock 1965). Saturation humidity ratio over ice at pressures from 30 to 100 kPa and for temperatures from −88.8 to 0°C (Smithsonian Institution). Saturation humidity ratio over water at pressures from 6 to 105 kPa and for temperatures from −50 to 59°C (Smithsonian Institution). Saturation vapor pressure over water for temperatures from −50 to 102°C (Smithsonian Institution). Speed of sound in dry air at pressures from 0.001 to 10 MPa for temperatures from 50 to 3000 K (Hilsenrath et al. 1960). At atmospheric pressure for temperatures from −90 to 60°C (Smithsonian Institution). Speed of sound in moist air. Relations using the formulation of Goff and Gratch and studies by Hardy et al. (1942) give methods for calculating this speed (Smithsonian Institution). Steam tables covering the range from –40 to 1315°C (Keenan et al. 1969). Transport properties of moist air. Diffusion coefficient, viscosity, thermal conductivity, and thermal diffusion factor of moist air are listed (Mason and Monchick 1965). The authors’ results are summarized in Table 5 and Figures 12 and 13. Virial coefficients and other information for use with Goff and Gratch formulation (Goff 1949). Volume of water in cubic metres for temperatures from −10 to 250°C (Smithsonian Institution 1954). Water properties. Includes properties of ordinary water substance for the gaseous, liquid, and solid phases (Dorsey 1940). SYMBOLS Fig. 13 Thermal Conductivity of Moist Air C1 to C18 = constants in Equations (5), (6), and (37) Psychrometrics 6.17 dv = absolute humidity of moist air, mass of water per unit volume of mixture f = enhancement factor, used in Equations (23a) and (25a) h = specific enthalpy of moist air hs* = specific enthalpy of saturated moist air at thermodynamic wetbulb temperature hw* = specific enthalpy of condensed water (liquid or solid) at thermodynamic wet-bulb temperature and pressure of 101.325 kPa Hs = rate of sensible heat gain for space Ht = rate of total energy gain for space m· da = mass flow of dry air, per unit time m· w = mass flow of water (any phase), per unit time Mda = mass of dry air in moist air sample Mw = mass of water vapor in moist air sample n = nda + nw, total number of moles in moist air sample nda = moles of dry air nw = moles of water vapor p = total pressure of moist air pda = partial pressure of dry air ps = vapor pressure of water in moist air at saturation. Differs from saturation pressure of pure water because of presence of air. pw = partial pressure of water vapor in moist air pws = pressure of saturated pure water qs = rate of addition (or withdrawal) of sensible heat R = universal gas constant, 8314.41 J/(kg mole·K) Rda = gas constant for dry air Rw = gas constant for water vapor s = specific entropy t = dry-bulb temperature of moist air td = dew-point temperature of moist air t* = thermodynamic wet-bulb temperature of moist air T = absolute temperature v = specific volume vT = total gas volume V = total volume of moist air sample W = humidity ratio of moist air, mass of water per unit mass of dry air Ws* = humidity ratio of moist air at saturation at thermodynamic wet-bulb temperature xda = mole-fraction of dry air, moles of dry air per mole of mixture xw = mole-fraction of water, moles of water per mole of mixture xws = mole-fraction of water vapor under saturated conditions, moles of vapor per mole of saturated mixture Z = altitude α = ln(pw), parameter used in Equations (37) and (38) γ = specific humidity of moist air, mass of water per unit mass of mixture µ = degree of saturation W/Ws ρ = moist air density φ = relative humidity, dimensionless Subscripts as = difference between saturated moist air and dry air da = dry air f = saturated liquid water fg = difference between saturated liquid water and saturated water vapor g = saturated water vapor i = saturated ice ig = difference between saturated ice and saturated water vapor s = saturated moist air t = total w = water in any phase Dorsey, N.E. 1940. Properties of ordinary water substance. Reinhold Publishing, New York. Goff, J.A. 1949. Standardization of thermodynamic properties of moist air. Heating, Piping, and Air Conditioning 21(11):118. Goff, J.A. and S. Gratch. 1945. Thermodynamic properties of moist air. ASHVE Transactions 51:125. Goff, J.A., J.R. Anderson, and S. Gratch. 1943. Final values of the interaction constant for moist air. ASHVE Transactions 49:269. Haines, R.W. 1961. How to construct high altitude psychrometric charts. Heating, Piping, and Air Conditioning 33(10):144. Hardy, H.C., D. Telfair, and W.H. Pielemeier. 1942. The velocity of sound in air. Journal of the Acoustical Society of America 13:226. Harrison, L.P. 1965. Fundamental concepts and definitions relating to humidity. Humidity and moisture measurement and control in science and industry 3:3. A. Wexler and W.A. Wildhack, eds. Reinhold Publishing, New York. Hilsenrath, J. et al. 1960. Tables of thermodynamic and transport properties of air, argon, carbon dioxide, carbon monoxide, hydrogen, nitrogen, oxygen, and steam. National Bureau of Standards. Circular 564, Pergamon Press, New York. Hyland, R.W. and A. Wexler. 1983a. Formulations for the thermodynamic properties of dry air from 173.15 K to 473.15 K, and of saturated moist air from 173.15 K to 372.15 K, at pressures to 5 MPa. ASHRAE Transactions 89(2A):520-35. Hyland, R.W. and A. Wexler. 1983b. Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K. ASHRAE Transactions 89(2A):500-519. Karig, H.E. 1946. Psychrometric charts for high altitude calculations. Refrigerating Engineering 52(11):433. Keenan, J.H. and J. Kaye. 1945. Gas tables. John Wiley and Sons, New York. Keenan, J.H., F.G. Keyes, P.G. Hill, and J.G. Moore. 1969. Steam tables. John Wiley and Sons, New York. Kuehn, T.H., J.W. Ramsey, and J.L. Threlkeld. 1998. Thermal environmental engineering, 3rd ed., p. 188. Prentice-Hall, Upper Saddle River, NJ. Kusuda, T. 1970. Algorithms for psychrometric calculations. NBS Publication BSS21 (January) for sale by Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. Mason, E.A. and L. Monchick. 1965. Survey of the equation of state and transport properties of moist gases. Humidity and moisture measurement and control in science and industry 3:257. Reinhold Publishing, New York. NASA. 1976. U.S. Standard atmosphere, 1976. National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, and the United States Air Force. Available from National Geophysical Data Center, Boulder, CO. NIST. 1990. Guidelines for realizing the international temperature scale of 1990 (ITS-90). NIST Technical Note 1265. National Institute of Technology and Standards, Gaithersburg, MD. Osborne, N.S. 1939. Stimson and Ginnings. Thermal properties of saturated steam. Journal of Research, National Bureau of Standards, 23(8):261. Olivieri, J. 1996. Psychrometrics—Theory and practice. ASHRAE, Atlanta. Palmatier, E.P. 1963. Construction of the normal temperature. ASHRAE psychrometric chart. ASHRAE Journal 5:55. REFERENCES Peppers, V.W. 1988. Unpublished paper. Available from ASHRAE. Preston-Thomas, H. 1990. The international temperature scale of 1990 (ITS90). Metrologia 27(1):3-10. Rohsenow, W.M. 1946. Psychrometric determination of absolute humidity at elevated pressures. Refrigerating Engineering 51(5):423. Chaddock, J.B. 1965. Moist air properties from tabulated virial coefficients. Humidity and moisture measurement and control in science and industry 3:273. A. Wexler and W.A. Wildhack, eds. Reinhold Publishing, New York. Smithsonian Institution. 1954. Smithsonian physical tables, 9th rev. ed. Available from the Smithsonian Institution, Washington, D.C. Smithsonian Institution. Smithsonian meteorological tables, 6th rev. ed. Out of print, but available in many libraries. Washington, D.C.

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