1.2009 ASHRAE HANDBOOK FUNDAMENTALS Inch-Pound EditionAmerican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.1791 Tullie Circle, N.E., Atlanta, GA 30329 (404) 636-8400 http://www.ashrae.org

2. 2009 by the American Society of Heating, Refrigerating and Air-Conditioning Engineers,Inc. All rights reserved. DEDICATED TO THE ADVANCEMENT OFTHE PROFESSION AND ITS ALLIED INDUSTRIES No part of this publication may be reproduced without permission in writing fromASHRAE, except by a reviewer who may quote brief passages or reproduce illustrations ina review with appropriate credit; nor may any part of this book be reproduced, stored in aretrieval system, or transmitted in any way or by any meanselectronic, photocopying,recording, or otherwithout permission in writing from ASHRAE. Requests for permis-sion should be submitted at www.ashrae.org/permissions. Volunteer members of ASHRAE Technical Committees and others compiled the infor-mation in this handbook, and it is generally reviewed and updated every four years. Com-ments, criticisms, and suggestions regarding the subject matter are invited. Any errors oromissions in the data should be brought to the attention of the Editor. Additions and correc-tions to Handbook volumes in print will be published in the Handbook published the yearfollowing their verification and, as soon as verified, on the ASHRAE Internet Web site. DISCLAIMERASHRAE has compiled this publication with care, but ASHRAE has not investigated,and ASHRAE expressly disclaims any duty to investigate, any product, service, process,procedure, design, or the like that may be described herein. The appearance of any technicaldata or editorial material in this publication does not constitute endorsement, warranty, orguaranty by ASHRAE of any product, service, process, procedure, design, or the like.ASHRAE does not warrant that the information in this publication is free of errors. Theentire risk of the use of any information in this publication is assumed by the user.ISBN 978-1-933742-54-0 ISSN 1523-7222 The paper for this book is both acid- and elemental-chlorine-free and was manufactured with pulp obtained from sources using sustainable forestrypractices. The printing used soy-based inks. 3. ASHRAE Research: Improving the Quality of LifeThe American Society of Heating, Refrigerating and Air-annually, enabling ASHRAE to report new data about materialConditioning Engineers is the worlds foremost technical society inproperties and building physics and to promote the application ofthe fields of heating, ventilation, air conditioning, and refrigeration. innovative technologies.Its members worldwide are individuals who share ideas, identify Chapters in the ASHRAE Handbook are updated through theneeds, support research, and write the industrys standards for test-experience of members of ASHRAE Technical Committees anding and practice. The result is that engineers are better able to keep through results of ASHRAE Research reported at ASHRAE meet-indoor environments safe and productive while protecting and pre-ings and published in ASHRAE special publications and inserving the outdoors for generations to come.ASHRAE Transactions.One of the ways that ASHRAE supports its members and indus-For information about ASHRAE Research or to become a mem-trys need for information is through ASHRAE Research. Thou- ber, contact ASHRAE, 1791 Tullie Circle, Atlanta, GA 30329; tele-sands of individuals and companies support ASHRAE Research phone: 404-636-8400; www.ashrae.org.Preface The 2009 ASHRAE HandbookFundamentals covers basic prin- Chapter 20, Space Air Diffusion, has been completely rewritten tociples and data used in the HVAC&R industry. The ASHRAE Tech-harmonize with related chapters in other volumes, with major sec-nical Committees that prepare these chapters strive not only totions on fully mixed, partially mixed, stratified, and task/ambientprovide new information, but also to clarify existing information, systems and the principles behind their design and operation.delete obsolete materials, and reorganize chapters to make the Hand- Chapter 21, Duct Design, has new data for round and rectangularbook more understandable and easier to use. An accompanying CD-fittings in agreement with the ASHRAE Duct Fitting Database, asROM contains all the volumes chapters in both I-P and SI units. well as new content on duct leakage requirements, spiral duct This edition includes a new chapter (35), Sustainability, which roughness, and flexible duct pressure loss correction.defines this concept for HVAC&R and describes the principles, Chapter 23, Insulation for Mechanical Systems, has added tablesdesign considerations, and detailed evaluations needed in designingfrom ASHRAE Standard 90.1-2007, and a new section on writingsustainable HVAC&R systems.specifications. Also new for this volume, chapter order and groupings have been Chapter 24, Airflow Around Buildings, has added a detailed dis-revised for more logical flow and use. Some of the other revisions cussion on computational evaluation of airflow, plus new refer-and additions to the volume are as follows:ences including updated versions of design standards and manuals of practice. Chapter 1, Psychrometrics, has new information on the composi- Chapters 25, 26, and 27 carry new titles, reorganized as chapterstion of dry air, and revised table data for thermodynamic proper- on Heat, Air, and Moisture Control Fundamentals, Material Prop-ties of water and moist air. erties, and Examples, respectively, with updated content through- Chapter 6, Mass Transfer, has added examples on evaluating diffu- out.sion coefficients, and on heat transfer and moisture removal rates. Chapter 29, Refrigerants, has new content on stratospheric ozone Chapter 7, Fundamentals of Control, includes new content on depletion, global climate change, and global environmental char-dampers, adaptive control, direct digital control (DDC) system acteristics of refrigerants.architecture and specifications, and wireless control. Chapter 30, Thermophysical Properties of Refrigerants, has up- Chapter 9, Thermal Comfort, has a new section on thermal com- dated data for R-125, R-245fa, R-170, R-290, R-600, and R-600a.fort and task performance, based on multiple new studies done in Chapter 36, Measurement and Instruments, has revised content onlaboratory and office environments. measurement of air velocity, infiltration, airtightness, and outdoor Chapter 10, Indoor Environmental Health, was reorganized to air ventilation, plus new information on particle image velocime-describe hazard sources, health effects, exposure standards, and try (PIV) and data acquisition and recording.exposure controls. New and updated topics include mold, Legio-nella, indoor air chemistry, thermal impacts, and water quality This volume is published, both as a bound print volume and instandards. electronic format on a CD-ROM, in two editions: one using inch- Chapter 14, Climatic Design Information, has new climate datapound (I-P) units of measurement, the other using the Internationalfor 5564 stations (an increase of 1142 new stations compared toSystem of Units (SI).2005 Fundamentals) on the CD-ROM accompanying this book.Corrections to the 2006, 2007, and 2008 Handbook volumes canA subset of data for selected stations is also included in the be found on the ASHRAE Web site at http://www.ashrae.org and inprinted chapter for convenient access. the Additions and Corrections section of this volume. Corrections Chapter 15, Fenestration, has been revised to include new exam-for this volume will be listed in subsequent volumes and on theples of solar heat gain coefficient (SHGC) calculations, and new ASHRAE Web site.research results on shading calculations and U-factors for variousReader comments are enthusiastically invited. To suggest im-specialized door types.provements for a chapter, please comment using the form on the Chapter 16, Ventilation and Infiltration, has new, detailed exam-ASHRAE Web site or, using the cutout page(s) at the end of this vol-ples, updates from ASHRAE Standards 62.1 and 62.2, discussionumes index, write to Handbook Editor, ASHRAE, 1791 Tullie Cir-of relevant LEED aspects, and new information on airtightness cle, Atlanta, GA 30329, or fax 678-539-2187, or e-mail mowen@and ventilation rates for commercial buildings.ashrae.org. Chapter 18, Nonresidential Cooling and Heating Load Calcu-lations, has been updated to reflect new ASHRAE research resultson climate data and on heat gains from office equipment, lighting, Mark S. Owenand commercial cooking appliances. Editor 4. The four-volume ASHRAE Handbook is a reference for engineers working in HVAC&R and for professionals in allied fields. The print edition isrevised on a four-year cycle, with one volume published each year. Tables of contents for the four most recent volumes appear on these pages, and acomposite index is at the end of this volume. In addition to the CD-ROM accompanying this book, ASHRAE publishes a HandbookCD+ containingall four volumes plus supplemental material and features. The Society also produces educational materials, standards, design guides, databases, andmany other useful publications. See the online bookstore of the ASHRAE Web site (www.ashrae.org) for information on these publications. 2009 FUNDAMENTALSPRINCIPLES21. Duct DesignChapter1.Psychrometrics 22. Pipe Sizing 2.Thermodynamics and Refrigeration Cycles23. Insulation for Mechanical Systems 3.Fluid Flow 24. Airflow Around Buildings 4.Heat Transfer 5.Two-Phase Flow BUILDING ENVELOPE 6.Mass TransferChapter 25. Heat, Air, and Moisture Control in Building 7.Fundamentals of ControlAssembliesFundamentals 8.Sound and Vibration26. Heat, Air, and Moisture Control in BuildingAssembliesMaterial PropertiesINDOOR ENVIRONMENTAL QUALITY27. Heat, Air, and Moisture Control in BuildingChapter9.Thermal ComfortAssembliesExamples10.Indoor Environmental Health11.Air Contaminants MATERIALS12.OdorsChapter 28. Combustion and Fuels13.Indoor Environmental Modeling29. Refrigerants30. Thermophysical Properties of RefrigerantsLOAD AND ENERGY CALCULATIONS31. Physical Properties of Secondary Coolants (Brines)Chapter 14.Climatic Design Information32. Sorbents and Desiccants15.Fenestration 33. Physical Properties of Materials16.Ventilation and Infiltration17.Residential Cooling and Heating Load CalculationsGENERAL18.Nonresidential Cooling and Heating LoadChapter 34. Energy Resources Calculations 35. Sustainability19.Energy Estimating and Modeling Methods 36. Measurement and Instruments37. Abbreviations and SymbolsHVAC DESIGN 38. Units and ConversionsChapter 20.Space Air Diffusion39. Codes and Standards2008 HVAC SYSTEMS AND EQUIPMENTAIR-CONDITIONING AND HEATING SYSTEMSHEATING EQUIPMENT AND COMPONENTSChapter1.HVAC System Analysis and Selection Chapter 30. Automatic Fuel-Burning Systems 2.Decentralized Cooling and Heating31. Boilers 3.Central Heating and Cooling32. Furnaces 4.Air Handling and Distribution33. Residential In-Space Heating Equipment 5.In-Room Terminal Systems 34. Chimney, Vent, and Fireplace Systems 6.Panel Heating and Cooling35. Hydronic Heat-Distributing Units and Radiators 7.Combined Heat and Power Systems 8.Applied Heat Pump and Heat Recovery Systems36. Solar Energy Equipment 9.Small Forced-Air Heating and Cooling Systems COOLING EQUIPMENT AND COMPONENTS10.Steam Systems11.District Heating and Cooling Chapter 37. Compressors12.Hydronic Heating and Cooling 38. Condensers13.Condenser Water Systems39. Cooling Towers14.Medium- and High-Temperature Water Heating 40. Evaporative Air-Cooling Equipment15.Infrared Radiant Heating 41. Liquid Coolers16.Ultraviolet Lamp Systems 42. Liquid-Chilling Systems17.Combustion Turbine Inlet CoolingGENERAL COMPONENTSAIR-HANDLING EQUIPMENT AND COMPONENTS Chapter 43. Centrifugal PumpsChapter 18.Duct Construction44. Motors, Motor Controls, and Variable-Speed Drives19.Room Air Distribution Equipment45. Pipes, Tubes, and Fittings20.Fans 46. Valves21.Humidifiers47. Heat Exchangers22.Air-Cooling and Dehumidifying Coils23.Desiccant Dehumidification and Pressure-Drying PACKAGED, UNITARY, AND SPLIT-SYSTEM Equipment EQUIPMENT24.Mechanical Dehumidifiers and Related Components25.Air-to-Air Energy Recovery Equipment Chapter 48. Unitary Air Conditioners and Heat Pumps26.Air-Heating Coils49. Room Air Conditioners and Packaged Terminal Air27.Unit Ventilators, Unit Heaters, and Makeup Air Conditioners Units28.Air Cleaners for Particulate ContaminantsGENERAL29.Industrial Gas Cleaning and Air Pollution ControlChapter 50. Thermal Storage Equipment51. Codes and Standards 5. CD-ROM with all content from 2009 Fundamentals inside back cover 2007 HVAC APPLICATIONSCOMFORT APPLICATIONSENERGY-RELATED APPLICATIONSChapter1. ResidencesChapter 32. Geothermal Energy 2. Retail Facilities 33. Solar Energy Use 3. Commercial and Public Buildings 34. Thermal Storage 4. Places of Assembly 5. Hotels, Motels, and Dormitories BUILDING OPERATIONS AND MANAGEMENT 6. Educational FacilitiesChapter 35. Energy Use and Management 7. Health Care Facilities36. Owning and Operating Costs 8. Justice Facilities37. Testing, Adjusting, and Balancing 9. Automobiles and Mass Transit38. Operation and Maintenance Management10. Aircraft39. Computer Applications11. Ships 40. Building Energy MonitoringINDUSTRIAL APPLICATIONS 41. Supervisory Control Strategies and Optimization42. HVAC CommissioningChapter 12. Industrial Air Conditioning13. Enclosed Vehicular Facilities GENERAL APPLICATIONS14. Laboratories15. Engine Test FacilitiesChapter 43. Building Envelopes16. Clean Spaces44. Building Air Intake and Exhaust Design17. Data Processing and Electronic Office Areas 45. Control of Gaseous Indoor Air Contaminants18. Printing Plants 46. Design and Application of Controls19. Textile Processing Plants 47. Sound and Vibration Control20. Photographic Material Facilities48. Water Treatment21. Museums, Galleries, Archives, and Libraries 49. Service Water Heating22. Environmental Control for Animals and Plants50. Snow Melting and Freeze Protection23. Drying and Storing Selected Farm Crops51. Evaporative Cooling24. Air Conditioning of Wood and Paper Product52. Fire and Smoke ManagementFacilities53. Radiant Heating and Cooling25. Power Plants54. Seismic and Wind Restraint Design26. Nuclear Facilities55. Electrical Considerations27. Mine Air Conditioning and Ventilation 56. Room Air Distribution28. Industrial Drying Systems 57. Integrated Building Design29. Ventilation of the Industrial Environment 58. Chemical, Biological, Radiological, and Explosive30. Industrial Local Exhaust SystemsIncidents31. Kitchen Ventilation 59. Codes and Standards2006 REFRIGERATIONREFRIGERATION SYSTEM PRACTICES29. Chocolates, Candies, Nuts, Dried Fruits, and DriedChapter1. Liquid Overfeed Systems Vegetables 2System Practices for Halocarbon RefrigerantsDISTRIBUTION OF CHILLED AND FROZEN FOOD 3. System Practices for Ammonia and Carbon DioxideRefrigerantsChapter 30. Cargo Containers, Rail Cars, Trailers, and Trucks 4. Secondary Coolants in Refrigeration Systems 31. Marine Refrigeration 5. Refrigerant System Chemistry32. Air Transport 6. Control of Moisture and Other Contaminants inRefrigerant Systems INDUSTRIAL APPLICATIONS 7. Lubricants in Refrigerant Systems Chapter 33. Insulation Systems for Refrigerant Piping 8. Refrigerant Containment, Recovery, Recycling, and 34. Ice ManufactureReclamation 35. Ice Rinks36. Concrete Dams and Subsurface SoilsFOOD STORAGE AND EQUIPMENT37. Refrigeration in the Chemical IndustryChapter9. Thermal Properties of Foods10. Cooling and Freezing Times of Foods LOW-TEMPERATURE APPLICATIONS11. Commodity Storage RequirementsChapter 38. Cryogenics12. Food Microbiology and Refrigeration 39. Ultralow-Temperature Refrigeration13. Refrigeration Load40. Biomedical Applications of Cryogenic Refrigeration14. Refrigerated-Facility Design15. Methods of Precooling Fruits, Vegetables, and REFRIGERATION EQUIPMENTCut FlowersChapter 41. Absorption Cooling, Heating, and RefrigerationFOOD REFRIGERATIONEquipment42. Forced-Circulation Air CoolersChapter 16. Industrial Food-Freezing Systems43. Component Balancing in Refrigeration Systems17. Meat Products18. Poultry Products44. Refrigerant-Control Devices19. Fishery Products45. Factory Dehydrating, Charging, and Testing20. Dairy ProductsUNITARY REFRIGERATION EQUIPMENT21. Eggs and Egg Products22. Deciduous Tree and Vine Fruit Chapter 46. Retail Food Store Refrigeration and Equipment23. Citrus Fruit, Bananas, and Subtropical Fruit47. Food Service and General Commercial24. VegetablesRefrigeration Equipment25. Fruit Juice Concentrates and Chilled-Juice Products 48. Household Refrigerators and Freezers26. Beverages27. Processed, Precooked, and Prepared FoodsGENERAL28. Bakery Products 49. Codes and Standards 6. LICENSE AGREEMENT 2009 ASHRAE HandbookFundamentals CD-ROMThe 2009 ASHRAE HandbookFundamentals is distributed with an accompanying CD-ROM, which provides electronic access to the volumes content.The License for this CD-ROM is for personal use only; this CD-ROM may not be used on aLAN or WAN.Using the CD-ROM indicates your acceptance of the terms and conditions of this agree-ment. If you do not agree with them, you should not use this CD-ROM.The title and all copyrights and ownership rights in the program and data are retained byASHRAE. You assume responsibility for the selection of the program and data to achieve yourintended results and for the installation, use, and results obtained from the program and data.You may use the program and data on a single machine. You may copy the program anddata into any machine-readable form for back-up purposes in support of your use of the programor data on a single machine. 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CONTENTSContributorsviiASHRAE Technical Committees, Task Groups, and Technical Resource GroupsixASHRAE Research: Improving the Quality of LifexPreface xPRINCIPLESChapter1. Psychrometrics (TC 1.1, Thermodynamics and Psychrometrics, TC 8.3, Absorption and Heat- Operated Machines)1.1 2. Thermodynamics and Refrigeration Cycles (TC 1.1) 2.1 3. Fluid Flow (TC 1.3, Heat Transfer and Fluid Flow)3.1 4. Heat Transfer (TC 1.3) 4.1 5. Two-Phase Flow (TC 1.3)5.1 6. Mass Transfer (TC 1.3) 6.1 7. Fundamentals of Control (TC 1.4, Control Theory and Application) 7.1 8. Sound and Vibration (TC 2.6, Sound and Vibration Control)8.1INDOOR ENVIRONMENTAL QUALITYChapter9. Thermal Comfort (TC 2.1, Physiology and Human Environment) 9.110. Indoor Environmental Health (Environmental Health Committee)10.111. Air Contaminants (TC 2.3, Gaseous Air Contaminants and Gas Contaminant Removal Equipment) 11.112. Odors (TC 2 .3) 12.113. Indoor Environmental Modeling (TC 4.10, Indoor Environmental Modeling)13.1LOAD AND ENERGY CALCULATIONSChapter 14. Climatic Design Information (TC 4.2, Climatic Information)14.115. Fenestration (TC 4.5, Fenestration) 15.116. Ventilation and Infiltration (TC 4.3, Ventilation Requirements and Infiltration ) 16.117. Residential Cooling and Heating Load Calculations (TC 4.1, Load Calculation Data and Procedures)17.118. Nonresidential Cooling and Heating Load Calculations (TC 4.1) 18.119. Energy Estimating and Modeling Methods (TC 4.7, Energy Calculations)19.1HVAC DESIGNChapter 20. Space Air Diffusion (TC 5.3, Room Air Distribution) 20.121. Duct Design (TC 5.2, Duct Design) 21.1 8. 22. Pipe Sizing (TC 6.1, Hydronic and Steam Equipment and Systems) 22.123. Insulation for Mechanical Systems (TC 1.8, Mechanical Systems Insulation)23.124. Airflow Around Buildings (TC 4.3)24.1BUILDING ENVELOPEChapter 25. Heat, Air, and Moisture Control in Building AssembliesFundamentals (TC 4.4, Building Materials and Building Envelope Performance)25.126. Heat, Air, and Moisture Control in Building AssembliesMaterial Properties (TC 4.4)26.127. Heat, Air, and Moisture Control in Insulated AssembliesExamples (TC 4.4)27.1MATERIALSChapter 28. Combustion and Fuels (TC 6.10, Fuels and Combustion) 28.129. Refrigerants (TC 3.1, Refrigerants and Secondary Coolants) 29.130. Thermophysical Properties of Refrigerants (TC 3.1) 30.131. Physical Properties of Secondary Coolants (Brines) (TC 3.1)31.132. Sorbents and Desiccants (TC 8.12, Dessicant Dehumidification Equipment and Components) 32.133. Physical Properties of Materials (TC 1.3)33.1GENERALChapter 34. Energy Resources (TC 2.8, Building Environmental Impacts and Sustainability) 34.135. Sustainability (TC 2.8)35.136. Measurement and Instruments (TC 1.2, Instruments and Measurements) 36.137. Abbreviations and Symbols (TC 1.6, Terminology)37.138. Units and Conversions (TC 1.6) 38.139. Codes and Standards39.1INDEX I.1Composite index to the 2006 Refrigeration, 2007 HVAC Applications, 2008 HVAC Systems andEquipment, and 2009 Fundamentals volumes 9. CHAPTER 1PSYCHROMETRICSComposition of Dry and Moist Air ............................................ 1.1 Thermodynamic Wet-Bulb and Dew-Point Temperature.......... 1.13U.S. Standard Atmosphere ......................................................... 1.1Numerical Calculation of Moist Air Properties....................... 1.13Thermodynamic Properties of Moist Air ................................... 1.2 Psychrometric Charts...............................................................1.14Thermodynamic Properties of Water at Saturation ................... 1.2Humidity Parameters ................................................................. 1.2 Typical Air-Conditioning Processes.........................................1.15Perfect Gas Relationships for Dry and Transport Properties of Moist Air............................................1.19Moist Air............................................................................... 1.12 Symbols .................................................................................... 1.19PSYCHROMETRICS uses thermodynamic properties to ana- lyze conditions and processes involving moist air. This chapterdiscusses perfect gas relations and their use in common heating,flat interface surface between moist air and the condensed phase.Saturation conditions change when the interface radius is very small(e.g., with ultrafine water droplets). The relative molecular mass ofcooling, and humidity control problems. Formulas developed by water is 18.015268 on the carbon-12 scale. The gas constant forHerrmann et al. (2009) may be used where greater precision is water vapor isrequired. Hyland and Wexler (1983a, 1983b), Nelson and Sauer (2002), Rw = 1545.349/18.015268 = 85.780 ftlbf /lbw R(2)and Herrmann et al. (2009) developed formulas for thermodynamicproperties of moist air and water modeled as real gases. However,perfect gas relations can be substituted in most air-conditioningU.S. STANDARD ATMOSPHEREproblems. Kuehn et al. (1998) showed that errors are less than 0.7%in calculating humidity ratio, enthalpy, and specific volume of sat-The temperature and barometric pressure of atmospheric air varyurated air at standard atmospheric pressure for a temperature range considerably with altitude as well as with local geographic andof 60 to 120F. Furthermore, these errors decrease with decreasingweather conditions. The standard atmosphere gives a standard ofpressure. reference for estimating properties at various altitudes. At sea level,standard temperature is 59F; standard barometric pressure is COMPOSITION OF DRY AND MOIST AIR 14.696 psia or 29.921 in. Hg. Temperature is assumed to decreaselinearly with increasing altitude throughout the troposphere (lowerAtmospheric air contains many gaseous components as well asatmosphere), and to be constant in the lower reaches of the strato-water vapor and miscellaneous contaminants (e.g., smoke, pollen,and gaseous pollutants not normally present in free air far from pol- sphere. The lower atmosphere is assumed to consist of dry air thatlution sources).behaves as a perfect gas. Gravity is also assumed constant at theDry air is atmospheric air with all water vapor and contaminantsstandard value, 32.1740 ft/s2. Table 1 summarizes property data forremoved. Its composition is relatively constant, but small variations altitudes to 30,000 ft.in the amounts of individual components occur with time, geo- Pressure values in Table 1 may be calculated fromgraphic location, and altitude. Harrison (1965) lists the approximatepercentage composition of dry air by volume as: nitrogen, 78.084;p = 14.696(1 6.8754 10 6Z) 5.2559 (3)oxygen, 20.9476; argon, 0.934; neon, 0.001818; helium, 0.000524;methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; The equation for temperature as a function of altitude isand minor components such as krypton, xenon, and ozone, 0.0002.Harrison (1965) and Hyland and Wexler (1983a) used a valueTable 1 Standard Atmospheric Data for Altitudes to 30,000 ft0.0314 (circa 1955) for carbon dioxide. Carbon dioxide reached0.0379 in 2005, is currently increasing by 0.00019 percent per yearAltitude, ft Temperature, F Pressure, psiaand is projected to reach 0.0438 in 2036 (Gatley et al. 2008; Keeling1000 62.615.236and Whorf 2005a, 2005b). Increases in carbon dioxide are offset by500 60.814.966decreases in oxygen; consequently, the oxygen percentage in 2036 0 59.014.696is projected to be 20.9352. Using the projected changes, the relative500 57.214.430molecular mass for dry air for at least the first half of the 21st cen-1,000 55.414.175tury is 28.966, based on the carbon-12 scale. The gas constant for 2,000 51.913.664dry air using the current Mohr and Taylor (2005) value for the uni-3,000 48.313.173versal gas constant is 4,000 44.712.682Rda = 1545.349/28.966 = 53.350 ftlbf /lbda R (1)5,000 41.212.230 6,000 37.611.778Moist air is a binary (two-component) mixture of dry air and 7,000 34.011.341water vapor. The amount of water vapor varies from zero (dry air) to 8,000 30.510.914a maximum that depends on temperature and pressure. Saturation 9,000 26.910.506is a state of neutral equilibrium between moist air and the condensed 10,000 23.410.108water phase (liquid or solid); unless otherwise stated, it assumes a15,0005.5 8.29620,00012.3 6.758The preparation of this chapter is assigned to TC 1.1, Thermodynamics and 30,00047.8 4.371Psychrometrics. Source: Adapted from NASA (1976).1.1 10. 1.2 2009 ASHRAE HandbookFundamentals t = 59 0.00356620Z (4) ln pws = C1/T + C2 + C3T + C4T 2 + C5T 3 + C6T 4 + C7 ln T(5)where where Z = altitude, ft C1 = 1.021 416 5 E+04 p = barometric pressure, psia C2 = 4.893 242 8 E+00t = temperature, FC3 = 5.376 579 4 E 03 Equations (3) and (4) are accurate from 16,500 ft to 36,000 ft. C4 = 1.920 237 7 E 07For higher altitudes, comprehensive tables of barometric pressureC5 = 3.557 583 2 E 10 C6 = 9.034 468 8 E 14and other physical properties of the standard atmosphere, in both SI C7 = 4.163 501 9 E 00and I-P units, can be found in NASA (1976). The saturation pressure over liquid water for the temperature rangeTHERMODYNAMIC PROPERTIES OF MOIST AIRof 32 to 392F is given byTable 2, developed from formulas by Herrmann et al. (2009), lnpws = C8/T + C9 + C10T + C11T 2 + C12T 3 + C13 ln T (6)shows values of thermodynamic properties of moist air based on theInternational Temperature Scale of 1990 (ITS-90). This ideal scale wherediffers slightly from practical temperature scales used for physical C8 = 1.044 039 7 E+04measurements. For example, the standard boiling point for water (atC9 = 1.129 465 0 E+0114.696 psia) occurs at 211.95F on this scale rather than at the tra- C10 = 2.702 235 5 E 02ditional 212F. Most measurements are currently based on theC11 = 1.289 036 0 E 05International Temperature Scale of 1990 (ITS-90) (Preston-ThomasC12 = 2.478 068 1 E 091990).C13 = 6.545 967 3 E+00The following properties are shown in Table 2: In both Equations (5) and (6),t = Fahrenheit temperature, based on the International Temperature pws = saturation pressure, psiaScale of 1990 (ITS-90) and expressed relative to absolute T = absolute temperature, R = F + 459.67temperature T in degrees Rankine (R) by the following relation: The coefficients of Equations (5) and (6) were derived from the T = t + 459.67Hyland-Wexler equations, which are given in SI units. Because ofWs = humidity ratio at saturation; gaseous phase (moist air) exists in rounding errors in the derivations and in some computers calculat-equilibrium with condensed phase (liquid or solid) at givening precision, results from Equations (5) and (6) may not agree pre-temperature and pressure (standard atmospheric pressure). At cisely with Table 3 values.given values of temperature and pressure, humidity ratio W can The vapor pressure ps of water in saturated moist air differs neg-have any value from zero to Ws.ligibly from the saturation vapor pressure pws of pure water at thevda = specific volume of dry air, ft3/lbda.same temperature. Consequently, ps can be used in equations invas = vs vda, difference between specific volume of moist air at place of pws with very little error:saturation and that of dry air, ft3/lbda, at same pressure andtemperature. ps = xws p vs = specific volume of moist air at saturation, ft3/lbda.hda = specific enthalpy of dry air, Btu/lbda. In Table 2, hda has been where xws is the mole fraction of water vapor in saturated moist airassigned a value of 0 at 0F and standard atmospheric pressure.at temperature t and pressure p, and p is the total barometric pressurehas = hs hda, difference between specific enthalpy of moist air at of moist air.saturation and that of dry air, Btu/lbda, at same pressure andtemperature. hs = specific enthalpy of moist air at saturation, Btu/lbda.HUMIDITY PARAMETERSsda = specific entropy of dry air, Btu/lbda R. In Table 2, sda isassigned a value of 0 at F and standard atmospheric pressure. Basic Parameters ss = specific entropy of moist air at saturation Btu/lbda R. Humidity ratio W (alternatively, the moisture content or mixing ratio) of a given moist air sample is defined as the ratio of the mass THERMODYNAMIC PROPERTIES OF of water vapor to the mass of dry air in the sample: WATER AT SATURATIONW = Mw /Mda (7) Table 3 shows thermodynamic properties of water at saturationfor temperatures from 80 to 300F, calculated by the formulationsW equals the mole fraction ratio xw /xda multiplied by the ratio ofdescribed by IAPWS (2007). Symbols in the table follow standardmolecular masses (18.015268/28.966 = 0.621945):steam table nomenclature. These properties are based on the Inter-national Temperature Scale of 1990 (ITS-90). The internal energy W = 0.621945xw /xda(8)and entropy of saturated liquid water are both assigned the valuezero at the triple point, 32.018F. Between the triple-point and crit-Specific humidity is the ratio of the mass of water vapor toical-point temperatures of water, two states (saturated liquid and total mass of the moist air sample:saturated vapor) may coexist in equilibrium.= Mw /(Mw + Mda) (9a) The water vapor saturation pressure is required to determinea number of moist air properties, principally the saturation humid- In terms of the humidity ratio,ity ratio. Values may be obtained from Table 3 or calculated fromthe following formulas (Hyland and Wexler 1983b). The 1983 for-= W/(1 + W) (9b)mulas are within 300 ppm of the latest IAPWS formulations. Forhigher accuracy, developers of software and others are referred to Absolute humidity (alternatively, water vapor density) dv is theIAPWS (2007) and (2008). ratio of the mass of water vapor to total volume of the sample: The saturation pressure over ice for the temperature range of148 to 32F is given bydv = Mw /V(10) 11. Psychrometrics 1.3 Table 2Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psiaTemp., F Humidity RatioSpecific Volume, ft3/lbda Specific Enthalpy, Btu/lbdaSpecific Entropy, Btu/lbda F Temp., F t Ws , lbw /lbdavda vas vs hda has hssdasst 800.0000049 9.553 0.000 9.553 19.2180.00519.2130.045930.04592 80 790.0000053 9.578 0.000 9.578 18.9770.00518.9720.045300.04528 79 780.0000057 9.603 0.000 9.604 18.7370.00618.7310.044670.04465 78 770.0000062 9.629 0.000 9.629 18.4970.00618.4900.044040.04402 77 760.0000067 9.654 0.000 9.654 18.2560.00718.2500.043410.04339 76 750.0000072 9.680 0.000 9.680 18.0160.00718.0090.042790.04277 75 740.0000078 9.705 0.000 9.705 17.7760.00817.7680.042160.04214 74 730.0000084 9.730 0.000 9.730 17.5350.00917.5270.041540.04152 73 720.0000090 9.756 0.000 9.756 17.2950.00917.2860.040920.04090 72 710.0000097 9.781 0.000 9.781 17.0550.01017.0450.040300.04027 71 700.0000104 9.806 0.000 9.806 16.8150.01116.8040.039680.03966 70 690.0000112 9.832 0.000 9.832 16.5740.01216.5630.039070.03904 69 680.0000120 9.857 0.000 9.857 16.3340.01216.3210.038450.03842 68 670.0000129 9.882 0.000 9.882 16.0940.01316.0800.037840.03781 67 660.0000139 9.908 0.000 9.908 15.8530.01415.8390.037230.03719 66 650.0000149 9.933 0.000 9.933 15.6130.01515.5980.036620.03658 65 640.0000160 9.958 0.000 9.959 15.3730.01715.3560.036010.03597 64 630.0000172 9.984 0.000 9.984 15.1320.01815.1150.035410.03536 63 620.000018410.009 0.00010.009 14.8920.01914.8730.034800.03475 62 610.000019810.034 0.00010.035 14.6520.02014.6320.034200.03414 61 600.000021210.060 0.00010.060 14.4120.02214.3900.033600.03354 60 590.000022710.085 0.00010.085 14.1710.02314.1480.033000.03293 59 580.000024310.110 0.00010.111 13.9310.02513.9060.032400.03233 58 570.000026010.136 0.00010.136 13.6910.02713.6640.031800.03173 57 560.000027910.161 0.00010.161 13.4510.02913.4220.031200.03113 56 550.000029810.186 0.00010.187 13.2100.03113.1800.030610.03053 55 540.000031910.212 0.00110.212 12.9700.03312.9370.030020.02993 54 530.000034110.237 0.00110.237 12.7300.03512.6950.029420.02933 53 520.000036510.262 0.00110.263 12.4900.03812.4520.028830.02874 52 510.000039010.288 0.00110.288 12.2490.04012.2090.028250.02814 51 500.000041610.313 0.00110.314 12.0090.04311.9660.027660.02755 50 490.000044510.338 0.00110.339 11.7690.04611.7230.027070.02695 49 480.000047510.364 0.00110.364 11.5290.04911.4790.026490.02636 48 470.000050710.389 0.00110.390 11.2890.05311.2360.025910.02577 47 460.000054110.414 0.00110.415 11.0480.05610.9920.025320.02518 46 450.000057710.439 0.00110.440 10.8080.06010.7480.024740.02459 45 440.000061510.465 0.00110.466 10.5680.06410.5040.024170.02400 44 430.000065610.490 0.00110.491 10.3280.06810.2590.023590.02341 43 420.000069910.515 0.00110.517 10.0870.07310.0150.023010.02283 42 410.000074410.541 0.00110.5429.8470.078 9.7700.022440.02224 41 400.000079310.566 0.00110.5679.6070.0839.524 0.021870.02166 40 390.000084410.591 0.00110.5939.3670.0889.279 0.021290.02107 39 380.000089810.617 0.00210.6189.1270.0949.033 0.020720.02049 38 370.000095610.642 0.00210.6448.8860.1008.787 0.020150.01990 37 360.000101710.667 0.00210.6698.6460.1068.540 0.019590.01932 36 350.000108110.693 0.00210.6958.4060.1138.293 0.019020.01874 35 340.000115010.718 0.00210.7208.1660.1208.046 0.018460.01816 34 330.000122210.743 0.00210.7457.9260.1287.798 0.017890.01757 33 320.000129810.769 0.00210.7717.6850.1367.550 0.017330.01699 32 310.000137910.794 0.00210.7967.4450.1447.301 0.016770.01641 31 300.000146510.819 0.00310.8227.2050.1537.052 0.016210.01583 30 290.000155510.845 0.00310.8476.9650.1636.802 0.015650.01525 29 280.000165010.870 0.00310.8736.7250.1736.552 0.015090.01467 28 270.000175110.895 0.00310.8986.4850.1846.301 0.014540.01409 27 260.000185710.920 0.00310.9246.2440.1956.050 0.013980.01351 26 250.000197010.946 0.00310.9496.0040.2075.797 0.013430.01293 25 240.000208810.971 0.00410.9755.7640.2195.545 0.012880.01234 24 230.000221310.996 0.00411.0005.5240.2335.291 0.012330.01176 23 220.000234511.022 0.00411.0265.2840.2465.037 0.011780.01118 22 210.000248511.047 0.00411.0515.0440.2614.782 0.011230.01060 21 200.000263211.072 0.00511.0774.8030.2774.527 0.010680.01002 20 190.000278611.098 0.00511.1034.5630.2934.270 0.010140.00943 19 180.000294911.123 0.00511.1284.3230.3104.013 0.009590.00885 18 170.000312111.148 0.00611.1544.0830.3293.754 0.009050.00826 17 160.000330211.174 0.00611.1793.8430.3483.495 0.008510.00768 16 150.000349311.199 0.00611.2053.6020.3683.234 0.007970.00709 15 140.000369411.224 0.00711.2313.3620.3892.973 0.007430.00650 14 130.000390511.249 0.00711.2573.1220.4122.710 0.006890.00591 13 120.000412711.275 0.00711.2822.8820.4362.446 0.006350.00532 12 110.000436111.300 0.00811.3082.6420.4602.181 0.005820.00473 11 12. 1.4 2009 ASHRAE HandbookFundamentalsTable 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia (Continued )Temp., FHumidity Ratio Specific Volume, ft3/lbda Specific Enthalpy, Btu/lbdaSpecific Entropy, Btu/lbda F Temp., F tWs , lbw /lbda vda vas vs hda has hssdasst 10 0.0004607 11.325 0.00811.3342.4020.4871.915 0.005280.00414 109 0.0004866 11.351 0.00911.3602.1610.5141.647 0.004750.0035498 0.0005138 11.376 0.00911.3851.9210.5431.378 0.004220.0029487 0.0005425 11.401 0.01011.4111.6810.5741.107 0.003690.0023476 0.0005725 11.427 0.01011.4371.4410.6060.835 0.003160.0017465 0.0006041 11.452 0.01111.4631.2010.6390.561 0.002630.0011454 0.0006373 11.477 0.01211.4890.9610.6750.286 0.002100.0005343 0.0006721 11.502 0.01211.5150.7200.7120.009 0.00157 0.0000832 0.0007087 11.528 0.01311.5410.4800.751 0.271 0.00105 0.0006921 0.0007471 11.553 0.01411.5670.2400.792 0.552 0.00052 0.001301 0 0.0007875 11.578 0.01511.593 0.0000.835 0.835 0.00000 0.00192 0 1 0.0008298 11.604 0.01511.619 0.2400.880 1.121 0.00052 0.00254 1 2 0.0008741 11.629 0.01611.645 0.4800.928 1.408 0.00104 0.00317 2 3 0.0009207 11.654 0.01711.671 0.7200.978 1.698 0.00156 0.00379 3 4 0.0009695 11.680 0.01811.698 0.9611.030 1.991 0.00208 0.00443 4 5 0.0010207 11.705 0.01911.724 1.2011.085 2.286 0.00260 0.00506 5 6 0.0010743 11.730 0.02011.750 1.4411.142 2.583 0.00311 0.00570 6 7 0.0011306 11.755 0.02111.777 1.6811.203 2.884 0.00363 0.00635 7 8 0.0011895 11.781 0.02211.803 1.9211.266 3.187 0.00414 0.00700 8 9 0.0012512 11.806 0.02411.830 2.1611.332 3.494 0.00466 0.00766 910 0.0013158 11.831 0.02511.856 2.4021.401 3.803 0.00517 0.00832 1011 0.0013835 11.857 0.02611.883 2.6421.474 4.116 0.00568 0.00898 1112 0.0014544 11.882 0.02811.910 2.8821.550 4.432 0.00619 0.00965 1213 0.0015286 11.907 0.02911.936 3.1221.630 4.752 0.00670 0.01033 1314 0.0016062 11.933 0.03111.963 3.3621.714 5.076 0.00721 0.01102 1415 0.0016874 11.958 0.03211.990 3.6031.801 5.403 0.00771 0.01171 1516 0.0017724 11.983 0.03412.017 3.8431.892 5.735 0.00822 0.01241 1617 0.0018613 12.008 0.03612.044 4.0831.988 6.071 0.00872 0.01312 1718 0.0019543 12.034 0.03812.071 4.3232.088 6.411 0.00923 0.01383 1819 0.0020515 12.059 0.04012.099 4.5632.193 6.756 0.00973 0.01455 1920 0.0021531 12.084 0.04212.126 4.8032.303 7.106 0.01023 0.01528 2021 0.0022593 12.110 0.04412.153 5.0442.417 7.461 0.01073 0.01602 2122 0.0023703 12.135 0.04612.181 5.2842.537 7.821 0.01123 0.01677 2223 0.0024863 12.160 0.04812.209 5.5242.662 8.186 0.01173 0.01753 2324 0.0026075 12.185 0.05112.236 5.7642.793 8.557 0.01222 0.01830 2425 0.0027340 12.211 0.05412.264 6.0042.930 8.934 0.01272 0.01908 2526 0.0028662 12.236 0.05612.292 6.2443.073 9.317 0.01321 0.01987 2627 0.0030042 12.261 0.05912.320 6.4853.222 9.707 0.01371 0.02067 2728 0.0031482 12.287 0.06212.349 6.7253.37810.103 0.01420 0.02148 2829 0.0032986 12.312 0.06512.377 6.9653.54110.506 0.01469 0.02231 2930 0.0034555 12.337 0.06812.405 7.2053.71110.916 0.01518 0.02315 3031 0.0036192 12.362 0.07212.434 7.4453.88811.334 0.01567 0.02400 3132 0.0037900 12.388 0.07512.463 7.6864.07311.759 0.01616 0.02486 3232 0.00379012.38770.0753 12.46307.6864.07311.759 0.01616 0.02486 3233 0.00394712.41300.0786 12.49157.9264.24412.169 0.01665 0.02570 3334 0.00410912.43820.0820 12.52028.1664.42012.586 0.01714 0.02654 3435 0.00427812.46350.0855 12.54908.4064.60313.009 0.01762 0.02740 3536 0.00445212.48880.0892 12.57808.6464.79313.439 0.01811 0.02827 3637 0.00463312.51410.0930 12.60718.8874.99013.877 0.01859 0.02915 3738 0.00482112.53940.0969 12.63639.1275.19414.321 0.01908 0.03004 3839 0.00501512.56470.1010 12.66579.3675.40514.772 0.01956 0.03095 3940 0.00521612.58990.1053 12.69529.6075.62515.232 0.02004 0.03187 4041 0.00542512.61520.1097 12.72499.8485.85215.699 0.02052 0.03280 4142 0.00564012.64050.1143 12.7548 10.0886.08716.175 0.02100 0.03375 4243 0.00586412.66580.1191 12.7849 10.3286.33116.659 0.02148 0.03472 4344 0.00609512.69110.1240 12.8151 10.5686.58317.151 0.02196 0.03570 4445 0.00633512.71630.1292 12.8455 10.8086.84417.653 0.02243 0.03669 4546 0.00658212.74160.1345 12.8761 11.0497.11518.164 0.02291 0.03770 4647 0.00683912.76690.1400 12.9069 11.2897.39518.684 0.02338 0.03873 4748 0.00710412.79220.1457 12.9379 11.5297.68519.214 0.02386 0.03978 4849 0.00737912.81750.1516 12.9691 11.7697.98519.755 0.02433 0.04084 4950 0.00766312.84270.1578 13.0005 12.0108.29620.306 0.02480 0.04192 5051 0.00795612.86800.1641 13.0322 12.2508.61720.867 0.02527 0.04302 5152 0.00826012.89330.1707 13.0640 12.4908.95021.440 0.02574 0.04414 5253 0.00857412.91860.1776 13.0962 12.7309.29422.024 0.02621 0.04528 5354 0.00889912.94390.1847 13.1285 12.9719.65022.621 0.02668 0.04645 5455 0.00923512.96910.1920 13.1611 13.211 10.01823.229 0.02715 0.04763 5556 0.00958212.99440.1996 13.1940 13.451 10.39923.850 0.02761 0.04884 5657 0.00994013.01970.2075 13.2272 13.691 10.79224.484 0.02808 0.05006 5758 0.01031113.04500.2156 13.2606 13.932 11.19925.131 0.02854 0.05132 5859 0.01069413.07020.2241 13.2943 14.172 11.62025.792 0.02901 0.05259 59 13. Psychrometrics 1.5Table 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia (Continued )Temp., FHumidity Ratio Specific Volume, ft3/lbda Specific Enthalpy, Btu/lbdaSpecific Entropy, Btu/lbda F Temp., F tWs , lbw /lbda vda vas vs hda has hssdasst60 0.01108913.09550.2328 13.3283 14.412 12.05526.467 0.02947 0.05389 6061 0.01149813.12080.2418 13.3626 14.653 12.50427.157 0.02993 0.05522 6162 0.01192113.14610.2512 13.3973 14.893 12.96827.861 0.03039 0.05657 6263 0.01235713.17130.2609 13.4322 15.133 13.44828.581 0.03085 0.05795 6364 0.01280713.19660.2709 13.4675 15.373 13.94429.318 0.03131 0.05936 6465 0.01327213.22190.2813 13.5032 15.614 14.45630.070 0.03177 0.06080 6566 0.01375313.24720.2920 13.5392 15.854 14.98630.840 0.03223 0.06226 6667 0.01424913.27240.3031 13.5755 16.094 15.53231.626 0.03268 0.06376 6768 0.01476113.29770.3146 13.6123 16.335 16.09732.431 0.03314 0.06529 6869 0.01528913.32300.3265 13.6494 16.575 16.68033.255 0.03360 0.06685 6970 0.01583513.34820.3388 13.6870 16.815 17.28234.097 0.03405 0.06844 7071 0.01639813.37350.3515 13.7250 17.056 17.90334.959 0.03450 0.07007 7172 0.01697913.39880.3646 13.7634 17.296 18.54535.841 0.03496 0.07173 7273 0.01757813.42410.3782 13.8022 17.536 19.20836.744 0.03541 0.07343 7374 0.01819713.44930.3922 13.8415 17.776 19.89237.668 0.03586 0.07516 7475 0.01883513.47460.4067 13.8813 18.017 20.59838.615 0.03631 0.07694 7576 0.01949413.49990.4217 13.9216 18.257 21.32739.584 0.03676 0.07875 7677 0.02017313.52510.4372 13.9624 18.498 22.07940.576 0.03720 0.08060 7778 0.02087413.55040.4533 14.0037 18.738 22.85541.593 0.03765 0.08250 7879 0.02159713.57570.4698 14.0455 18.978 23.65642.634 0.03810 0.08444 7980 0.02234313.60100.4869 14.0879 19.219 24.48243.701 0.03854 0.08642 8081 0.02311213.62620.5046 14.1308 19.459 25.33544.794 0.03899 0.08845 8182 0.02390513.65150.5229 14.1744 19.699 26.21545.914 0.03943 0.09052 8283 0.02472313.67680.5418 14.2185 19.940 27.12247.062 0.03988 0.09264 8384 0.02556613.70200.5613 14.2633 20.180 28.05948.239 0.04032 0.09481 8485 0.02643613.72730.5814 14.3087 20.420 29.02549.445 0.04076 0.09703 8586 0.02733313.75260.6022 14.3548 20.661 30.02150.682 0.04120 0.09930 8687 0.02825713.77780.6237 14.4015 20.901 31.04951.950 0.04164 0.10163 8788 0.02921113.80310.6459 14.4490 21.142 32.10953.250 0.04208 0.10401 8889 0.03019313.82840.6688 14.4972 21.382 33.20254.584 0.04252 0.10645 8990 0.03120613.85360.6925 14.5462 21.622 34.32955.952 0.04296 0.10895 9091 0.03225113.87890.7170 14.5959 21.863 35.49257.355 0.04340 0.11150 9192 0.03332713.90420.7422 14.6464 22.103 36.69158.795 0.04383 0.11412 9293 0.03443713.92940.7683 14.6977 22.344 37.92860.272 0.04427 0.11681 9394 0.03558113.95470.7952 14.7499 22.584 39.20361.787 0.04470 0.11955 9495 0.03676013.98000.8230 14.8030 22.825 40.51863.343 0.04514 0.12237 9596 0.03797614.00520.8518 14.8570 23.065 41.87464.939 0.04557 0.12525 9697 0.03922814.03050.8814 14.9119 23.305 43.27266.578 0.04600 0.12821 9798 0.04052014.05580.9120 14.9678 23.546 44.71468.260 0.04643 0.13124 9899 0.04185114.08100.9436 15.0247 23.786 46.20169.987 0.04686 0.13434 99 100 0.04322214.10630.9763 15.0826 24.027 47.73471.761 0.04729 0.13752100 101 0.04463614.13161.0100 15.1416 24.267 49.31573.582 0.04772 0.14079101 102 0.04609414.15681.0448 15.2016 24.508 50.94575.453 0.04815 0.14413102 103 0.04759614.18211.0807 15.2628 24.748 52.62677.374 0.04858 0.14756103 104 0.04914514.20741.1178 15.3252 24.989 54.35979.348 0.04901 0.15108104 105 0.05074114.23261.1561 15.3887 25.229 56.14681.375 0.04943 0.15469105 106 0.05238614.25791.1957 15.4535 25.470 57.98983.459 0.04986 0.15839106 107 0.05408214.28311.2365 15.5196 25.710 59.88985.600 0.05028 0.16219107 108 0.05583014.30841.2787 15.5871 25.951 61.84987.800 0.05071 0.16608108 109 0.05763214.33371.3222 15.6559 26.191 63.87090.061 0.05113 0.17008109 110 0.05949014.35891.3672 15.7261 26.432 65.954 92.3860.05155 0.17419110 111 0.06140514.38421.4136 15.7978 26.672 68.104 94.7770.05197 0.17840111 112 0.06338014.40951.4615 15.8710 26.913 70.321 97.2340.05240 0.18272112 113 0.06541614.43471.5111 15.9458 27.154 72.608 99.7620.05282 0.18716113 114 0.06751614.46001.5622 16.0222 27.394 74.967102.3620.05324 0.19172114 115 0.06968014.48521.6150 16.1003 27.635 77.401105.0360.05365 0.19640115 116 0.07191314.51051.6696 16.1801 27.875 79.911107.7870.05407 0.20121116 117 0.07421514.53581.7259 16.2617 28.116 82.502110.6170.05449 0.20615117 118 0.07659014.56101.7842 16.3452 28.356 85.174113.5300.05491 0.21123118 119 0.07904014.58631.8443 16.4306 28.597 87.932116.5290.05532 0.21644119 120 0.08156614.61161.9065 16.5180 28.83890.777 119.6150.05574 0.22180120 121 0.08417314.63681.9707 16.6075 29.07893.714 122.7920.05615 0.22731121 122 0.08686314.66212.0370 16.6991 29.31996.746 126.0640.05657 0.23298122 123 0.08963814.68732.1056 16.7929 29.55999.875 129.4340.05698 0.23881123 124 0.09250314.71262.1765 16.8891 29.800 103.105 132.9050.05739 0.24480124 125 0.09545914.73792.2498 16.9876 30.041 106.441 136.4810.05781 0.25096125 126 0.09851014.76312.3255 17.0886 30.281 109.885 140.1660.05822 0.25730126 127 0.10166114.78842.4038 17.1922 30.522 113.442 143.9640.05863 0.26382127 128 0.10491414.81362.4848 17.2985 30.763 117.116 147.8790.05904 0.27054128 129 0.10827314.83892.5686 17.4075 31.003 120.912 151.9150.05945 0.27745129 14. 1.62009 ASHRAE HandbookFundamentalsTable 2 Thermodynamic Properties of Moist Air at Standard Atmospheric Pressure, 14.696 psia (Concluded )Temp., FHumidity RatioSpecific Volume, ft3/lbda Specific Enthalpy, Btu/lbdaSpecific Entropy, Btu/lbda F Temp., F tWs , lbw /lbdavda vas vs hda has hssdasst 130 0.11174214.8641 2.6552 17.5194 31.244124.833 156.077 0.05985 0.28457130 131 0.11532614.8894 2.7449 17.6343 31.485128.886 160.370 0.06026 0.29190131 132 0.11902914.9147 2.8376 17.7523 31.725133.074 164.799 0.06067 0.29945132 133 0.12285614.9399 2.9336 17.8735 31.966137.404 169.370 0.06108 0.30723133 134 0.12681114.9652 3.0329 17.9981 32.207141.880 174.087 0.06148 0.31525134 135 0.13089914.9904 3.1357 18.1262 32.447146.510 178.957 0.06189 0.32352135 136 0.13512715.0157 3.2422 18.2579 32.688151.298 183.986 0.06229 0.33204136 137 0.13949915.0410 3.3525 18.3935 32.929156.252 189.181 0.06270 0.34083137 138 0.14402215.0662 3.4668 18.5330 33.170161.378 194.548 0.06310 0.34989138 139 0.14870215.0915 3.5851 18.6766 33.410166.684 200.095 0.06350 0.35925139 140 0.15354515.1167 3.7078 18.8245 33.651172.177 205.828 0.06390 0.36891140 141 0.15855815.1420 3.8350 18.9769 33.892177.866 211.757 0.06430 0.37888141 142 0.16375015.1672 3.9668 19.1340 34.133183.758 217.890 0.06470 0.38918142 143 0.16912715.1925 4.1036 19.2960 34.373189.863 224.236 0.06510 0.39982143 144 0.17469915.2177 4.2454 19.4632 34.614196.190 230.804 0.06550 0.41082144 145 0.18047315.2430 4.3927 19.6357 34.855202.750 237.605 0.06590 0.42219145 146 0.18646015.2683 4.5455 19.8138 35.096209.553 244.649 0.06630 0.43395146 147 0.19266815.2935 4.7042 19.9977 35.337216.610 251.947 0.06670 0.44612147 148 0.19910915.3188 4.8691 20.1878 35.577223.934 259.512 0.06709 0.45871148 149 0.20579415.3440 5.0404 20.3844 35.818231.538 267.356 0.06749 0.47175149 150 0.21273415.3693 5.2185 20.5878 36.059239.434 275.493 0.06789 0.48525150 151 0.21994215.3945 5.4037 20.7982 36.300247.638 283.938 0.06828 0.49925151 152 0.22743215.4198 5.5963 21.0161 36.541256.166 292.706 0.06867 0.51376152 153 0.23521815.4450 5.7969 21.2419 36.782265.032 301.814 0.06907 0.52881153 154 0.24331615.4703 6.0057 21.4759 37.023274.257 311.279 0.06946 0.54443154 155 0.25174115.4956 6.2232 21.7187 37.263283.857 321.121 0.06985 0.56065155 156 0.26051215.5208 6.4498 21.9706 37.504293.854 331.359 0.07024 0.57750156 157 0.26964715.5461 6.6862 22.2323 37.745304.270 342.015 0.07063 0.59501157 158 0.27916715.5713 6.9328 22.5041 37.986315.127 353.113 0.07103 0.61322158 159 0.28909315.5966 7.1902 22.7868 38.227326.451 364.678 0.07142 0.63217159 160 0.29945015.6218 7.4591 23.0809 38.468338.268 376.736 0.07180 0.65190160 161 0.31026215.6471 7.7401 23.3872 38.709350.609 389.318 0.07219 0.67245161 162 0.32155615.6723 8.0340 23.7063 38.950363.504 402.454 0.07258 0.69389162 163 0.33336315.6976 8.3415 24.0391 39.191376.988 416.179 0.07297 0.71625163 164 0.34571515.7228 8.6636 24.3864 39.432391.097 430.529 0.07335 0.73959164 165 0.35864515.7481 9.0010 24.7491 39.673405.871 445.544 0.07374 0.76399165 166 0.37219315.7733 9.3550 25.1283 39.914421.354 461.268 0.07413 0.78950166 167 0.38639915.7986 9.7265 25.5251 40.155437.594 477.749 0.07451 0.81621167 168 0.40130715.823810.1168 25.9406 40.396454.641 495.037 0.07490 0.84418168 169 0.41696815.849110.5272 26.3763 40.637472.553 513.190 0.07528 0.87351169 170 0.43343515.874310.9591 26.8334 40.878491.391 532.269 0.07566 0.90430170 171 0.45076715.899611.4141 27.3137 41.119511.224 552.343 0.07604 0.93664171 172 0.46902915.924811.8939 27.8188 41.360532.125 573.485 0.07643 0.97066172 173 0.48829315.950112.4006 28.3507 41.601554.177 595.778 0.07681 1.00649173 174 0.50863615.975312.9361 28.9114 41.842577.471 619.313 0.07719 1.04425174 175 0.53014816.000613.5029 29.5035 42.083602.109 644.192 0.07757 1.08412175 176 0.55292616.025814.1035 30.1293 42.324628.201 670.525 0.07795 1.12627176 177 0.57707816.051114.7408 30.7919 42.565655.873 698.439 0.07833 1.17088177 178 0.60272616.076315.4182 31.4946 42.807685.265 728.072 0.07871 1.21818178 179 0.63000516.101616.1393 32.2409 43.048716.533 759.581 0.07908 1.26840179 180 0.65906816.126816.9081 33.0349 43.289749.853 793.142 0.07946 1.32183180 181 0.69009016.152117.7293 33.8814 43.530785.424 828.954 0.07984 1.37876181 182 0.72326516.177318.6082 34.7855 43.771823.471 867.242 0.08021 1.43955182 183 0.75881616.202619.5506 35.7532 44.012864.252 908.264 0.08059 1.50459183 184 0.79699916.227820.5636 36.7915 44.253908.058 952.311 0.08096 1.57433184 185 0.83810616.253121.6549 37.9080 44.495955.227 999.722 0.08134 1.64930185 186 0.88247416.278322.8335 39.1118 44.736 1006.1481050.884 0.08171 1.73010186 187 0.93049716.303624.1100 40.4136 44.977 1061.2711106.248 0.08209 1.81742187 188 0.98263216.328825.4966 41.8255 45.218 1121.1231166.341 0.08246 1.91207188 189 1.03941516.354127.0078 43.3619 45.460 1186.3211231.780 0.08283 2.01501189 190 1.10148116.379328.6605 45.0398 45.701 1257.5961303.297 0.08320 2.12736190 191 1.16958816.404630.4750 46.8796 45.942 1335.8181381.760 0.08357 2.25046191 192 1.24464216.429832.4757 48.9056 46.183 1422.0301468.214 0.08394 2.38593192 193 1.32774316.455134.6920 51.1471 46.425 1517.4991563.924 0.08431 2.53570193 194 1.42023616.480337.1600 53.6403 46.666 1623.7701670.436 0.08468 2.70217194 195 1.52378116.505639.9242 56.4297 46.907 1742.7541789.661 0.08505 2.88826195 196 1.64045716.530843.0402 59.5710 47.149 1876.8411923.990 0.08542 3.09767196 197 1.77289916.556146.5787 63.1348 47.390 2029.0622076.452 0.08579 3.33503197 198 1.92449416.581350.6306 67.2119 47.631 2203.3152250.946 0.08616 3.60635198 199 2.09967916.606655.3146 71.9212 47.873 2404.7022452.574 0.08652 3.91946199 200 2.30437216.631860.7896 77.4214 48.114 2640.0312688.145 0.08689 4.28482200 15. Psychrometrics1.7 Table 3 Thermodynamic Properties of Water at SaturationTemp., AbsoluteSpecific Volume, ft3/lbwSpecific Enthalpy, Btu/lbw Specific Entropy, Btu/lbw FTemp.,F Pressure Sat. Solid Evap.Sat. VaporSat. SolidEvap.Sat. Vapor Sat. Solid Evap.Sat. Vapor F t pws , psia vi /vf vig /vfgvg hi /hfhig /hfghgsi /sf sig /sfgsg t800.000116 0.0173219538071953807193.381219.19 1025.81 0.40643.2112 2.8048 80790.000125 0.0173218146351814635192.981219.23 1026.25 0.40543.2029 2.7975 79780.000135 0.0173216860361686036192.591219.28 1026.69 0.40433.1946 2.7903 78770.000145 0.0173215671591567159192.191219.33 1027.13 0.40333.1864 2.7831 77760.000157 0.0173214572241457224191.801219.38 1027.58 0.40233.1782 2.7759 76750.000169 0.0173313555191355519191.401219.42 1028.02 0.40123.1700 2.7688 75740.000182 0.0173312613901261390191.001219.46 1028.46 0.40023.1619 2.7617 74730.000196 0.0173311742391174239190.601219.51 1028.90 0.39923.1539 2.7547 73720.000211 0.0173310935181093518190.201219.55 1029.35 0.39813.1458 2.7477 72710.000227 0.0173310187241018724189.801219.59 1029.79 0.39713.1379 2.7408 71700.000244 0.01733 949394949394 189.401219.63 1030.23 0.39613.1299 2.7338 70690.000263 0.01733 885105885105 189.001219.67 1030.67 0.39503.1220 2.7270 69680.000283 0.01733 825469825469 188.591219.71 1031.11 0.39403.1141 2.7201 68670.000304 0.01733 770128770128 188.191219.75 1031.56 0.39303.1063 2.7133 67660.000326 0.01734 718753718753 187.781219.78 1032.00 0.39193.0985 2.7065 66650.000350 0.01734 671043671043 187.381219.82 1032.44 0.39093.0907 2.6998 65640.000376 0.01734 626720626720 186.971219.85 1032.88 0.38993.0830 2.6931 64630.000404 0.01734 585529585529 186.561219.89 1033.33 0.38883.0753 2.6865 63620.000433 0.01734 547234547234 186.151219.92 1033.77 0.38783.0677 2.6799 62610.000464 0.01734 511620511620 185.741219.95 1034.21 0.38683.0601 2.6733 61600.000498 0.01734 478487478487 185.331219.98 1034.65 0.38583.0525 2.6667 60590.000533 0.01734 447651447651 184.921220.01 1035.09 0.38473.0449 2.6602 59580.000571 0.01735 418943418943 184.501220.04 1035.54 0.38373.0374 2.6537 58570.000612 0.01735 392207392207 184.091220.07 1035.98 0.38273.0299 2.6473 57560.000655 0.01735 367299367299 183.671220.09 1036.42 0.38163.0225 2.6409 56550.000701 0.01735 344086344086 183.261220.12 1036.86 0.38063.0151 2.6345 55540.000749 0.01735 322445322445 182.841220.15 1037.30 0.37963.0077 2.6282 54530.000801 0.01735 302263302263 182.421220.17 1037.75 0.37853.0004 2.6219 53520.000857 0.01735 283436283436 182.001220.19 1038.19 0.37752.9931 2.6156 52510.000916 0.01736 265866265866 181.581220.21 1038.63 0.37652.9858 2.6093 51500.000978 0.01736 249464249464 181.161220.24 1039.07 0.37552.9786 2.6031 50490.001045 0.01736 234148234148 180.741220.26 1039.52 0.37442.9714 2.5970 49480.001115 0.01736 219841219841 180.321220.28 1039.96 0.37342.9642 2.5908 48470.001191 0.01736 206472206472 179.891220.29 1040.40 0.37242.9571 2.5847 47460.001270 0.01736 193976193976 179.471220.31 1040.84 0.37132.9500 2.5786 46450.001355 0.01736 182292182292 179.041220.33 1041.28 0.37032.9429 2.5726 45440.001445 0.01736 171363171363 178.621220.34 1041.73 0.36932.9359 2.5666 44430.001540 0.01737 161139161139 178.191220.36 1042.17 0.36832.9288 2.5606 43420.001641 0.01737 151570151570 177.761220.37 1042.61 0.36722.9219 2.5546 42410.001749 0.01737 142611142611 177.331220.38 1043.05 0.36622.9149 2.5487 41400.001862 0.01737 134222134222 176.901220.39 1043.49 0.36522.9080 2.5428 40390.001983 0.01737 126363126363 176.471220.41 1043.94 0.36422.9011 2.5370 39380.002111 0.01737 118999118999 176.041220.41 1044.38 0.36312.8942 2.5311 38370.002246 0.01737 112096112096 175.601220.42 1044.82 0.36212.8874 2.5253 37360.002389 0.01738 105624105625 175.171220.43 1045.26 0.36112.8806 2.5196 36350.002541 0.0173899555 99555 174.731220.44 1045.70 0.36002.8739 2.5138 35340.002701 0.0173893860 93860 174.301220.44 1046.15 0.35902.8671 2.5081 34330.002871 0.0173888516 88516 173.861220.45 1046.59 0.35802.8604 2.5024 33320.003051 0.0173883500 83500 173.421220.45 1047.03 0.35702.8537 2.4968 32310.003241 0.0173878790 78790 172.981220.45 1047.47 0.35592.8471 2.4911 31300.003442 0.01738 7436674366 172.541220.46 1047.91 0.35492.8405 2.4855 30290.003654 0.01738 7020970209 172.101220.46 1048.36 0.35392.8339 2.4800 29280.003878 0.01739 6630366303 171.661220.46 1048.80 0.35292.8273 2.4744 28270.004115 0.01739 6263162631 171.221220.46 1049.24 0.35182.8208 2.4689 27260.004365 0.01739 5917959179 170.771220.45 1049.68 0.35082.8143 2.4634 26250.004629 0.01739 5593155931 170.331220.45 1050.12 0.34982.8078 2.4580 25240.004908 0.01739 5287652876 169.881220.45 1050.56 0.34882.8013 2.4525 24230.005202 0.01739 5000050001 169.431220.44 1051.01 0.34772.7949 2.4471 23220.005512 0.01739 4729447294 168.991220.43 1051.45 0.34672.7885 2.4418 22210.005839 0.01740 4474544745 168.541220.43 1051.89 0.34572.7821 2.4364 21200.006184 0.01740 4234542345 168.091220.42 1052.33 0.34472.7758 2.4311 20190.006548 0.01740 4008440084 167.641220.41 1052.77 0.34362.7694 2.4258 19180.006932 0.01740 3795337953 167.191220.40 1053.21 0.34262.7632 2.4205 18170.007335 0.01740 3594435944 166.731220.39 1053.65 0.34162.7569 2.4153 17160.007761 0.01740 3405034050 166.281220.38 1054.10 0.34062.7506 2.4101 16150.008209 0.01740 3226432264 165.821220.36 1054.54 0.33962.7444 2.4049 15140.008681 0.01741 3058030580 165.371220.35 1054.98 0.33852.7382 2.3997 14Note: Subscript i denotes values for t 32F and subscript f denotes values for t 32F. 16. 1.82009 ASHRAE HandbookFundamentalsTable 3 Thermodynamic Properties of Water at Saturation (Continued )Temp.,AbsoluteSpecific Volume, ft3/lbw Specific Enthalpy, Btu/lbw Specific Entropy, Btu/lbw FTemp.,FPressure Sat. SolidEvap. Sat. VaporSat. Solid Evap.Sat. Vapor Sat. Solid Evap.Sat. Vapor F tpws , psia vi /vfvig /vfg vg hi /hf hig /hfghgsi /sf sig /sfgsg t13 0.0091770.01741 2899028990 164.911220.33 1055.42 0.33752.7321 2.3946 1312 0.0097000.01741 2749027490 164.461220.32 1055.86 0.33652.7259 2.3895 1211 0.0102490.01741 2607326073 164.001220.30 1056.30 0.33552.7198 2.3844 1110 0.0108270.01741 2473624736 163.541220.28 1056.74 0.33442.7137 2.3793 10 9 0.0114350.01741 2347323473 163.081220.26 1057.18 0.33342.7077 2.37439 8 0.0120750.01741 2227922279 162.621220.24 1057.63 0.33242.7016 2.36928 7 0.0127470.01742 2115121152 162.151220.22 1058.07 0.33142.6956 2.36427 6 0.0134530.01742 2008620086 161.691220.20 1058.51 0.33032.6896 2.35936 5 0.0141940.01742 1907819078 161.231220.17 1058.95 0.32932.6837 2.35435 4 0.0149740.01742 1812518125 160.761220.15 1059.39 0.32832.6777 2.34944 3 0.0157920.01742 1722317223 160.291220.12 1059.83 0.32732.6718 2.34453 2 0.0166510.01742 1637016370 159.831220.10 1060.27 0.32632.6659 2.33962 1 0.0175530.01742 1556315563 159.361220.07 1060.71 0.32522.6600 2.334810 0.0184990.01743 1479914799 158.891220.04 1061.15 0.32422.6542 2.330001 0.0194920.01743 1407614076 158.421220.01 1061.59 0.32322.6483 2.325112 0.0205330.01743 1339113391 157.951219.98 1062.03 0.32222.6425 2.320423 0.0216250.01743 1274212742 157.481219.95 1062.47 0.32122.6368 2.315634 0.0227700.01743 1212712127 157.001219.92 1062.91 0.32012.6310 2.310945 0.0239710.01743 1154511545 156.531219.88 1063.35 0.31912.6253 2.306256 0.0252290.01743 1099210992 156.051219.85 1063.79 0.31812.6196 2.301567 0.0265470.01744 1046910469 155.581219.81 1064.23 0.31712.6139 2.296878 0.0279290.017449972 9972 155.101219.77 1064.67 0.31602.6082 2.292189 0.0293750.017449501 9501 154.621219.74 1065.11 0.31502.6025 2.28759 10 0.0308900.017449055 9055 154.151219.70 1065.55 0.31402.5969 2.282910 11 0.0324760.017448631 8631 153.671219.66 1065.99 0.31302.5913 2.278311 12 0.0341360.017448228 8228 153.181219.61 1066.43 0.31202.5857 2.273812 13 0.0358740.017447846 7846 152.701219.57 1066.87 0.31092.5802 2.269213 14 0.0376920.017457484 7484 152.221219.53 1067.31 0.30992.5746 2.264714 15 0.0395930.017457139 7139 151.741219.48 1067.75 0.30892.5691 2.260215 16 0.0415820.017456812 6812 151.251219.44 1068.19 0.30792.5636 2.255716 17 0.0436620.017456501 6501 150.771219.39 1068.63 0.30692.5581 2.251317 18 0.0458370.017456205 6205 150.281219.34 1069.06 0.30582.5527 2.246818 19 0.0481090.017455925 5925 149.791219.29 1069.50 0.30482.5473 2.242419 20 0.0504850.017465658 5658 149.301219.24 1069.94 0.30382.5418 2.238020 21 0.0529670.017465404 5404 148.811219.19 1070.38 0.30282.5364 2.233721 22 0.0555600.017465162 5162 148.321219.14 1070.82 0.30182.5311 2.229322 23 0.0582680.017464932 4932 147.831219.09 1071.26 0.30072.5257 2.225023 24 0.0610960.017464714 4714 147.341219.03 1071.69 0.29972.5204 2.220724 25 0.0640480.017464506 4506 146.851218.98 1072.13 0.29872.5151 2.216425 26 0.0671300.017464308 4308 146.351218.92 1072.57 0.29772.5098 2.212126 27 0.0703470.017474119 4119 145.861218.86 1073.01 0.29672.5045 2.207827 28 0.0737040.017473939 3939 145.361218.80 1073.44 0.29572.4992 2.203628 29 0.0772060.017473768 3768 144.861218.74 1073.88 0.29462.4940 2.199429 30 0.0808580.017473605 3605 144.361218.68 1074.32 0.29362.4888 2.195230 31 0.0846680.017473450 3450 143.861218.62 1074.76 0.29262.4836 2.191031 32 0.0886400.017473302 3302 143.361218.56 1075.19 0.29162.4784 2.186832 32 0.08865 0.016023302.023302.04 0.02 1075.21 1075.190.00002.1869 2.186832 33 0.09229 0.016023178.063178.080.99 1074.64 1075.630.00202.1813 2.183333 34 0.09607 0.016023059.303059.322.00 1074.07 1076.070.00412.1757 2.179734 35 0.09998 0.016022945.512945.523.00 1073.50 1076.510.00612.1701 2.176235 36 0.10403 0.016022836.452836.464.01 1072.93 1076.950.00812.1646 2.172736 37 0.10823 0.016022731.912731.925.02 1072.37 1077.380.01022.1591 2.169337 38 0.11258 0.016022631.682631.706.02 1071.80 1077.820.01222.1536 2.165838 39 0.11708 0.016022535.572535.597.03 1071.23 1078.260.01422.1482 2.162439 40 0.12173 0.016022443.392443.418.03 1070.67 1078.700.01622.1427 2.159040 41 0.12656 0.016022354.972354.989.04 1070.10 1079.140.01822.1373 2.155641 42 0.13155 0.016022270.132270.15 10.04 1069.53 1079.570.02022.1319 2.152242 43 0.13671 0.016022188.722188.74 11.05 1068.97 1080.010.02222.1266 2.148843 44 0.14205 0.016022110.582110.60 12.05 1068.40 1080.450.02422.1212 2.145444 45 0.14757 0.016022035.582035.59 13.05 1067.84 1080.890.02622.1159 2.142145 46 0.15328 0.016021963.561963.58 14.06 1067.27 1081.330.02822.1106 2.138846 47 0.15919 0.016021894.411894.42 15.06 1066.70 1081.760.03022.1053 2.135547 48 0.16530 0.016021827.991828.00 16.06 1066.14 1082.200.03212.1001 2.132248 49 0.17161 0.016021764.191764.20 17.06 1065.57 1082.640.03412.0948 2.128949 50 0.17813 0.016021702.881702.90 18.07 1065.01 1083.070.03612.0896 2.125750 51 0.18487 0.016021643.981643.99 19.07 1064.44 1083.510.03812.0844 2.122551 52 0.19184 0.016031587.361587.38 20.07 1063.88 1083.950.04002.0792 2.119252*Extrapolated to represent metastable equilibrium with undercooled liquid. 17. Psychrometrics 1.9 Table 3 Thermodynamic Properties of Water at Saturation (Continued )Temp., AbsoluteSpecific Volume, ft3/lbw Specific Enthalpy, Btu/lbw Specific Entropy, Btu/lbw FTemp.,F Pressure Sat. Solid Evap. Sat. Vapor Sat. Solid Evap.Sat. Vapor Sat. Solid Evap.Sat. Vapor F t pws , psia vi /vf vig /vfg vghi /hf hig /hfghgsi /sf sig /sfgsg t53 0.19903 0.016031532.941532.96 21.07 1063.31 1084.380.04202.0741 2.11605354 0.20646 0.016031480.621480.64 22.07 1062.75 1084.820.04392.0689 2.11295455 0.21414 0.016031430.311430.32 23.07 1062.18 1085.260.04592.0638 2.10975556 0.22206 0.016031381.921381.94 24.08 1061.62 1085.690.04782.0587 2.10655657 0.23024 0.016031335.381335.39 25.08 1061.05 1086.130.04972.0536 2.10345758 0.23868 0.016031290.601290.61 26.08 1060.49 1086.560.05172.0486 2.10035859 0.24740 0.016031247.511247.53 27.08 1059.92 1087.000.05362.0435 2.09725960 0.25639 0.016031206.051206.07 28.08 1059.36 1087.440.05552.0385 2.09416061 0.26567 0.016041166.141166.16 29.08 1058.79 1087.870.05752.0335 2.09106162 0.27524 0.016041127.721127.74 30.08 1058.23 1088.310.05942.0285 2.08796263 0.28511 0.016041090.731090.74 31.08 1057.66 1088.740.06132.0236 2.08496364 0.29529 0.016041055.111055.12 32.08 1057.10 1089.180.06322.0186 2.08186465 0.30579 0.016041020.801020.82 33.08 1056.53 1089.610.06512.0137 2.07886566 0.31662 0.01604 987.75 987.77 34.08 1055.97 1090.050.06702.0088 2.07586667 0.32777 0.01605 955.91 955.93 35.08 1055.40 1090.480.06892.0039 2.07286768 0.33927 0.01605 925.23 925.25 36.08 1054.84 1090.920.07081.9990 2.06996869 0.35113 0.01605 895.67 895.68 37.08 1054.27 1091.350.07271.9942 2.06696970 0.36334 0.01605 867.17 867.19 38.08 1053.71 1091.780.07461.9894 2.06407071 0.37592 0.01605 839.70 839.72 39.08 1053.14 1092.220.07651.9846 2.06107172 0.38889 0.01606 813.21 813.23 40.08 1052.57 1092.650.07841.9798 2.05817273 0.40224 0.01606 787.67 787.69 41.08 1052.01 1093.080.08021.9750 2.05527374 0.41599 0.01606 763.04 763.06 42.08 1051.44 1093.520.08211.9702 2.05237475 0.43015 0.01606 739.28 739.30 43.07 1050.88 1093.950.08401.9655 2.04957576 0.44473 0.01606 716.36 716.38 44.07 1050.31 1094.380.08591.9607 2.04667677 0.45973 0.01607 694.25 694.26 45.07 1049.74 1094.820.08771.9560 2.04387778 0.47518 0.01607 672.90 672.92 46.07 1049.18 1095.250.08961.9513 2.04097879 0.49108 0.01607 652.31 652.32 47.07 1048.61 1095.680.09141.9467 2.03817980 0.50744 0.01607 632.43 632.44 48.07 1048.05 1096.110.09331.9420 2.03538081 0.52427 0.01608 613.23 613.25 49.07 1047.48 1096.550.09511.9374 2.03258182 0.54159 0.01608 594.70 594.72 50.07 1046.91 1096.980.09701.9328 2.02978283 0.55940 0.01608 576.80 576.82 51.07 1046.34 1097.410.09881.9281 2.02708384 0.57772 0.01608 559.52 559.54 52.06 1045.78 1097.840.10071.9236 2.02428485 0.59656 0.01609 542.83 542.84 53.06 1045.21 1098.270.10251.9190 2.02158586 0.61593 0.01609 526.70 526.71 54.06 1044.64 1098.700.10431.9144 2.01888687 0.63585 0.01609 511.11 511.13 55.06 1044.07 1099.130.10621.9099 2.01608788 0.65632 0.01609 496.05 496.07 56.06 1043.51 1099.560.10801.9054 2.01338889 0.67736 0.01610 481.50 481.51 57.06 1042.94 1100.000.10981.9009 2.01078990 0.69899 0.01610 467.43 467.45 58.05 1042.37 1100.430.11161.8964 2.00809091 0.72122 0.01610 453.83 453.85 59.05 1041.80 1100.860.11341.8919 2.00539192 0.74405 0.01611 440.68 440.70 60.05 1041.23 1101.280.11521.8874 2.00279293 0.76751 0.01611 427.97 427.98 61.05 1040.67 1101.710.11711.8830 2.00009394 0.79161 0.01611 415.67 415.68 62.05 1040.10 1102.140.11891.8786 1.99749495 0.81636 0.01612 403.77 403.79 63.05 1039.53 1102.570.12071.8741 1.99489596 0.84178 0.01612 392.27 392.28 64.04 1038.96 1103.000.12251.8697 1.99229697 0.86788 0.01612 381.14 381.15 65.04 1038.39 1103.430.12421.8654 1.98969798 0.89468 0.01612 370.37 370.38 66.04 1037.82 1103.860.12601.8610 1.98709899 0.92220 0.01613 359.94 359.96 67.04 1037.25 1104.290.12781.8566 1.984599 100 0.95044 0.01613 349.85 349.87 68.04 1036.68 1104.710.12961.8523 1.9819 100 101 0.97943 0.01613 340.09 340.10 69.04 1036.11 1105.140.13141.8480 1.9794 101 102 1.00917 0.01614 330.63 330.65 70.03 1035.54 1105.570.13321.8437 1.9769 102 103 1.03970 0.01614 321.48 321.50 71.03 1034.97 1106.000.13501.8394 1.9743 103 104 1.07102 0.01614 312.62 312.63 72.03 1034.39 1106.420.13671.8351 1.9718 104 105 1.10315 0.01615 304.03 304.05 73.03 1033.82 1106.850.13851.8308 1.9693 105 106 1.13611 0.01615 295.72 295.73 74.03 1033.25 1107.280.14031.8266 1.9669 106 107 1.16992 0.01616 287.66 287.68 75.02 1032.68 1107.700.14201.8224 1.9644 107 108 1.20459 0.01616 279.86 279.88 76.02 1032.11 1108.130.14381.8181 1.9619 108 109 1.24014 0.01616 272.30 272.32 77.02 1031.53 1108.550.14551.8139 1.9595 109 110 1.27660 0.01617 264.97 264.99 78.02 1030.96 1108.980.14731.8098 1.9570 110 111 1.31397 0.01617 257.87 257.89 79.02 1030.39 1109.410.14901.8056 1.9546 111 112 1.35228 0.01617 250.99 251.01 80.02 1029.82 1109.830.15081.8014 1.9522 112 113 1.39155 0.01618 244.32 244.34 81.01 1029.24 1110.250.15251.7973 1.9498 113 114 1.43179 0.01618 237.85 237.87 82.01 1028.67 1110.680.15431.7931 1.9474 114 115 1.47304 0.01618 231.58 231.60 83.01 1028.09 1111.100.15601.7890 1.9450 115 116 1.51530 0.01619 225.50 225.51 84.01 1027.52 1111.530.15771.7849 1.9427 116 117 1.55860 0.01619 219.60 219.62 85.01 1026.94 1111.950.15951.7808 1.9403 117 118 1.60296 0.01620 213.88 213.90 86.00 1026.37 1112.370.16121.7767 1.9380 118 119 1.64839 0.01620 208.33 208.35 87.00 1025.79 1112.800.16291.7727 1.9356 119 120 1.69493 0.01620 202.95 202.96 88.00 1025.22 1113.220.16471.7686 1.9333 120 18. 1.10 2009 ASHRAE HandbookFundamentals Table 3 Thermodynamic Properties of Water at Saturation (Continued )Temp., AbsoluteSpecific Volume, ft3/lbwSpecific Enthalpy, Btu/lbw Specific Entropy, Btu/lbw FTemp.,F Pressure Sat. Solid Evap. Sat. VaporSat. Solid Evap.Sat. Vapor Sat. Solid Evap.Sat. Vapor F t pws , psia vi /vf vig /vfg vg hi /hf hig /hfghgsi /sf sig /sfgsg t 121 1.74259 0.01621197.72197.7489.00 1024.64 1113.640.16641.7646 1.9310 121 122 1.79140 0.01621192.65192.6790.00 1024.06 1114.060.16811.7606 1.9287 122 123 1.84137 0.01622187.73187.7591.00 1023.49 1114.480.16981.7565 1.9264 123 124 1.89254 0.01622182.96182.9792.00 1022.91 1114.910.17151.7526 1.9241 124 125 1.94492 0.01623178.32178.3492.99 1022.33 1115.330.17321.7486 1.9218 125 126 1.99853 0.01623173.82173.8493.99 1021.76 1115.750.17491.7446 1.9195 126 127 2.05341 0.01623169.45169.4794.99 1021.18 1116.170.17661.7406 1.9173 127 128 2.10957 0.01624165.21165.2295.99 1020.60 1116.590.17831.7367 1.9150 128 129 2.16704 0.01624161.09161.1096.99 1020.02 1117.010.18001.7328 1.9128 129 130 2.22584 0.01625157.09157.10 97.991019.44 1117.430.18171.7288 1.9106 130 131 2.28600 0.01625153.20153.22 98.991018.86 1117.850.18341.7249 1.9084 131 132 2.34754 0.01626149.42149.44 99.981018.28 1118.260.18511.7210 1.9061 132 133 2.41050 0.01626145.75145.77100.981017.70 1118.680.18681.7171 1.9039 133 134 2.47489 0.01626142.19142.21101.981017.12 1119.100.18851.7133 1.9018 134 135 2.54074 0.01627138.73138.74102.981016.54 1119.520.19021.7094 1.8996 135 136 2.60809 0.01627135.36135.38103.981015.96 1119.940.19181.7056 1.8974 136 137 2.67694 0.01628132.09132.10104.981015.37 1120.350.19351.7017 1.8953 137 138 2.74735 0.01628128.91128.92105.981014.79 1120.770.19521.6979 1.8931 138 139 2.81932 0.01629125.81125.83106.981014.21 1121.190.19691.6941 1.8910 139 140 2.89289 0.01629122.81122.82107.981013.62 1121.600.19851.6903 1.8888 140 141 2.96810 0.01630119.88119.90108.981013.04 1122.020.20021.6865 1.8867 141 142 3.04496 0.01630117.04117.06109.981012.46 1122.430.20191.6827 1.8846 142 143 3.12350 0.01631114.28114.29110.981011.87 1122.850.20351.6790 1.8825 143 144 3.20377 0.01631111.59111.60111.971011.29 1123.260.20521.6752 1.8804 144 145 3.28578 0.01632108.97108.99112.971010.70 1123.680.20681.6715 1.8783 145 146 3.36957 0.01632106.43106.44113.971010.12 1124.090.20851.6678 1.8762 146 147 3.45516 0.01633103.95103.97114.971009.53 1124.500.21011.6640 1.8742 147 148 3.54260 0.01633101.54101.56115.971008.94 1124.910.21181.6603 1.8721 148 149 3.63190 0.01634 99.20 99.22116.971008.35 1125.330.21341.6566 1.8701 149 150 3.72311 0.0163496.92 96.93 117.971007.77 1125.740.21511.6530 1.8680 150 151 3.81626 0.0163594.70 94.71 118.971007.18 1126.150.21671.6493 1.8660 151 152 3.91137 0.0163592.54 92.55 119.971006.59 1126.560.21831.6456 1.8640 152 153 4.00849 0.0163690.43 90.45 120.971006.00 1126.970.22001.6420 1.8620 153 154 4.10764 0.0163688.38 88.40 121.971005.41 1127.380.22161.6384 1.8599 154 155 4.20885 0.0163786.39 86.40 122.971004.82 1127.790.22321.6347 1.8580 155 156 4.31218 0.0163784.45 84.46 123.971004.23 1128.200.22491.6311 1.8560 156 157 4.41764 0.0163882.55 82.57 124.971003.64 1128.610.22651.6275 1.8540 157 158 4.52527 0.0163880.71 80.73 125.981003.04 1129.020.22811.6239 1.8520 158 159 4.63511 0.0163978.92 78.93 126.981002.45 1129.430.22971.6203 1.8500 159 160 4.74720.0163977.17077.186127.981001.86 1129.830.23131.6168 1.8481 160 161 4.86160.0164075.46775.483128.981001.26 1130.240.23291.6132 1.8461 161 162 4.97830.0164073.80873.824129.981000.67 1130.650.23461.6096 1.8442 162 163 5.09730.0164172.19172.207130.981000.08 1131.060.23621.6061 1.8423 163 164 5.21870.0164270.61670.632131.98 999.48 1131.460.23781.6026 1.8403 164 165 5.34260.0164269.08069.097132.98 998.88 1131.870.23941.5991 1.8384 165 166 5.46890.0164367.58467.600133.98 998.29 1132.270.24101.5955 1.8365 166 167 5.59780.0164366.12566.141134.98 997.69 1132.680.24261.5920 1.8346 167 168 5.72920.0164464.70364.720135.99 997.09 1133.080.24421.5886 1.8327 168 169 5.86320.0164463.31763.333136.99 996.49 1133.480.24581.5851 1.8308 169 170 5.99980.0164561.96561.982137.99 995.90 1133.890.24741.5816 1.8290 170 171 6.13900.0164560.64760.664138.99 995.30 1134.290.24891.5782 1.8271 171 172 6.28100.0164659.36259.379139.99 994.70 1134.690.25051.5747 1.8252 172 173 6.42580.0164758.10958.125141.00 994.10 1135.090.25211.5713 1.8234 173 174 6.57330.0164756.88656.903142.00 993.49 1135.490.25371.5678 1.8215 174 175 6.72370.0164855.69455.710143.00 992.89 1135.890.25531.5644 1.8197 175 176 6.87690.0164854.53154.547144.00 992.29 1136.290.25691.5610 1.8179 176 177 7.03310.0164953.39653.412145.00 991.69 1136.690.25841.5576 1.8160 177 178 7.19220.0165052.28952.305146.01 991.08 1137.090.26001.5542 1.8142 178 179 7.35440.0165051.20851.225147.01 990.48 1137.490.26161.5508 1.8124 179 180 7.51960.0165150.15450.171148.01 989.87 1137.890.26311.5475 1.8106 180 181 7.68790.0165149.12549.142149.02 989.27 1138.280.26471.5441 1.8088 181 182 7.85930.0165248.12148.138150.02 988.66 1138.680.26631.5408 1.8070 182 183 8.03390.0165347.14147.158151.02 988.05 1139.070.26781.5374 1.8052 183 184 8.21180.0165346.18446.201152.03 987.44 1139.470.26941.5341 1.8035 184 185 8.39300.0165445.25145.267153.03 986.84 1139.860.27091.5308 1.8017 185 186 8.57750.0165444.33944.355154.03 986.23 1140.260.27251.5274 1.7999 186 187 8.76530.0165543.44843.465155.04 985.62 1140.650.27411.5241 1.7982 187 188 8.95660.0165642.57942.596156.04 985.01 1141.050.27561.5208 1.7964 188 189 9.15140.0165641.73041.747157.04 984.39 1141.440.27721.5175 1.7947 189 19. Psychrometrics 1.11Table 3 Thermodynamic Properties of Water at Saturation (Continued )Temp.,AbsoluteSpecific Volume, ft3/lbwSpecific Enthalpy, Btu/lbw Specific Entropy, Btu/lbw FTemp.,FPressure Sat. Solid Evap. Sat. VaporSat. Solid Evap.Sat. Vapor Sat. Solid Evap.Sat. Vapor F tpws , psia vi /vf vig /vfg vg hi /hf hig /hfghgsi /sf sig /sfgsg t 1909.34970.0165740.90140.918158.05 983.78 1141.830.27871.5143 1.7930 190 1919.55150.0165840.09240.108159.05 983.17 1142.220.28021.5110 1.7912 191 1929.75700.0165839.30139.317160.06 982.55 1142.610.28181.5077 1.7895 192 1939.96620.0165938.52838.545161.06 981.94 1143.000.28331.5045 1.7878 193 194 10.17910.0165937.77337.790162.07 981.32 1143.390.28491.5012 1.7861 194 195 10.39580.0166037.03637.053163.07 980.71 1143.780.28641.4980 1.7844 195 196 10.61630.0166136.31536.332164.08 980.09 1144.170.28791.4948 1.7827 196 197 10.84070.0166135.61135.628165.08 979.47 1144.560.28951.4916 1.7810 197 198 11.06900.0166234.92434.940166.09 978.86 1144.940.29101.4884 1.7793 198 199 11.30130.0166334.25134.268167.09 978.24 1145.330.29251.4852 1.7777 199 200 11.53760.0166333.59433.611168.10 977.62 1145.710.29401.4820 1.7760 200 201 11.77810.0166432.95232.968169.10 976.99 1146.100.29561.4788 1.7743 201 202 12.02270.0166532.32432.341170.11 976.37 1146.480.29711.4756 1.7727 202 203 12.27150.0166531.71031.727171.12 975.75 1146.870.29861.4724 1.7710 203 204 12.52460.0166631.11031.127172.12 975.13 1147.250.30011.4693 1.7694 204 205 12.78190.0166730.52430.540173.13 974.50 1147.630.30161.4661 1.7678 205 206 13.04370.0166729.95029.967174.14 973.88 1148.010.30311.4630 1.7661 206 207 13.30990.0166829.38929.406175.14 973.25 1148.400.30471.4599 1.7645 207 208 13.58060.0166928.84028.857176.15 972.62 1148.780.30621.4567 1.7629 208 209 13.85580.0166928.30428.321177.16 972.00 1149.150.30771.4536 1.7613 209 210 14.13570.0167027.77927.796178.17 971.37 1149.530.30921.4505 1.7597 210 212 14.70940.0167126.76426.781180.18 970.11 1150.290.31221.4443 1.7565 212 214 15.30230.0167325.79225.809182.20 968.85 1151.040.31521.4382 1.7533 214 216 15.91490.0167424.86224.879184.21 967.58 1151.790.31821.4320 1.7502 216 218 16.54750.0167623.97123.988186.23 966.31 1152.540.32111.4259 1.7471 218 220 17.20080.0167723.11823.135188.25 965.03 1153.280.32411.4198 1.7440 220 222 17.87530.0167922.30122.317190.27 963.75 1154.020.32711.4138 1.7409 222 224 18.57140.0168021.51721.534192.29 962.47 1154.760.33001.4078 1.7378 224 226 19.28960.0168120.76620.783194.31 961.19 1155.490.33301.4018 1.7348 226 228 20.03070.0168320.04620.063196.33 959.89 1156.220.33591.3959 1.7318 228 230 20.79490.0168419.35619.373198.35 958.60 1156.950.33881.3899 1.7288 230 232 21.58300.0168618.69318.710200.37 957.30 1157.680.34181.3840 1.7258 232 234 22.39550.0168718.05718.074202.40 956.00 1158.400.34471.3782 1.7229 234 236 23.23290.0168917.44717.464204.42 954.69 1159.110.34761.3723 1.7199 236 238 24.09580.0169116.86116.878206.45 953.38 1159.830.35051.3665 1.7170 238 240 24.98490.0169216.29916.316208.47 952.06 1160.540.35341.3607 1.7141 240 242 25.90060.0169415.75815.775210.50 950.74 1161.240.35631.3550 1.7113 242 244 26.84360.0169515.23915.256212.53 949.42 1161.950.35921.3492 1.7084 244 246 27.81450.0169714.74014.757214.56 948.09 1162.650.36201.3435 1.7056 246 248 28.81400.0169814.26014.277216.59 946.75 1163.340.36491.3378 1.7028 248 250 29.84260.0170013.79913.816218.62 945.41 1164.030.36781.3322 1.7000 250 252 30.90090.0170213.35613.373220.65 944.07 1164.720.37061.3266 1.6972 252 254 31.98970.0170312.92912.946222.68 942.72 1165.410.37351.3209 1.6944 254 256 33.10950.0170512.51812.535224.72 941.37 1166.090.37631.3154 1.6917 256 258 34.26110.0170712.12312.140226.75 940.01 1166.760.37921.3098 1.6890 258 260 35.44500.0170811.74311.760228.79 938.65 1167.440.38201.3043 1.6862 260 262 36.66200.0171011.37711.394230.83 937.28 1168.100.38481.2988 1.6836 262 264 37.91270.0171211.02411.041232.87 935.90 1168.770.38761.2933 1.6809 264 266 39.19780.0171410.68510.702234.90 934.52 1169.430.39041.2878 1.6782 266 268 40.51810.0171510.35710.374236.94 933.14 1170.080.39321.2824 1.6756 268 270 41.87420.0171710.04210.059238.99 931.75 1170.730.39601.2769 1.6730 270 272 43.26690.01719 9.738 9.755241.03 930.35 1171.380.39881.2715 1.6704 272 274 44.69680.01721 9.445 9.462243.07 928.95 1172.020.40161.2662 1.6678 274 276 46.16470.01722 9.162 9.180245.12 927.54 1172.660.40441.2608 1.6652 276 278 47.67140.01724 8.890 8.907247.16 926.13 1173.300.40711.2555 1.6626 278 280 49.21750.01726 8.627 8.644249.21 924.71 1173.920.40991.2502 1.6601 280 282 50.80390.01728 8.373 8.390251.26 923.29 1174.550.41271.2449 1.6575 282 284 52.43130.01730 8.128 8.146253.31 921.86 1175.170.41541.2396 1.6550 284 286 54.10040.01731 7.892 7.909255.36 920.42 1175.780.41821.2344 1.6525 286 288 55.81210.01733 7.664 7.681257.41 918.98 1176.400.42091.2291 1.6500 288 290 57.56720.01735 7.444 7.461259.47 917.53 1177.000.42361.2239 1.6476 290 292 59.36640.01737 7.231 7.248261.52 916.08 1177.600.42641.2187 1.6451 292 294 61.21050.01739 7.025 7.043263.58 914.62 1178.200.42911.2136 1.6427 294 296 63.10030.01741 6.827 6.844265.64 913.15 1178.790.43181.2084 1.6402 296 298 65.03680.01743 6.635 6.652267.70 911.68 1179.380.43451.2033 1.6378 298 300 67.02060.01745 6.449 6.467269.76 910.20 1179.960.43721.1982 1.6354 300 20. 1.12 2009 ASHRAE HandbookFundamentals Densityof a moist air mixture is the ratio of total mass to totalpV = nRT(18)volume:or= (Mda + Mw)/V = (1/v)(1 + W) (11) ( pda + pw)V = (nda + nw)RT(19)where v is the moist air specific volume, ft3/lbda, as defined bywhere p = pda + pw is the total mixture pressure and n = nda + nw isEquation (26). the total number of moles in the mixture. From Equations (16) to (19), the mole fractions of dry air and water vapor are, respec-Humidity Parameters Involving Saturation tively, The following definitions of humidity parameters involve thexda = pda /( pda + pw) = pda /p(20)concept of moist air saturation: and Saturation humidity ratio Ws(t, p) is the humidity ratio ofmoist air saturated with respect to water (or ice) at the same temper- xw = pw /(pda + pw) = pw /p(21)ature t and pressure p. Degree of saturation is the ratio of air humidity ratio W toFrom Equations (8), (20), and (21), the humidity ratio W ishumidity ratio Ws of saturated moist air at the same temperature andpwpressure:W = 0.621945 -------------- -(22)p pwW- = ------ (12) Ws The degree of saturation is defined in Equation (12), where t, pp ws Relative humidity is the ratio of the mole fraction of waterWs = 0.621945 ----------------- (23)vapor xw in a given moist air sample to the mole fraction xws in an airp p wssample saturated at the same temperature and pressure:The term pws represents the saturation pressure of water vapor inxw the absence of air at the given temperature t. This pressure pws is a = ------- -(13) function only of temperature and differs slightly from the vapor x ws t, ppressure of water in saturated moist air.The relative humidity is defined in Equation (13). Substitut-Combining Equations (8), (12), and (13)ing Equation (21) for xw and xws,= ------------------------------------------------------------ (14) pw1 + 1 W s 0.621945= -------- (24)p wst, p Dew-point temperature td is the temperature of moist air satu-rated at pressure p, with the same humidity ratio W as that of theSubstituting Equation (23) for Ws into Equation (14),given sample of moist air. It is defined as the solution td ( p, W) of thefollowing equation: = -------------------------------------------- -(25)1 1 pw pWs( p, td) = W(15)Both and are zero for dry air and unity for saturated moist air. Thermodynamic wet-bulb temperature t* is the temperatureAt intermediate states, their values differ, substantially so at higherat which water (liquid or solid), by evaporating into moist air at dry-temperatures.bulb temperature t and humidity ratio W, can bring air to saturationThe specific volume v of a moist air mixture is expressed inadiabatically at the same temperature t* while total pressure p is terms of a unit mass of dry air:constant. This parameter is considered separately in the section onThermodynamic Wet-Bulb and Dew-Point Temperature. v = V/Mda = V/(28.966nda) (26) where V is the total volume of the mixture, Mda is the total mass ofPERFECT GAS RELATIONSHIPS FORdry air, and nda is the number of moles of dry air. By Equations (16)DRY AND MOIST AIRand (26), with the relation p = pda + pw, When moist air is considered a mixture of independent perfectgases (i.e., dry air and water vapor), each is assumed to obey the per- RTR da T v = ------------------------------------- = --------------- (27)fect gas equation of state as follows: 28.966 p p wp pwDry air:pdaV = nda RT (16)Using Equation (22),Water vapor: pwV = nw RT(17) RT 1 + 1.607858WR da T 1 + 1.607858W v = ------------------------------------------------- = ------------------------------------------------------- (28)28.966ppwherepda = partial pressure of dry airIn Equations (27) and (28), v is specific volume, T is absolute tem-pw= partial pressure of water vaporperature, p is total pressure, pw is partial pressure of water vapor, and V= total mixture volume W is humidity ratio.nda = number of moles of dry airIn specific units, Equation (28) may be expressed asnw= number of moles of water vapor R= universal gas constant, 1545.349 ftlbf /lb mol R v = 0.370486(t + 459.67)(1 + 1.607858W )/pT = absolute temperature, R where The mixture also obeys the perfect gas equation: v = specific volume, ft3/lbda 21. Psychrometrics1.13t = dry-bulb temperature, F 1093 0.556t* W s 0.240 t t* * W = humidity ratio, lbw /lbda W = --------------------------------------------------------------------------------------- (35) p = total pressure, in. Hg 1093 + 0.444t t*The enthalpy of a mixture of perfect gases equals the sum of the where t and t* are in F. Below freezing, the corresponding equa-individual partial enthalpies of the components. Therefore, the spe- tions arecific enthalpy of moist air can be written as follows: h*w 143.35 0.48(32 t*) (36)h = hda + Whg(29)1220 0.04t* W s 0.240 t t* *where hda is the specific enthalpy for dry air in Btu/lbda and hg is theW = ------------------------------------------------------------------------------------ (37)specific enthalpy for saturated water vapor in Btu/lbw at the temper- 1220 + 0.444t 0.48t*ature of the mixture. As an approximation, A wet/ice-bulb thermometer is imprecise when determininghda 0.240t (30)moisture content at 32F. hg 1061 + 0.444t(31)The dew-point temperature td of moist air with humidity ratio W and pressure p was defined as the solution td (p, w) of Ws ( p, td).where t is the dry-bulb temperature in F. The moist air specificFor perfect gases, this reduces toenthalpy in Btu/lb da then becomes pws(td) = pw = ( pW )/(0.621945 + W) (38) h = 0.240t + W(1061 + 0.444t) (32) where pw is the water vapor partial pressure for the moist air sample THERMODYNAMIC WET-BULB ANDand pws(td) is the saturation vapor pressure at temperature td . TheDEW-POINT TEMPERATUREsaturation vapor pressure is obtained from Table 3 or by using Equa- tion (5) or (6). Alternatively, the dew-point temperature can be cal- For any state of moist air, a temperature t* exists at which liquid culated directly by one of the following equations (Peppers 1988):(or solid) water evaporates into the air to bring it to saturation atexactly this same temperature and total pressure (Harrison 1965). Between dew points of 32 to 200F,During adiabatic saturation, saturated air is expelled at a temper-td = C14 + C15 + C16 2 + C17 3 + C18 ( pw )0.1984(39)ature equal to that of the injected water. In this constant-pressureprocess,Below 32F, Humidity ratio increases from initial value W to Ws*, correspond-td = 90.12 + 26.142 + 0.89272(40)ing to saturation at temperature t* Enthalpy increases from initial value h to hs*, corresponding to wheresaturation at temperature t*td = dew-point temperature, F Mass of water added per unit mass of dry air is (Ws* W), which = ln pwadds energy to the moist air of amount (Ws* W)hw*, where pw =water vapor partial pressure, psiahw* denotes specific enthalpy in Btu/lbw of water added at tem- C14 =100.45perature t* C15 =33.193Therefore, if the process is strictly adiabatic, conservation of en-C16 =2.319thalpy at constant total pressure requires that C17 =0.17074C18 =1.2063h + (Ws*W)hw = hs **(33)Ws*, hw*, and hs* are functions only of temperature t* for a fixedNUMERICAL CALCULATION OFvalue of pressure. The value of t* that satisfies Equation (33) for MOIST AIR PROPERTIESgiven values of h, W, and p is the thermodynamic wet-bulb The following are outlines, citing equations and tables alreadytemperature. presented, for calculating moist air properties using perfect gas rela-A psychrometer consists of two thermometers; one thermome- tions. These relations are accurate enough for most engineering cal-ters bulb is covered by a wick that has been thoroughly wetted with culations in air-conditioning practice, and are readily adapted towater. When the wet bulb is placed in an airstream, water evaporates either hand or computer calculating methods. For more details, referfrom the wick, eventually reaching an equilibrium temperatureto Tables 15 through 18 in Chapter 1 of Olivieri (1996). Graphicalcalled the wet-bulb temperature. This process is not one of adia-procedures are discussed in the section on Psychrometric Charts.batic saturation, which defines the thermodynamic wet-bulb tem-perature, but one of simultaneous heat and mass transfer from theSITUATION 1.wet bulb. The fundamental mechanism of this process is describedGiven: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure pby the Lewis relation [Equation (38) in Chapter 5]. Fortunately, onlysmall corrections must be applied to wet-bulb thermometer readingsTo Obtain Use Commentsto obtain the thermodynamic wet-bulb temperature. pws (t*)Table 3 or Equation (5) or (6) Sat. press. for temp. t*As defined, thermodynamic wet-bulb temperature is a uniqueW s*Equation (23)Using pws (t*)property of a given moist air sample independent of measurement W Equation (35) or (37)techniques. pws (t) Table 3 or Equation (5) or (6) Sat. press. for temp. tEquation (33) is exact because it defines the thermodynamic wet-WsEquation (23)Using pws (t)bulb temperature t*. Substituting the approximate perfect gas rela- Equation (12)Using Wstion [Equation (32)] for h, the corresponding expression for hs*, and Equation (25)Using pws (t)the approximate relation for saturated liquid water v Equation (28)h Equation (32) h*w t* 32(34)pwEquation (38)into Equation (33), and solving for the humidity ratio, tdTable 3 with Equation (38), (39), or (40) 22. 1.142009 ASHRAE HandbookFundamentalsSITUATION 2. The dry-bulb temperature ranges covered by the charts are Given: Dry-bulb temperature t, Dew-point temperature td , Pressure