2021 ASHRAE Handbook Fundamentals (I P).pdf

2021 ASHRAE
HANDBOOK
FUNDAMENTALS
ASHRAE, 180 Technology Parkway, Peachtree Corners, GA 30092
www.ashrae.org
Inch-Pound Edition

© 2021 ASHRAE. All rights reserved.
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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 or
omissions 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 year
following their verification and, as soon as verified, on the ASHRAE website.
DISCLAIMER
ASHRAE 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 technical
data or editorial material in this publication does not constitute endorsement, warranty, or
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ASHRAE does not warrant that the information in this publication is free of errors. The
entire risk of the use of any information in this publication is assumed by the user.
ISBN 978-1-947192-89-8
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 forestry practices.

CONTENTS
Contributors
ASHRAE Technical Committees, Task Groups, and Technical Resource Groups
ASHRAE Research: Improving the Quality of Life
Preface
PRINCIPLES
Chapter 1. Psychrometrics (TC 1.1, Thermodynamics and Psychrometrics; TC 8.3, Absorption and Heat
Operated Machines)
2. Thermodynamics and Refrigeration Cycles (TC 1.1)
3. Fluid Flow (TC 1.3, Heat Transfer and Fluid Flow)
4. Heat Transfer (TC 1.3)
5. Two-Phase Flow (TC 1.3)
6. Mass Transfer (TC 1.3)
7. Fundamentals of Control (TC 1.4, Control Theory and Application)
8. Sound and Vibration (TC 2.6, Sound and Vibration)
INDOOR ENVIRONMENTAL QUALITY
Chapter 9. Thermal Comfort (TC 2.1, Physiology and Human Environment)
10. Indoor Environmental Health (Environmental Health Committee)
11. Air Contaminants (TC 2.3, Gaseous Air Contaminants and Gas Contaminant Removal
Equipment)
12. Odors (TC 2.3)
13. Indoor Environmental Modeling (TC 4.10, Indoor Environmental Modeling)
LOAD AND ENERGY CALCULATIONS
Chapter 14. Climatic Design Information (TC 4.2, Climatic Information)
15. Fenestration (TC 4.5, Fenestration)
16. Ventilation and Infiltration (TC 4.3, Ventilation Requirements and Infiltration)
17. Residential Cooling and Heating Load Calculations (TC 4.1, Load Calculation Data and
Procedures)
18. Nonresidential Cooling and Heating Load Calculations (TC 4.1)
19. Energy Estimating and Modeling Methods (TC 4.7, Energy Calculations)
HVAC DESIGN
Chapter 20. Space Air Diffusion (TC 5.3, Room Air Distribution)
21. Duct Design (TC 5.2, Duct Design)
22. Pipe Design (TC 6.1, Hydronic and Steam Equipment and Systems)
23. Insulation for Mechanical Systems (TC 1.8, Mechanical Systems Insulation)
24. Airflow Around Buildings (TC 4.3)
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BUILDING ENVELOPE
Chapter 25. Heat, Air, and Moisture Control in Building Assemblies—Fundamentals
(TC 4.4, Building Materials and Building Envelope Performance)
26. Heat, Air, and Moisture Control in Building Assemblies—Material Properties (TC 4.4)
27. Heat, Air, and Moisture Control in Building Assemblies—Examples (TC 4.4)
MATERIALS
Chapter 28. Combustion and Fuels (TC 6.10, Fuels and Combustion)
29. Refrigerants (TC 3.1, Refrigerants and Secondary Coolants)
30. Thermophysical Properties of Refrigerants (TC 3.1)
31. Physical Properties of Secondary Coolants (Brines) (TC 3.1)
32. Sorbents and Desiccants (TC 8.10, Mechanical and Desiccant Dehumidification Equipment,
Heat Pipes and Components)
33. Physical Properties of Materials (TC 1.3)
GENERAL
Chapter 34. Energy Resources (TC 2.8, Building Environmental Impacts and Sustainability)
35. Sustainability (TC 2.8)
36. Global Climate Change (TC 2.5, Global Climate Change)
37. Moisture Management in Buildings (TC 1.12, Moisture Management in Buildings)
38. Measurement and Instruments (TC 1.2, Instruments and Measurements)
39. Abbreviations and Symbols (TC 1.6, Terminology)
40. Units and Conversions (TC 1.6)
41. Codes and Standards
ADDITIONS AND CORRECTIONS
INDEX
Composite index to the 2018 Refrigeration, 2019 HVAC Applications, 2020 HVAC Systems and
Equipment, and 2021 Fundamentals volumes
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CONTRIBUTORS
In addition to the Technical Committees, the following individuals contributed significantly
to this volume. The appropriate chapter numbers follow each contributor’s name.
Kashif Nawaz (1, 4, 5)
Oak Ridge National Laboratory
Don Gatley (1)
Gatley & Associates, Inc.
Sebastian Herrmann (1)
Hochschule Zittau/Görlitz, University of
Applied Sciences
Reinhard Radermacher (2)
University of Maryland
Hoseong Lee (2)
Korea University
Rick Couvillion (3, 4, 6)
University of Arkansas
Michael Ohadi (4, 6)
University of Maryland
Mirza Shah (5)
Amir H. Shooshtari (6)
University of Maryland-College Park
David Kahn (7)
RMH Group
Marcelo Acosta (7)
Armstrong Fluid Technology
Christopher F. Benson (7)
University of Utah
Steve Wise (8)
Wise Associates
Eric Sturm (8)
Ingersoll-Rand/Trane
John Elson (9)
Kansas State University
Lan Chi Nguyen Weekes (10)
InAIR Environmental, Ltd.
Elliott Horner (10)
UL Environment
Andrew Persily (10)
National Institute of Standards and
Technology
Dennis Stanke (10)
Brian Krafthefer (11)
BCK Consulting
Ashish Mathur (11)
UVDI Inc.
Chang-Seo Lee (11)
Concordia University
Carolyn (Gemma) Kerr (11)
Didier Thevenard (14)
Canadian Solar
Michael Roth (14)
Klimaat Consulting & Innovation, Inc.
Christian Gueymard (14)
Solar Consulting Services
Peter Lyons (15)
Peter Lyons & Associates
Charlie Curcija (15)
Lawrence Berkeley National Laboratory
Joe Hetzel (15)
Door & Access Systems Manufacturers
Association
Brian A. Rock (16)
The University of Kansas
Steven J. Emmerich (16)
National Institute of Science and
Technology
Steven T. Taylor (16)
Taylor Engineering
Charles S. Barnaby (17)
Steve Bruning (18)
Newcomb & Boyd
James F. Pegues (18)
Carrier Corp.
Robert Doeffinger (18)
ZMM, Inc.
Erik Kolderup (19)
Kolderup Consulting
Timothy McDowell (19)
Thermal Energy Systems Specialists
Neal Kruis (19)
Big Ladder Software
Mitchell Paulus (19)
Texas A&M University
Malcolm Cook (19)
Loughborough University
John Pruett (19)
LEED AP ZMM Inc.
Sukjoon Oh (19)
Texas A&M University
Ron Judkoff (19)
National Renewable Energy Laboratory
Joel Neymark (19)
J. Neymark & Associates
Tianzhen Hong (19)
Lawrence Berkeley National Laboratory
Joe Huang (19)
White Box Technologies
Yuebin Yu (19)
University of Nebraska-Lincoln
Joshua New (19)
Ralph Muelheisen (19)
Argonne National Laboratory
Bass Abushakra (19)
U.S. Military Academy
Curtis Peters (20)
Nailor Industries
Kenneth J. Loudermilk (20)
Titus Products
Krishnan Viswanath (20)
Dynacraft Air Controls & Air Technology
& Systems
Ryan Johnson (20)
Price Industries, Inc.
Chad Huggins (20)
Krueger
James Aswegan (20)
Titus Products
Herman Behls (21)
Behls & Associates
Patrick J. Brooks (21)
Eastern Sheet Metal
Scott Fisher (22)
Steve Runyan (22)
State Farm Mutual Automobile Insurance
Company
Bert Blocken (24)
Eindhoven University of Technology
Ted Stathopoulos (24)
Concordia University
Yoshihide Tominaga (24)
Niigata Institute of Technology
Marcus Bianchi (25, 26)
Owens Corning
Hugo Hens (25, 26, 36)
University of Leuven
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Paulo Cesar Tabares Velasco (25)
Colorado School of Mines
Diana Fisler (25)
Johns Manville
Peter Adams (25)
Morrison Hershfield, Ltd.
Laverne Dalgleish (25)
Air Barrier Association of America, Inc.
Alexander G. McGowan (26, 36)
WSP Canada, Inc.
Samuel Glass (26)
U.S. Department of Agriculture, Forest
Products Laboratory
Hartwig Künzel (26, 36)
Fraunhofer Institüt für Bauphysik
Jonathan Kane (28)
UEI Test Instruments, Inc.
David Herrin (28)
University of Kentucky
Larry Brand (28)
Gas Technology Institute
Paul Sohler (28)
Crown Boiler Co.
Tom Neill (28)
Mestek Inc.
Cory Weiss (28)
Field Controls LLC
Mehdi M. Doura (28)
Lochinvar LLC
Bill Roy (28)
Timco Rubber
Jennifer Guerrero-Ferreira (28)
Bekaert Corporation
Barbara Minor (29)
Chemours Company
Van Baxter (29)
Mark McLinden (30)
National Institute of Standards and
Technology
Kevin Connor (31)
The Dow Chemical Company
Kevin R. Brown (34, 35)
ABM
Donald M. Brundage (34)
Southern Company Services
Douglas D. Fick (34, 35)
TRC Worldwide MEP
Costas Balaras (35)
National Observatory of Athens
Lew Harriman (36)
Mason-Grant Co.
Ed Light (36)
Building Dynamics, LLC
Florian Antretter (36)
Fraunhofer Institüt für Bauphysik
Terry Beck (37)
Kansas State University
John P. Scott (37)
CanmetENERGY, Natural Resources
Canada
Muhammad Tauha Ali (37)
Masdar Institute of Science and
Technology
Huojun Yang (37)
North Dakota State University
Stephen Idem (37)
Tennessee Technological University
ASHRAE HANDBOOK COMMITTEE
Michael P. Patton, Chair
2021 Fundamentals Volume Subcommittee: Bass Abushakra, Chair
Jason A. Atkisson Guy S. Frankenfield Kevin B. Gallen Javier C. Korenko Stephanie J. Mages
ASHRAE HANDBOOK STAFF
Mark S. Owen, Publisher
Director of Publications and Education
Heather E. Kennedy, Editor
David Soltis, Group Manager, and Jayne E. Jackson, Publication Traffic Administrator, Publishing Services
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ASHRAE TECHNICAL COMMITTEES, TASK GROUPS, AND
TECHNICAL RESOURCE GROUPS
SECTION 1.0—FUNDAMENTALS AND GENERAL
1.1 Thermodynamics and Psychrometrics
1.2 Instruments and Measurements
1.3 Heat Transfer and Fluid Flow
1.4 Control Theory and Application
1.5 Computer Applications
1.6 Terminology
1.7 Business, Management & General Legal Education
1.8 Mechanical Systems Insulation
1.9 Electrical Systems
1.10 Combined Heat and Power Systems
1.11 Electric Motors and Motor Control
1.12 Moisture Management in Buildings
1.13 Optimization
SECTION 2.0—ENVIRONMENTAL QUALITY
2.1 Physiology and Human Environment
2.2 Plant and Animal Environment
2.3 Gaseous Air Contaminants and Gas Contaminant Removal
Equipment
2.4 Particulate Air Contaminants and Particulate Contaminant
Removal Equipment
2.5 Global Climate Change
2.6 Sound and Vibration
2.7 Seismic, Wind and Flood Resistant Design
2.8 Building Environmental Impacts and Sustainability
2.9 Ultraviolet Air and Surface Treatment
2.10 Resilience and Security
SECTION 3.0—MATERIALS AND PROCESSES
3.1 Refrigerants and Secondary Coolants
3.2 Refrigerant System Chemistry and Contaminant Control
3.4 Lubrication
3.6 Water Treatment
3.8 Refrigerant Containment
SECTION 4.0—LOAD CALCULATIONS AND ENERGY
REQUIREMENTS
4.1 Load Calculation Data and Procedures
4.2 Climatic Information
4.3 Ventilation Requirements and Infiltration
4.4 Building Materials and Building Envelope Performance
4.5 Fenestration
4.7 Energy Calculations
4.10 Indoor Environmental Modeling
TRG4 Indoor Air Quality Procedure Development
SECTION 5.0—VENTILATION AND AIR DISTRIBUTION
5.1 Fans
5.2 Duct Design
5.3 Room Air Distribution
5.4 Industrial Process Air Cleaning (Air Pollution Control)
5.5 Air-to-Air Energy Recovery
5.6 Control of Fire and Smoke
5.7 Evaporative Cooling
5.9 Enclosed Vehicular Facilities
5.10 Kitchen Ventilation
5.11 Humidifying Equipment
SECTION 6.0—HEATING EQUIPMENT, HEATING AND
COOLING SYSTEMS AND APPLICATIONS
6.1 Hydronic and Steam Equipment and Systems
6.2 District Energy
6.3 Central Forced Air Heating and Cooling Systems
6.5 Radiant Heating and Cooling
6.6 Service Water Heating Systems
6.7 Solar and Other Renewable Energies
6.8 Geothermal Heat Pump and Energy Recovery Applications
6.9 Thermal Storage
6.10 Fuels and Combustion
SECTION 7.0—BUILDING PERFORMANCE
7.1 Integrated Building Design
7.2 HVAC&R Construction & Design Build Technologies
7.3 Operation, Maintenance and Cost Management
7.4 Exergy Analysis for Sustainable Buildings (EXER)
7.5 Smart Building Systems
7.6 Building Energy Performance
7.7 Testing and Balancing
7.8 Building Commissioning
SECTION 8.0—AIR-CONDITIONING AND REFRIGERATION
SYSTEM COMPONENTS
8.1 Positive Displacement Compressors
8.2 Centrifugal Machines
8.3 Absorption and Heat Operated Machines
8.4 Air-to-Refrigerant Heat Transfer Equipment
8.5 Liquid-to-Refrigerant Heat Exchangers
8.6 Cooling Towers and Evaporative Condensers
8.7 Variable Refrigerant Flow (VRF)
8.8 Refrigerant System Controls and Accessories
8.9 Residential Refrigerators and Food Freezers
8.10 Mechanical and Desiccant Dehumidification Equipment,
Heat Pipes and Components
8.11 Unitary and Room Air Conditioners and Heat Pumps
SECTION 9.0—BUILDING APPLICATIONS
9.1 Large Building Air-Conditioning Systems
9.2 Industrial Air Conditioning and Ventilation
9.3 Transportation Air Conditioning
9.6 Healthcare Facilities
9.7 Educational Facilities
9.8 Large Building Air-Conditioning Applications
9.9 Mission Critical Facilities, Data Centers, Technology
Spaces and Electronic Equipment
9.10 Laboratory Systems
9.11 Clean Spaces
9.12 Tall Buildings
TRG9 Cold Climate Design
SECTION 10.0—REFRIGERATION SYSTEMS
10.1 Custom Engineered Refrigeration Systems
10.2 Refrigeration Applications
10.3 Refrigerant Piping, Controls, and Accessories
10.6 Transport Refrigeration
10.7 Commercial Food and Beverage Refrigeration Equipment
SECTION MTG—MULTIDISCIPLINARY TASK GROUPS
MTG.ACR Air Change Rate
MTG.BIM Building Information Modeling
MTG.CFA Controlled Environment Agriculture
MTG.CYB Cybersecurity for HVAC Systems and Related
Infrastructure
MTG.EBO Effective Building Operations
MTG.HCDG Hot Climate Design Guide
MTG.HWBE Health and Wellness in the Built Environment
MTG.IAST Impact of ASHRAE Standards and Technology on
Energy Savings/Performance
MTG.LowGWP Lower Global Warming Potential Alternative
Refrigerants
MTG.OBB Occupant Behavior in Buildings
MTG.RAC Refrigeration and Air Conditioning Plant
Assessment Guide
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ASHRAE Research: Improving the Quality of Life
ASHRAE is the world’s foremost technical society in the fields
of heating, ventilation, air conditioning, and refrigeration. Its mem-
bers worldwide are individuals who share ideas, identify needs, sup-
port research, and write the industry’s standards for testing and
practice. The result is that engineers are better able to keep indoor
environments safe and productive while protecting and preserving
the outdoors for generations to come.
One of the ways that ASHRAE supports its members’ and indus-
try’s need for information is through ASHRAE Research. Thou-
sands of individuals and companies support ASHRAE Research
annually, enabling ASHRAE to report new data about material
properties and building physics and to promote the application of
innovative technologies.
Chapters in the ASHRAE Handbook are updated through the
experience of members of ASHRAE Technical Committees and
through results of ASHRAE Research reported at ASHRAE confer-
ences and published in ASHRAE special publications, ASHRAE
Transactions, and ASHRAE’s journal of archival research, Science
and Technology for the Built Environment.
For information about ASHRAE Research or to become a mem-
ber, contact ASHRAE, 180 Technology Parkway, Peachtree Cor-
ners, GA 30092; telephone: 404-636-8400; www.ashrae.org.
Preface
The 2021 ASHRAE Handbook—Fundamentals covers basic
principles and data used in the HVAC&R industry. The ASHRAE
Technical Committees that prepare these chapters provide new
information, clarify existing content, delete obsolete materials, and
reorganize chapters to make the Handbook more understandable
and easier to use.
Eligible ASHRAE members can download PDFs of this volume,
in either I-P or SI units and either as a complete volume or by indi-
vidual chapter, by logging into technologyportal.ashrae.org.
This edition includes a new chapter on global climate change.
Individual Handbook chapters have long addressed sustainability,
global warming potential, greenhouse gases, recycling, and recla-
mation as they apply to those chapters’ specific topics, but
ASHRAE is pleased to present an entirely new chapter dedicated
entirely to designing and operating in a changing world environ-
ment.
In addition to the new chapter, this volume’s content has been
extensively updated since the 2017 edition. Chapter 14, Climatic
Design Information, for instance, has expanded its coverage and
added data from 1119 new weather stations around the world, for a
total of 9237 stations.
This volume is published, as a bound print volume and in elec-
tronic format as PDF and online, in two editions: one using inch-
pound (I-P) units of measurement, the other using the International
System of Units (SI).
Corrections to the 2018, 2019, and 2020 Handbook volumes can
be found on the ASHRAE website at www.ashrae.org and in the
Additions and Corrections section of this volume. Corrections for
this volume will be listed in subsequent volumes and on the
ASHRAE website.
Reader comments are enthusiastically invited. To suggest im-
provements for a chapter, please comment using the form on the
ASHRAE website or write to Handbook Editor, ASHRAE, 180
Technology Parkway, Peachtree Corners, GA 30092, fax 678-
539-2168, or e-mail hkennedy@ashrae.org.
Heather E. Kennedy
Editor
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1.1
CHAPTER 1
PSYCHROMETRICS
Composition of Dry and Moist Air ............................................ 1.1
U.S. Standard Atmosphere......................................................... 1.1
Thermodynamic Properties of Moist Air ................................... 1.2
Thermodynamic Properties of Water at Saturation................... 1.6
Humidity Parameters............................................................... 1.12
Perfect Gas Relationships for Dry and Moist Air.................... 1.12
Thermodynamic Wet-Bulb and Dew-Point Temperature ........ 1.13
Numerical Calculation of Moist Air Properties....................... 1.14
Psychrometric Charts............................................................... 1.14
Typical Air-Conditioning Processes ........................................ 1.16
Transport Properties of Moist Air............................................ 1.19
Symbols .................................................................................... 1.19
Transport Properties of Water at Saturation........................... 1.xX
PSYCHROMETRICS uses thermodynamic and transport prop-
erties to analyze conditions and processes involving moist air. This
chapter discusses perfect gas relations and their use in common heat-
ing, cooling, and humidity control problems. Formulas developed by
Herrmann et al. (2009) may be used where greater precision is
required.
Herrmann et al. (2009), Hyland and Wexler (1983a, 1983b), and
Nelson and Sauer (2002) developed formulas for thermodynamic
properties of moist air and water modeled as real gases. However,
perfect gas relations can be substituted 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 satu-
rated air at standard atmospheric pressure for a temperature range of
–60 to 120°F. Furthermore, these errors decrease with decreasing
pressure.
Hermann et al. (2020) prepared formulas for transport properties
of moist air.
1. 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 pol-
lution sources).
Dry air is atmospheric air with all water vapor and contaminants
removed. Its composition is relatively constant, but small variations
in the amounts of individual components occur with time, geo-
graphic 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; 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.
Harrison (1965) and Hyland and Wexler (1983a) used a value 0.0314
(circa 1955) for carbon dioxide. Carbon dioxide reached 0.0379 in
2005, is currently increasing by 0.00019 percent per year and is pro-
jected to reach 0.0438 in 2036 (Gatley et al. 2008; Keeling and
Whorf 2005a, 2005b). Increases in carbon dioxide are offset by
decreases in oxygen; consequently, the oxygen percentage in 2036 is
projected to be 20.9352. Using the projected changes, the relative
molecular mass for dry air for at least the first half of the 21st century
is 28.966, based on the carbon-12 scale. The gas constant for dry air
using the Mohr and Taylor (2005) value for the universal gas con-
stant is
Rda = 1545.349/28.966 = 53.350 ft·lbf /lbda·°R (1)
Moist air is a binary (two-component) mixture of dry air and
water vapor. The amount of water vapor varies from zero (dry air) to
a maximum that depends on temperature and pressure. Saturation is
a state of neutral equilibrium between moist air and the condensed
water phase (liquid or solid); unless otherwise stated, it assumes a
flat interface surface between moist air and the condensed phase.
Saturation conditions change when the interface radius is very small
(e.g., with ultrafine water droplets). According to the Industrial For-
mulation IAPWS-IF97 (R7-97 2012), the relative molecular mass of
water is 18.015257. The gas constant for water vapor is
Rw = 1545.349/18.015257 = 85.780 ft·lbf /lbw·°R (2)
2. U.S. 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 ref-
erence for estimating properties at various altitudes. At sea level,
standard temperature is 59°F; standard barometric pressure is
14.696 psia or 29.921 in. Hg. Temperature is assumed to decrease
linearly with increasing altitude throughout the troposphere (lower
atmosphere), and to be constant in the lower reaches of the strato-
sphere. The lower atmosphere is assumed to consist of dry air that
behaves as a perfect gas. Gravity is also assumed constant at the stan-
dard value, 32.1740 ft/s2. Table 1 summarizes property data for alti-
tudes to 30,000 ft.
Pressure values in Table 1 may be calculated from
p = 14.696(1 – 6.8754  10–6Z)5.2559 (3)
The equation for temperature as a function of altitude is
t = 59 – 0.00356620Z (4)
where
Z = altitude, ft
p = barometric pressure, psia
t = temperature, °F
Equations (3) and (4) are accurate from –16,500 ft to 36,000 ft.
For higher altitudes, comprehensive tables of barometric pressure
and other physical properties of the standard atmosphere, in both SI
and I-P units, can be found in NASA (1976).
3. THERMODYNAMIC PROPERTIES OF MOIST
AIR
Table 2, calculated using ASHRAE’s (2021) LibHuAirProp soft-
ware (based on ASHRAE RP-1485; Hermann et al. 2009, 2020),
shows values of thermodynamic properties of saturated moist air and
dry air at 14.696 psia and temperatures from –80 to 200°F.
The following properties are shown in Table 2:
t = Fahrenheit temperature, based on the ITS-90 and expressed
relative to absolute temperature T in degrees Rankine (°R) by the
following relation:
The preparation of this chapter is assigned to TC 1.1, Thermodynamics and
Psychrometrics.
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1.2 2021 ASHRAE Handbook—Fundamentals
T = t + 459.67
Ws = humidity ratio at saturation; 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, ft3/lbda.
vas = vs – vda, difference between specific volume of moist air at
saturation and that of dry air, ft3/lbda, at same pressure and
temperature.
vs = specific volume of moist air at saturation, ft3/lbda.
hda = specific enthalpy of dry air, Btu/lbda. In Table 2, hda is assigned a
value of 0 at 0°F and standard atmospheric pressure.
has = hs – hda, difference between specific enthalpy of moist air at
saturation and that of dry air, Btu/lbda, at same pressure and
temperature.
hs = specific enthalpy of moist air at saturation, Btu/lbda.
sda = specific entropy of dry air, Btu/lbda· °R. In Table 2, sda is
assigned a value of 0 at 0°F and standard atmospheric pressure.
ss = specific entropy of moist air at saturation Btu/lbda· °R.
4. THERMODYNAMIC PROPERTIES OF WATER
AT SATURATION
Table 3 shows thermodynamic properties of water at saturation for
temperatures from 80 to 300°F, calculated using ASHRAE
(2021) LibHuAirProp software, based on IAPWS formulations
described in IAPWS R7-97 (2012), R10-06 (2009), and R14-08
(2011). The internal energy and entropy of saturated liquid water
are both assigned the value zero at the triple point, 32.018°F.
Between the triple-point and critical-point temperatures of water,
both saturated liquid and saturated vapor may coexist in equi-
librium; below the triple-point temperature, both saturated ice and
saturated vapor may coexist in equilibrium.
Table 1 Standard Atmospheric Data for Altitudes to 30,000 ft
Altitude, ft Temperature, °F Pressure, psia
–1000 62.6 15.236
–500 60.8 14.966
0 59.0 14.696
500 57.2 14.430
1,000 55.4 14.175
2,000 51.9 13.664
3,000 48.3 13.173
4,000 44.7 12.682
5,000 41.2 12.230
6,000 37.6 11.778
7,000 34.0 11.341
8,000 30.5 10.914
9,000 26.9 10.506
10,000 23.4 10.108
15,000 5.5 8.296
20,000 –12.3 6.758
30,000 –47.8 4.371
Source: Adapted from NASA (1976).
Table 2 Thermodynamic Properties of Saturated Moist and Dry Air at Standard Atmospheric Pressure, 14.696 psia
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Specific Heat Capacity,
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
vda vs hda hs t cp,s sda ss
–80 0.0000049 9.553 9.553 –19.218 –19.213 0.2403 0.2404 –0.04593 –0.04592
–79 0.0000053 9.578 9.578 –18.977 –18.972 0.2403 0.2403 –0.04530 –0.04529
–78 0.0000057 9.603 9.604 –18.737 –18.731 0.2403 0.2403 –0.04467 –0.04465
–77 0.0000062 9.629 9.629 –18.497 –18.490 0.2403 0.2403 –0.04404 –0.04402
–76 0.0000067 9.654 9.654 –18.256 –18.250 0.2403 0.2403 –0.04341 –0.04339
–75 0.0000072 9.680 9.680 –18.016 –18.009 0.2403 0.2403 –0.04279 –0.04277
–74 0.0000078 9.705 9.705 –17.776 –17.768 0.2403 0.2403 –0.04216 –0.04214
–73 0.0000084 9.730 9.730 –17.535 –17.527 0.2403 0.2403 –0.04154 –0.04152
–72 0.0000090 9.756 9.756 –17.295 –17.286 0.2403 0.2403 –0.04092 –0.04090
–71 0.0000097 9.781 9.781 –17.055 –17.045 0.2403 0.2403 –0.04030 –0.04027
–70 0.0000104 9.806 9.806 –16.814 –16.804 0.2403 0.2403 –0.03968 –0.03966
–69 0.0000112 9.832 9.832 –16.574 –16.563 0.2403 0.2403 –0.03907 –0.03904
–68 0.0000120 9.857 9.857 –16.334 –16.321 0.2403 0.2403 –0.03845 –0.03842
–67 0.0000129 9.882 9.882 –16.094 –16.080 0.2403 0.2403 –0.03784 –0.03781
–66 0.0000139 9.908 9.908 –15.853 –15.839 0.2403 0.2403 –0.03723 –0.03719
–65 0.0000149 9.933 9.933 –15.613 –15.598 0.2403 0.2403 –0.03662 –0.03658
–64 0.0000160 9.958 9.959 –15.373 –15.356 0.2403 0.2403 –0.03601 –0.03597
–63 0.0000172 9.984 9.984 –15.132 –15.115 0.2403 0.2403 –0.03541 –0.03536
–62 0.0000184 10.009 10.009 –14.892 –14.873 0.2403 0.2403 –0.03480 –0.03475
–61 0.0000198 10.034 10.035 –14.652 –14.632 0.2403 0.2403 –0.03420 –0.03414
–60 0.0000212 10.060 10.060 –14.412 –14.390 0.2403 0.2403 –0.03360 –0.03354
–59 0.0000227 10.085 10.085 –14.171 –14.148 0.2403 0.2403 –0.03300 –0.03293
–58 0.0000243 10.110 10.111 –13.931 –13.906 0.2403 0.2403 –0.03240 –0.03233
–57 0.0000260 10.136 10.136 –13.691 –13.664 0.2403 0.2403 –0.03180 –0.03173
–56 0.0000279 10.161 10.161 –13.451 –13.422 0.2402 0.2403 –0.03120 –0.03113
–55 0.0000298 10.186 10.187 –13.210 –13.179 0.2402 0.2403 –0.03061 –0.03053
–54 0.0000319 10.212 10.212 –12.970 –12.937 0.2402 0.2402 –0.03002 –0.02993
–53 0.0000341 10.237 10.237 –12.730 –12.695 0.2402 0.2402 –0.02942 –0.02933
–52 0.0000365 10.262 10.263 –12.490 –12.452 0.2402 0.2402 –0.02883 –0.02874
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Psychrometrics 1.3
–51 0.0000390 10.288 10.288 –12.249 –12.209 0.2402 0.2402 –0.02825 –0.02814
–50 0.0000416 10.313 10.314 –12.009 –11.966 0.2402 0.2402 –0.02766 –0.02755
–49 0.0000445 10.338 10.339 –11.769 –11.723 0.2402 0.2402 –0.02707 –0.02695
–48 0.0000475 10.364 10.364 –11.529 –11.479 0.2402 0.2402 –0.02649 –0.02636
–47 0.0000507 10.389 10.390 –11.289 –11.236 0.2402 0.2402 –0.02591 –0.02577
–46 0.0000541 10.414 10.415 –11.048 –10.992 0.2402 0.2402 –0.02532 –0.02518
–45 0.0000577 10.439 10.440 –10.808 –10.748 0.2402 0.2402 –0.02474 –0.02459
–44 0.0000615 10.465 10.466 –10.568 –10.504 0.2402 0.2402 –0.02417 –0.02400
–43 0.0000656 10.490 10.491 –10.328 –10.259 0.2402 0.2402 –0.02359 –0.02341
–42 0.0000699 10.515 10.517 –10.087 –10.015 0.2402 0.2402 –0.02301 –0.02283
–41 0.0000744 10.541 10.542 –9.847 –9.770 0.2402 0.2402 –0.02244 –0.02224
–40 0.0000793 10.566 10.567 –9.607 –9.524 0.2402 0.2402 –0.02187 –0.02166
–39 0.0000844 10.591 10.593 –9.367 –9.279 0.2402 0.2402 –0.02129 –0.02107
–38 0.0000898 10.617 10.618 –9.127 –9.033 0.2402 0.2402 –0.02072 –0.02049
–37 0.0000956 10.642 10.644 –8.886 –8.787 0.2402 0.2402 –0.02015 –0.01990
–36 0.0001017 10.667 10.669 –8.646 –8.540 0.2402 0.2402 –0.01959 –0.01932
–35 0.0001081 10.693 10.695 –8.406 –8.293 0.2402 0.2402 –0.01902 –0.01874
–34 0.0001150 10.718 10.720 –8.166 –8.046 0.2402 0.2402 –0.01846 –0.01816
–33 0.0001222 10.743 10.745 –7.926 –7.798 0.2402 0.2402 –0.01789 –0.01757
–32 0.0001298 10.769 10.771 –7.685 –7.550 0.2402 0.2402 –0.01733 –0.01699
–31 0.0001379 10.794 10.796 –7.445 –7.301 0.2402 0.2402 –0.01677 –0.01641
–30 0.0001465 10.819 10.822 –7.205 –7.052 0.2402 0.2402 –0.01621 –0.01583
–29 0.0001555 10.845 10.847 –6.965 –6.802 0.2402 0.2402 –0.01565 –0.01525
–28 0.0001650 10.870 10.873 –6.725 –6.552 0.2402 0.2402 –0.01509 –0.01467
–27 0.0001751 10.895 10.898 –6.485 –6.301 0.2402 0.2402 –0.01454 –0.01409
–26 0.0001857 10.920 10.924 –6.244 –6.050 0.2402 0.2402 –0.01398 –0.01351
–25 0.0001970 10.946 10.949 –6.004 –5.797 0.2402 0.2402 –0.01343 –0.01293
–24 0.0002088 10.971 10.975 –5.764 –5.545 0.2402 0.2402 –0.01288 –0.01234
–23 0.0002213 10.996 11.000 –5.524 –5.291 0.2402 0.2402 –0.01233 –0.01176
–22 0.0002345 11.022 11.026 –5.284 –5.037 0.2402 0.2402 –0.01178 –0.01118
–21 0.0002485 11.047 11.051 –5.043 –4.782 0.2402 0.2402 –0.01123 –0.01060
–20 0.0002632 11.072 11.077 –4.803 –4.527 0.2402 0.2402 –0.01068 –0.01002
–19 0.0002786 11.098 11.103 –4.563 –4.270 0.2402 0.2402 –0.01014 –0.00943
–18 0.0002949 11.123 11.128 –4.323 –4.013 0.2402 0.2402 –0.00959 –0.00885
–17 0.0003121 11.148 11.154 –4.083 –3.754 0.2402 0.2402 –0.00905 –0.00826
–16 0.0003302 11.174 11.179 –3.843 –3.495 0.2402 0.2402 –0.00851 –0.00768
–15 0.0003493 11.199 11.205 –3.602 –3.234 0.2402 0.2402 –0.00797 –0.00709
–14 0.0003694 11.224 11.231 –3.362 –2.973 0.2402 0.2402 –0.00743 –0.00650
–13 0.0003905 11.249 11.257 –3.122 –2.710 0.2402 0.2402 –0.00689 –0.00591
–12 0.0004127 11.275 11.282 –2.882 –2.446 0.2402 0.2403 –0.00635 –0.00532
–11 0.0004361 11.300 11.308 –2.642 –2.181 0.2402 0.2403 –0.00582 –0.00473
–10 0.0004607 11.325 11.334 –2.402 –1.915 0.2402 0.2403 –0.00528 –0.00414
–9 0.0004866 11.351 11.360 –2.161 –1.647 0.2402 0.2403 –0.00475 –0.00354
–8 0.0005138 11.376 11.385 –1.921 –1.378 0.2402 0.2403 –0.00422 –0.00294
–7 0.0005425 11.401 11.411 –1.681 –1.108 0.2402 0.2403 –0.00369 –0.00234
–6 0.0005725 11.427 11.437 –1.441 –0.835 0.2402 0.2403 –0.00316 –0.00174
–5 0.0006041 11.452 11.463 –1.201 –0.561 0.2402 0.2403 –0.00263 –0.00114
–4 0.0006373 11.477 11.489 –0.961 –0.286 0.2402 0.2403 –0.00210 –0.00053
–3 0.0006721 11.502 11.515 –0.720 –0.009 0.2402 0.2403 –0.00157 0.00008
–2 0.0007087 11.528 11.541 –0.480 0.271 0.2402 0.2403 –0.00105 0.00069
–1 0.0007471 11.553 11.567 –0.240 0.552 0.2402 0.2403 –0.00052 0.00130
0 0.0007875 11.578 11.593 0.000 0.835 0.2402 0.2403 0.00000 0.00192
1 0.0008298 11.604 11.619 0.240 1.121 0.2402 0.2403 0.00052 0.00254
2 0.0008741 11.629 11.645 0.480 1.408 0.2402 0.2403 0.00104 0.00317
Table 2 Thermodynamic Properties of Saturated Moist and Dry Air at Standard Atmospheric Pressure, 14.696 psia (Continued)
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
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3 0.0009207 11.654 11.671 0.720 1.698 0.2402 0.2404 0.00156 0.00379
4 0.0009695 11.680 11.698 0.961 1.991 0.2402 0.2404 0.00208 0.00443
5 0.0010207 11.705 11.724 1.201 2.286 0.2402 0.2404 0.00260 0.00506
6 0.0010743 11.730 11.750 1.441 2.583 0.2402 0.2404 0.00311 0.00570
7 0.0011306 11.755 11.777 1.681 2.884 0.2402 0.2404 0.00363 0.00635
8 0.0011895 11.781 11.803 1.921 3.187 0.2402 0.2404 0.00414 0.00700
9 0.0012512 11.806 11.830 2.161 3.493 0.2402 0.2404 0.00466 0.00765
10 0.0013158 11.831 11.856 2.402 3.803 0.2402 0.2404 0.00517 0.00832
11 0.0013835 11.857 11.883 2.642 4.116 0.2402 0.2405 0.00568 0.00898
12 0.0014544 11.882 11.910 2.882 4.432 0.2402 0.2405 0.00619 0.00965
13 0.0015286 11.907 11.936 3.122 4.752 0.2402 0.2405 0.00670 0.01033
14 0.0016062 11.933 11.963 3.362 5.076 0.2402 0.2405 0.00721 0.01102
15 0.0016874 11.958 11.990 3.603 5.403 0.2402 0.2405 0.00771 0.01171
16 0.0017724 11.983 12.017 3.843 5.735 0.2402 0.2405 0.00822 0.01241
17 0.0018613 12.008 12.044 4.083 6.071 0.2402 0.2406 0.00872 0.01311
18 0.0019543 12.034 12.071 4.323 6.411 0.2402 0.2406 0.00922 0.01383
19 0.0020515 12.059 12.099 4.563 6.756 0.2402 0.2406 0.00973 0.01455
20 0.0021531 12.084 12.126 4.803 7.106 0.2402 0.2406 0.01023 0.01528
21 0.0022593 12.110 12.153 5.044 7.461 0.2402 0.2406 0.01073 0.01602
22 0.0023703 12.135 12.181 5.284 7.821 0.2402 0.2407 0.01123 0.01677
23 0.0024863 12.160 12.209 5.524 8.186 0.2402 0.2407 0.01173 0.01753
24 0.0026075 12.185 12.236 5.764 8.557 0.2402 0.2407 0.01222 0.01830
25 0.0027340 12.211 12.264 6.004 8.934 0.2402 0.2408 0.01272 0.01908
26 0.0028662 12.236 12.292 6.244 9.317 0.2402 0.2408 0.01321 0.01987
27 0.0030042 12.261 12.320 6.485 9.707 0.2402 0.2408 0.01371 0.02067
28 0.0031482 12.287 12.349 6.725 10.103 0.2402 0.2408 0.01420 0.02148
29 0.0032986 12.312 12.377 6.965 10.506 0.2402 0.2409 0.01469 0.02231
30 0.0034555 12.337 12.405 7.205 10.916 0.2402 0.2409 0.01518 0.02315
31 0.0036192 12.362 12.434 7.445 11.334 0.2402 0.2409 0.01567 0.02400
32 0.0037900 12.388 12.463 7.6857 11.759 0.2402 0.2410 0.01616 0.02486
33 0.0039468 12.413 12.492 7.9259 12.169 0.2402 0.2410 0.01665 0.02570
34 0.0041093 12.438 12.520 8.1661 12.586 0.2402 0.2411 0.01714 0.02654
35 0.0042778 12.464 12.549 8.4063 13.009 0.2402 0.2411 0.01762 0.02740
36 0.0044524 12.489 12.578 8.6465 13.439 0.2402 0.2411 0.01811 0.02827
37 0.0046333 12.514 12.607 8.8867 13.876 0.2402 0.2412 0.01859 0.02915
38 0.0048208 12.539 12.636 9.1269 14.321 0.2402 0.2412 0.01908 0.03004
39 0.0050151 12.565 12.666 9.3671 14.772 0.2402 0.2413 0.01956 0.03095
40 0.0052163 12.590 12.695 9.6073 15.232 0.2402 0.2413 0.02004 0.03187
41 0.0054247 12.615 12.725 9.8475 15.699 0.2402 0.2413 0.02052 0.03280
42 0.0056404 12.641 12.755 10.088 16.175 0.2402 0.2414 0.02100 0.03375
43 0.0058639 12.666 12.785 10.328 16.658 0.2402 0.2414 0.02148 0.03472
44 0.0060952 12.691 12.815 10.568 17.151 0.2402 0.2415 0.02196 0.03569
45 0.0063346 12.716 12.845 10.808 17.653 0.2402 0.2416 0.02243 0.03669
46 0.0065824 12.742 12.876 11.049 18.163 0.2402 0.2416 0.02291 0.03770
47 0.0068389 12.767 12.907 11.289 18.684 0.2402 0.2417 0.02338 0.03873
48 0.0071042 12.792 12.938 11.529 19.214 0.2402 0.2417 0.02386 0.03978
49 0.0073787 12.817 12.969 11.769 19.755 0.2402 0.2418 0.02433 0.04084
50 0.0076627 12.843 13.001 12.010 20.305 0.2402 0.2418 0.02480 0.04192
51 0.0079563 12.868 13.032 12.250 20.867 0.2402 0.2419 0.02527 0.04302
52 0.0082601 12.893 13.064 12.490 21.440 0.2403 0.2420 0.02574 0.04414
53 0.0085741 12.919 13.096 12.730 22.024 0.2403 0.2420 0.02621 0.04528
54 0.0088989 12.944 13.129 12.971 22.620 0.2403 0.2421 0.02668 0.04645
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
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Psychrometrics 1.5
55 0.0092345 12.969 13.161 13.211 23.229 0.2403 0.2422 0.02715 0.04763
56 0.0095815 12.994 13.194 13.451 23.850 0.2403 0.2423 0.02761 0.04883
57 0.0099402 13.020 13.227 13.691 24.483 0.2403 0.2423 0.02808 0.05006
58 0.010311 13.045 13.261 13.932 25.131 0.2403 0.2424 0.02854 0.05131
59 0.010694 13.070 13.294 14.172 25.792 0.2403 0.2425 0.02901 0.05259
60 0.011089 13.096 13.328 14.412 26.467 0.2403 0.2426 0.02947 0.05389
61 0.011498 13.121 13.363 14.653 27.156 0.2403 0.2427 0.02993 0.05522
62 0.011921 13.146 13.397 14.893 27.861 0.2403 0.2428 0.03039 0.05657
63 0.012357 13.171 13.432 15.133 28.581 0.2403 0.2429 0.03085 0.05795
64 0.012807 13.197 13.468 15.373 29.317 0.2403 0.2430 0.03131 0.05936
65 0.013272 13.222 13.503 15.614 30.070 0.2403 0.2431 0.03177 0.06080
66 0.013753 13.247 13.539 15.854 30.839 0.2403 0.2432 0.03223 0.06226
67 0.014249 13.272 13.576 16.094 31.626 0.2403 0.2433 0.03268 0.06376
68 0.014761 13.298 13.612 16.335 32.431 0.2403 0.2434 0.03314 0.06529
69 0.015289 13.323 13.649 16.575 33.254 0.2403 0.2435 0.03360 0.06685
70 0.015835 13.348 13.687 16.815 34.097 0.2403 0.2436 0.03405 0.06844
71 0.016398 13.374 13.725 17.056 34.959 0.2403 0.2438 0.03450 0.07007
72 0.016979 13.399 13.763 17.296 35.841 0.2403 0.2439 0.03495 0.07173
73 0.017578 13.424 13.802 17.536 36.744 0.2403 0.2440 0.03541 0.07343
74 0.018197 13.449 13.842 17.777 37.668 0.2403 0.2441 0.03586 0.07516
75 0.018835 13.475 13.881 18.017 38.614 0.2403 0.2443 0.03631 0.07694
76 0.019494 13.500 13.922 18.257 39.583 0.2403 0.2444 0.03676 0.07875
77 0.020173 13.525 13.962 18.498 40.576 0.2403 0.2446 0.03720 0.08060
78 0.020874 13.550 14.004 18.738 41.592 0.2404 0.2447 0.03765 0.08250
79 0.021597 13.576 14.046 18.978 42.634 0.2404 0.2449 0.03810 0.08444
80 0.022343 13.601 14.088 19.219 43.700 0.2404 0.2450 0.03854 0.08642
81 0.023112 13.626 14.131 19.459 44.793 0.2404 0.2452 0.03899 0.08844
82 0.023905 13.651 14.174 19.699 45.914 0.2404 0.2454 0.03943 0.09052
83 0.024723 13.677 14.219 19.940 47.062 0.2404 0.2456 0.03988 0.09264
84 0.025566 13.702 14.263 20.180 48.238 0.2404 0.2457 0.04032 0.09481
85 0.026436 13.727 14.309 20.420 49.445 0.2404 0.2459 0.04076 0.09703
86 0.027333 13.753 14.355 20.661 50.681 0.2404 0.2461 0.04120 0.09930
87 0.028257 13.778 14.402 20.901 51.949 0.2404 0.2463 0.04164 0.1016
88 0.029211 13.803 14.449 21.142 53.250 0.2404 0.2465 0.04208 0.1040
89 0.030193 13.828 14.497 21.382 54.583 0.2404 0.2467 0.04252 0.1064
90 0.031206 13.854 14.546 21.622 55.951 0.2404 0.2469 0.04296 0.1089
91 0.032251 13.879 14.596 21.863 57.354 0.2404 0.2472 0.04339 0.1115
92 0.033327 13.904 14.646 22.103 58.794 0.2404 0.2474 0.04383 0.1141
93 0.034437 13.929 14.698 22.344 60.271 0.2404 0.2476 0.04427 0.1168
94 0.035581 13.955 14.750 22.584 61.787 0.2404 0.2479 0.04470 0.1196
95 0.036760 13.980 14.803 22.825 63.342 0.2404 0.2481 0.04514 0.1224
96 0.037976 14.005 14.857 23.065 64.938 0.2404 0.2484 0.04557 0.1252
97 0.039228 14.031 14.912 23.305 66.577 0.2405 0.2486 0.04600 0.1282
98 0.040520 14.056 14.968 23.546 68.259 0.2405 0.2489 0.04643 0.1312
99 0.041851 14.081 15.025 23.786 69.987 0.2405 0.2492 0.04686 0.1343
100 0.043222 14.106 15.083 24.027 71.760 0.2405 0.2495 0.04729 0.1375
101 0.044636 14.132 15.142 24.267 73.581 0.2405 0.2498 0.04772 0.1408
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
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102 0.046094 14.157 15.202 24.508 75.452 0.2405 0.2501 0.04815 0.1441
103 0.047596 14.182 15.263 24.748 77.373 0.2405 0.2504 0.04858 0.1476
104 0.049145 14.207 15.325 24.989 79.347 0.2405 0.2507 0.04901 0.1511
105 0.050741 14.233 15.389 25.229 81.374 0.2405 0.2510 0.04943 0.1547
106 0.052386 14.258 15.454 25.470 83.458 0.2405 0.2514 0.04986 0.1584
107 0.054082 14.283 15.520 25.710 85.598 0.2405 0.2517 0.05028 0.1622
108 0.055830 14.308 15.587 25.951 87.799 0.2405 0.2521 0.05071 0.1661
109 0.057632 14.334 15.656 26.191 90.060 0.2405 0.2525 0.05113 0.1701
110 0.059490 14.359 15.726 26.432 92.385 0.2405 0.2528 0.05155 0.1742
111 0.061405 14.384 15.798 26.672 94.775 0.2405 0.2532 0.05197 0.1784
112 0.063380 14.409 15.871 26.913 97.233 0.2405 0.2536 0.05240 0.1827
113 0.065416 14.435 15.946 27.154 99.761 0.2406 0.2541 0.05282 0.1872
114 0.067516 14.460 16.022 27.394 102.36 0.2406 0.2545 0.05324 0.1917
115 0.069680 14.485 16.100 27.635 105.03 0.2406 0.2549 0.05365 0.1964
116 0.071913 14.511 16.180 27.875 107.79 0.2406 0.2554 0.05407 0.2012
117 0.074215 14.536 16.262 28.116 110.62 0.2406 0.2558 0.05449 0.2061
118 0.076590 14.561 16.345 28.356 113.53 0.2406 0.2563 0.05491 0.2112
119 0.079040 14.586 16.431 28.597 116.53 0.2406 0.2568 0.05532 0.2164
120 0.081566 14.612 16.518 28.838 119.61 0.2406 0.2573 0.05574 0.2218
121 0.084173 14.637 16.607 29.078 122.79 0.2406 0.2578 0.05615 0.2273
122 0.086863 14.662 16.699 29.319 126.06 0.2406 0.2584 0.05657 0.2330
123 0.089638 14.687 16.793 29.559 129.43 0.2406 0.2589 0.05698 0.2388
124 0.092503 14.713 16.889 29.800 132.90 0.2406 0.2595 0.05739 0.2448
125 0.095459 14.738 16.988 30.041 136.48 0.2406 0.2600 0.05781 0.2510
126 0.098510 14.763 17.089 30.281 140.16 0.2406 0.2606 0.05822 0.2573
127 0.10166 14.788 17.192 30.522 143.96 0.2407 0.2612 0.05863 0.2638
128 0.10491 14.814 17.298 30.763 147.88 0.2407 0.2619 0.05904 0.2705
129 0.10827 14.839 17.407 31.003 151.91 0.2407 0.2625 0.05945 0.2774
130 0.11174 14.864 17.519 31.244 156.07 0.2407 0.2632 0.05985 0.2846
131 0.11533 14.889 17.634 31.485 160.37 0.2407 0.2639 0.06026 0.2919
132 0.11903 14.915 17.752 31.725 164.80 0.2407 0.2646 0.06067 0.2994
133 0.12286 14.940 17.873 31.966 169.37 0.2407 0.2653 0.06108 0.3072
134 0.12681 14.965 17.998 32.207 174.08 0.2407 0.2660 0.06148 0.3152
135 0.13090 14.990 18.126 32.447 178.95 0.2407 0.2668 0.06189 0.3235
136 0.13513 15.016 18.258 32.688 183.98 0.2407 0.2676 0.06229 0.3320
137 0.13950 15.041 18.393 32.929 189.18 0.2407 0.2684 0.06269 0.3408
138 0.14402 15.066 18.533 33.170 194.55 0.2407 0.2692 0.06310 0.3499
139 0.14870 15.091 18.677 33.410 200.09 0.2407 0.2700 0.06350 0.3592
140 0.15354 15.117 18.825 33.651 205.83 0.2408 0.2709 0.06390 0.3689
141 0.15856 15.142 18.977 33.892 211.75 0.2408 0.2718 0.06430 0.3789
142 0.16375 15.167 19.134 34.133 217.89 0.2408 0.2727 0.06470 0.3892
143 0.16913 15.192 19.296 34.373 224.23 0.2408 0.2737 0.06510 0.3998
144 0.17470 15.218 19.463 34.614 230.80 0.2408 0.2746 0.06550 0.4108
145 0.18047 15.243 19.636 34.855 237.60 0.2408 0.2756 0.06590 0.4222
146 0.18646 15.268 19.814 35.096 244.64 0.2408 0.2767 0.06630 0.4339
147 0.19267 15.294 19.998 35.337 251.94 0.2408 0.2777 0.06670 0.4461
148 0.19911 15.319 20.188 35.577 259.51 0.2408 0.2788 0.06709 0.4587
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

Psychrometrics 1.7
149 0.20579 15.344 20.384 35.818 267.35 0.2408 0.2799 0.06749 0.4717
150 0.21273 15.369 20.588 36.059 275.49 0.2408 0.2811 0.06788 0.4852
151 0.21994 15.395 20.798 36.300 283.93 0.2409 0.2822 0.06828 0.4992
152 0.22743 15.420 21.016 36.541 292.70 0.2409 0.2835 0.06867 0.5138
153 0.23522 15.445 21.242 36.782 301.81 0.2409 0.2847 0.06907 0.5288
154 0.24332 15.470 21.476 37.023 311.27 0.2409 0.2860 0.06946 0.5444
155 0.25174 15.496 21.719 37.263 321.12 0.2409 0.2873 0.06985 0.5606
156 0.26051 15.521 21.971 37.504 331.35 0.2409 0.2887 0.07024 0.5775
157 0.26965 15.546 22.232 37.745 342.01 0.2409 0.2901 0.07063 0.5950
158 0.27917 15.571 22.504 37.986 353.11 0.2409 0.2915 0.07103 0.6132
159 0.28909 15.597 22.787 38.227 364.67 0.2409 0.2930 0.07141 0.6322
160 0.29945 15.622 23.081 38.468 376.73 0.2409 0.2945 0.07180 0.6519
161 0.31026 15.647 23.387 38.709 389.31 0.2409 0.2960 0.07219 0.6724
162 0.32156 15.672 23.706 38.950 402.45 0.2410 0.2976 0.07258 0.6939
163 0.33336 15.698 24.039 39.191 416.17 0.2410 0.2993 0.07297 0.7162
164 0.34571 15.723 24.386 39.432 430.52 0.2410 0.3010 0.07335 0.7396
165 0.35865 15.748 24.749 39.673 445.54 0.2410 0.3027 0.07374 0.7640
166 0.37219 15.773 25.128 39.914 461.26 0.2410 0.3046 0.07413 0.7895
167 0.38640 15.799 25.525 40.155 477.74 0.2410 0.3064 0.07451 0.8162
168 0.40131 15.824 25.941 40.396 495.03 0.2410 0.3083 0.07490 0.8442
169 0.41697 15.849 26.376 40.637 513.18 0.2410 0.3103 0.07528 0.8735
170 0.43344 15.874 26.833 40.878 532.26 0.2410 0.3123 0.07566 0.9043
171 0.45077 15.900 27.314 41.119 552.33 0.2410 0.3144 0.07604 0.9366
172 0.46903 15.925 27.819 41.360 573.48 0.2411 0.3165 0.07643 0.9706
173 0.48829 15.950 28.351 41.601 595.77 0.2411 0.3187 0.07681 1.0065
174 0.50864 15.975 28.911 41.842 619.30 0.2411 0.3210 0.07719 1.0442
175 0.53015 16.001 29.503 42.083 644.18 0.2411 0.3234 0.07757 1.0841
176 0.55293 16.026 30.129 42.324 670.51 0.2411 0.3258 0.07795 1.1262
177 0.57708 16.051 30.792 42.565 698.43 0.2411 0.3283 0.07833 1.1708
178 0.60273 16.076 31.495 42.807 728.06 0.2411 0.3308 0.07871 1.2181
179 0.63000 16.102 32.241 43.048 759.57 0.2411 0.3335 0.07908 1.2684
180 0.65907 16.127 33.035 43.289 793.13 0.2411 0.3362 0.07946 1.3218
181 0.69009 16.152 33.881 43.530 828.94 0.2412 0.3390 0.07984 1.3787
182 0.72326 16.177 34.786 43.771 867.23 0.2412 0.3419 0.08021 1.4395
183 0.75882 16.203 35.753 44.012 908.25 0.2412 0.3449 0.08059 1.5045
184 0.79700 16.228 36.791 44.253 952.30 0.2412 0.3480 0.08096 1.5743
185 0.83811 16.253 37.908 44.495 999.71 0.2412 0.3512 0.08134 1.6493
186 0.88247 16.278 39.112 44.736 1050.9 0.2412 0.3545 0.08171 1.7300
187 0.93050 16.304 40.414 44.977 1106.2 0.2412 0.3579 0.08209 1.8174
188 0.98263 16.329 41.825 45.218 1166.3 0.2412 0.3614 0.08246 1.9120
189 1.0394 16.354 43.362 45.460 1231.8 0.2412 0.3650 0.08283 2.0149
190 1.1015 16.379 45.040 45.701 1303.3 0.2413 0.3688 0.08320 2.1273
191 1.1696 16.405 46.880 45.942 1381.7 0.2413 0.3726 0.08357 2.2504
192 1.2446 16.430 48.906 46.183 1468.2 0.2413 0.3766 0.08394 2.3859
193 1.3277 16.455 51.147 46.425 1563.9 0.2413 0.3807 0.08431 2.5356
194 1.4202 16.480 53.640 46.666 1670.4 0.2413 0.3850 0.08468 2.7021
195 1.5238 16.506 56.430 46.907 1789.6 0.2413 0.3894 0.08505 2.8882
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

196 1.6405 16.531 59.571 47.149 1924.0 0.2413 0.3940 0.08542 3.0976
197 1.7729 16.556 63.135 47.390 2076.4 0.2413 0.3988 0.08579 3.3349
198 1.9245 16.581 67.212 47.631 2250.9 0.2413 0.4037 0.08616 3.6062
199 2.0997 16.607 71.921 47.873 2452.5 0.2414 0.4087 0.08652 3.9193
200 2.3044 16.632 77.421 48.114 2688.1 0.2414 0.4140 0.08689 4.2847
Table 3 Thermodynamic Properties of Water at Saturation
Temp.,
°F
t
Absolute
Pressure
pws, psia
Specific Volume, ft3/lb Specific Enthalpy, Btu/lb
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
–80 0.000116 0.01732 1953807 –193.38 1025.8 0.3930 0.4423 –0.4064 2.8048
–79 0.000125 0.01732 1814635 –192.98 1026.3 0.3940 0.4424 –0.4054 2.7975
–78 0.000135 0.01732 1686036 –192.59 1026.7 0.3949 0.4424 –0.4043 2.7903
–77 0.000145 0.01732 1567159 –192.19 1027.1 0.3958 0.4424 –0.4033 2.7831
–76 0.000157 0.01732 1457224 –191.80 1027.6 0.3968 0.4424 –0.4023 2.7759
–75 0.000169 0.01733 1355519 –191.40 1028.0 0.3977 0.4424 –0.4012 2.7688
–74 0.000182 0.01733 1261390 –191.00 1028.5 0.3987 0.4424 –0.4002 2.7617
–73 0.000196 0.01733 1174239 –190.60 1028.9 0.3996 0.4424 –0.3992 2.7547
–72 0.000211 0.01733 1093518 –190.20 1029.3 0.4006 0.4424 –0.3981 2.7477
–71 0.000227 0.01733 1018724 –189.80 1029.8 0.4015 0.4425 –0.3971 2.7408
–70 0.000244 0.01733 949394 –189.40 1030.2 0.4024 0.4425 –0.3961 2.7338
–69 0.000263 0.01733 885105 –189.00 1030.7 0.4034 0.4425 –0.3950 2.7270
–68 0.000283 0.01733 825469 –188.59 1031.1 0.4043 0.4425 –0.3940 2.7201
–67 0.000304 0.01733 770128 –188.19 1031.6 0.4053 0.4425 –0.3930 2.7133
–66 0.000326 0.01734 718753 –187.78 1032.0 0.4062 0.4425 –0.3919 2.7065
–65 0.000350 0.01734 671043 –187.38 1032.4 0.4072 0.4425 –0.3909 2.6998
–64 0.000376 0.01734 626720 –186.97 1032.9 0.4081 0.4426 –0.3899 2.6931
–63 0.000404 0.01734 585529 –186.56 1033.3 0.4091 0.4426 –0.3888 2.6865
–62 0.000433 0.01734 547234 –186.15 1033.8 0.4100 0.4426 –0.3878 2.6799
–61 0.000464 0.01734 511620 –185.74 1034.2 0.4110 0.4426 –0.3868 2.6733
–60 0.000498 0.01734 478487 –185.33 1034.7 0.4119 0.4426 –0.3858 2.6667
–59 0.000533 0.01734 447651 –184.92 1035.1 0.4129 0.4426 –0.3847 2.6602
–58 0.000571 0.01735 418943 –184.50 1035.5 0.4138 0.4427 –0.3837 2.6537
–57 0.000612 0.01735 392207 –184.09 1036.0 0.4148 0.4427 –0.3827 2.6473
–56 0.000655 0.01735 367299 –183.67 1036.4 0.4157 0.4427 –0.3816 2.6409
–55 0.000701 0.01735 344086 –183.26 1036.9 0.4167 0.4427 –0.3806 2.6345
–54 0.000749 0.01735 322445 –182.84 1037.3 0.4176 0.4427 –0.3796 2.6282
–53 0.000801 0.01735 302263 –182.42 1037.7 0.4186 0.4428 –0.3785 2.6219
–52 0.000857 0.01735 283436 –182.00 1038.2 0.4195 0.4428 –0.3775 2.6156
–51 0.000916 0.01736 265866 –181.58 1038.6 0.4205 0.4428 –0.3765 2.6093
–50 0.000978 0.01736 249464 –181.16 1039.1 0.4214 0.4428 –0.3755 2.6031
–49 0.001045 0.01736 234148 –180.74 1039.5 0.4224 0.4429 –0.3744 2.5970
–48 0.001115 0.01736 219841 –180.32 1040.0 0.4234 0.4429 –0.3734 2.5908
–47 0.001191 0.01736 206472 –179.89 1040.4 0.4243 0.4429 –0.3724 2.5847
–46 0.001270 0.01736 193976 –179.47 1040.8 0.4253 0.4429 –0.3713 2.5786
–45 0.001355 0.01736 182292 –179.04 1041.3 0.4262 0.4430 –0.3703 2.5726
–44 0.001445 0.01736 171363 –178.62 1041.7 0.4272 0.4430 –0.3693 2.5666
–43 0.001540 0.01737 161139 –178.19 1042.2 0.4281 0.4430 –0.3683 2.5606
–42 0.001641 0.01737 151570 –177.76 1042.6 0.4291 0.4430 –0.3672 2.5546
–41 0.001749 0.01737 142611 –177.33 1043.1 0.4300 0.4431 –0.3662 2.5487
–40 0.001862 0.01737 134222 –176.90 1043.5 0.4310 0.4431 –0.3652 2.5428
–39 0.001983 0.01737 126363 –176.47 1043.9 0.4320 0.4431 –0.3642 2.5370
Temp. t, °F
Humidity Ratio Ws,
lbw/lbda
Specific Volume,
ft3/lbda
Specific Enthalpy,
Btu/lbda
Btu/lb·°F
Specific Entropy,
Btu/lbda·°F
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

Psychrometrics 1.9
–38 0.002111 0.01737 118999 –176.04 1044.4 0.4329 0.4432 –0.3631 2.5311
–37 0.002246 0.01737 112096 –175.60 1044.8 0.4339 0.4432 –0.3621 2.5253
–36 0.002389 0.01738 105625 –175.17 1045.3 0.4348 0.4432 –0.3611 2.5196
–35 0.002541 0.01738 99555 –174.73 1045.7 0.4358 0.4433 –0.3600 2.5138
–34 0.002701 0.01738 93860 –174.30 1046.1 0.4368 0.4433 –0.3590 2.5081
–33 0.002871 0.01738 88516 –173.86 1046.6 0.4377 0.4434 –0.3580 2.5024
–32 0.003051 0.01738 83500 –173.42 1047.0 0.4387 0.4434 –0.3570 2.4968
–31 0.003241 0.01738 78790 –172.98 1047.5 0.4396 0.4434 –0.3559 2.4911
–30 0.003442 0.01738 74366 –172.54 1047.9 0.4406 0.4435 –0.3549 2.4855
–29 0.003654 0.01738 70209 –172.10 1048.4 0.4416 0.4435 –0.3539 2.4800
–28 0.003878 0.01739 66303 –171.66 1048.8 0.4425 0.4436 –0.3529 2.4744
–27 0.004115 0.01739 62631 –171.22 1049.2 0.4435 0.4436 –0.3518 2.4689
–26 0.004365 0.01739 59179 –170.77 1049.7 0.4445 0.4437 –0.3508 2.4634
–25 0.004629 0.01739 55931 –170.33 1050.1 0.4454 0.4437 –0.3498 2.4580
–24 0.004908 0.01739 52876 –169.88 1050.6 0.4464 0.4437 –0.3488 2.4525
–23 0.005202 0.01739 50001 –169.43 1051.0 0.4473 0.4438 –0.3477 2.4471
–22 0.005512 0.01739 47294 –168.99 1051.4 0.4483 0.4439 –0.3467 2.4418
–21 0.005839 0.01740 44745 –168.54 1051.9 0.4493 0.4439 –0.3457 2.4364
–20 0.006184 0.01740 42345 –168.09 1052.3 0.4502 0.4440 –0.3447 2.4311
–19 0.006548 0.01740 40084 –167.64 1052.8 0.4512 0.4440 –0.3436 2.4258
–18 0.006932 0.01740 37953 –167.19 1053.2 0.4522 0.4441 –0.3426 2.4205
–17 0.007335 0.01740 35944 –166.73 1053.7 0.4531 0.4441 –0.3416 2.4153
–16 0.007761 0.01740 34050 –166.28 1054.1 0.4541 0.4442 –0.3406 2.4101
–15 0.008209 0.01740 32264 –165.82 1054.5 0.4551 0.4443 –0.3396 2.4049
–14 0.008681 0.01741 30580 –165.37 1055.0 0.4560 0.4443 –0.3385 2.3997
–13 0.009177 0.01741 28990 –164.91 1055.4 0.4570 0.4444 –0.3375 2.3946
–12 0.009700 0.01741 27490 –164.46 1055.9 0.4580 0.4445 –0.3365 2.3895
–11 0.010249 0.01741 26073 –164.00 1056.3 0.4589 0.4445 –0.3355 2.3844
–10 0.010827 0.01741 24736 –163.54 1056.7 0.4599 0.4446 –0.3344 2.3793
–9 0.011435 0.01741 23473 –163.08 1057.2 0.4609 0.4447 –0.3334 2.3743
–8 0.012075 0.01741 22279 –162.62 1057.6 0.4618 0.4448 –0.3324 2.3692
–7 0.012747 0.01742 21152 –162.15 1058.1 0.4628 0.4448 –0.3314 2.3642
–6 0.013453 0.01742 20086 –161.69 1058.5 0.4638 0.4449 –0.3303 2.3593
–5 0.014194 0.01742 19078 –161.23 1058.9 0.4647 0.4450 –0.3293 2.3543
–4 0.014974 0.01742 18125 –160.76 1059.4 0.4657 0.4451 –0.3283 2.3494
–3 0.015792 0.01742 17223 –160.29 1059.8 0.4667 0.4452 –0.3273 2.3445
–2 0.016651 0.01742 16370 –159.83 1060.3 0.4677 0.4453 –0.3263 2.3396
–1 0.017553 0.01742 15563 –159.36 1060.7 0.4686 0.4454 –0.3252 2.3348
0 0.018499 0.01743 14799 –158.89 1061.2 0.4696 0.4455 –0.3242 2.3300
1 0.019492 0.01743 14076 –158.42 1061.6 0.4706 0.4456 –0.3232 2.3251
2 0.020533 0.01743 13391 –157.95 1062.0 0.4715 0.4457 –0.3222 2.3204
3 0.021625 0.01743 12742 –157.48 1062.5 0.4725 0.4458 –0.3212 2.3156
4 0.022770 0.01743 12127 –157.00 1062.9 0.4735 0.4459 –0.3201 2.3109
5 0.023971 0.01743 11545 –156.53 1063.4 0.4745 0.4460 –0.3191 2.3062
6 0.025229 0.01743 10992 –156.05 1063.8 0.4754 0.4461 –0.3181 2.3015
7 0.026547 0.01744 10469 –155.58 1064.2 0.4764 0.4462 –0.3171 2.2968
8 0.027929 0.01744 9972.3 –155.10 1064.7 0.4774 0.4463 –0.3160 2.2921
9 0.029375 0.01744 9501.4 –154.62 1065.1 0.4783 0.4464 –0.3150 2.2875
10 0.030890 0.01744 9054.6 –154.15 1065.6 0.4793 0.4466 –0.3140 2.2829
11 0.032476 0.01744 8630.7 –153.67 1066.0 0.4803 0.4467 –0.3130 2.2783
12 0.034136 0.01744 8228.3 –153.18 1066.4 0.4813 0.4468 –0.3120 2.2738
13 0.035874 0.01744 7846.3 –152.70 1066.9 0.4822 0.4470 –0.3109 2.2692
Table 3 Thermodynamic Properties of Water at Saturation (Continued)
Temp.,
°F
t
Absolute
Pressure
pws, psia
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

14 0.037692 0.01745 7483.6 –152.22 1067.3 0.4832 0.4471 –0.3099 2.2647
15 0.039593 0.01745 7139.1 –151.74 1067.7 0.4842 0.4472 –0.3089 2.2602
16 0.041582 0.01745 6811.9 –151.25 1068.2 0.4852 0.4474 –0.3079 2.2557
17 0.043662 0.01745 6501.0 –150.77 1068.6 0.4861 0.4475 –0.3069 2.2513
18 0.045837 0.01745 6205.5 –150.28 1069.1 0.4871 0.4477 –0.3058 2.2468
19 0.048109 0.01745 5924.6 –149.79 1069.5 0.4881 0.4478 –0.3048 2.2424
20 0.050485 0.01746 5657.6 –149.30 1069.9 0.4891 0.4480 –0.3038 2.2380
21 0.052967 0.01746 5403.6 –148.81 1070.4 0.4900 0.4481 –0.3028 2.2337
22 0.055560 0.01746 5162.1 –148.32 1070.8 0.4910 0.4483 –0.3018 2.2293
23 0.058268 0.01746 4932.3 –147.83 1071.3 0.4920 0.4484 –0.3007 2.2250
24 0.061096 0.01746 4713.7 –147.34 1071.7 0.4930 0.4486 –0.2997 2.2207
25 0.064048 0.01746 4505.6 –146.85 1072.1 0.4939 0.4488 –0.2987 2.2164
26 0.067130 0.01746 4307.6 –146.35 1072.6 0.4949 0.4489 –0.2977 2.2121
27 0.070347 0.01747 4119.0 –145.86 1073.0 0.4959 0.4492 –0.2967 2.2078
28 0.073704 0.01747 3939.4 –145.36 1073.4 0.4969 0.4495 –0.2957 2.2036
29 0.077206 0.01747 3768.4 –144.86 1073.9 0.4979 0.4499 –0.2946 2.1994
30 0.080858 0.01747 3605.5 –144.36 1074.3 0.4988 0.4503 –0.2936 2.1952
31 0.084668 0.01747 3450.2 –143.86 1074.8 0.4998 0.4506 –0.2926 2.1910
32 0.088649 0.01602 3302.0 –0.01788 1075.2 1.0079 0.4510 0.0000 2.1868
33 0.092293 0.01602 3178.1 0.98981 1075.6 1.0074 0.4511 0.0020 2.1833
34 0.096069 0.01602 3059.3 1.9970 1076.1 1.0070 0.4512 0.0041 2.1797
35 0.099981 0.01602 2945.5 3.0039 1076.5 1.0066 0.4513 0.0061 2.1762
36 0.10403 0.01602 2836.5 4.0102 1076.9 1.0062 0.4513 0.0081 2.1727
37 0.10823 0.01602 2731.9 5.0163 1077.4 1.0058 0.4514 0.0102 2.1693
38 0.11258 0.01602 2631.7 6.0219 1077.8 1.0054 0.4515 0.0122 2.1658
39 0.11708 0.01602 2535.6 7.0272 1078.3 1.0051 0.4516 0.0142 2.1624
40 0.12173 0.01602 2443.4 8.0321 1078.7 1.0048 0.4517 0.0162 2.1590
41 0.12656 0.01602 2355.0 9.0367 1079.1 1.0044 0.4518 0.0182 2.1556
42 0.13155 0.01602 2270.1 10.041 1079.6 1.0041 0.4519 0.0202 2.1522
43 0.13671 0.01602 2188.7 11.045 1080.0 1.0038 0.4520 0.0222 2.1488
44 0.14205 0.01602 2110.6 12.049 1080.5 1.0036 0.4521 0.0242 2.1454
45 0.14757 0.01602 2035.6 13.052 1080.9 1.0033 0.4522 0.0262 2.1421
46 0.15328 0.01602 1963.6 14.055 1081.3 1.0031 0.4523 0.0282 2.1388
47 0.15919 0.01602 1894.4 15.058 1081.8 1.0028 0.4524 0.0302 2.1355
48 0.16530 0.01602 1828.0 16.061 1082.2 1.0026 0.4526 0.0321 2.1322
49 0.17161 0.01602 1764.2 17.064 1082.6 1.0024 0.4527 0.0341 2.1289
50 0.17813 0.01602 1702.9 18.066 1083.1 1.0022 0.4528 0.0361 2.1257
51 0.18487 0.01602 1644.0 19.068 1083.5 1.0020 0.4529 0.0381 2.1225
52 0.19184 0.01603 1587.4 20.070 1083.9 1.0018 0.4530 0.0400 2.1192
53 0.19903 0.01603 1533.0 21.071 1084.4 1.0016 0.4531 0.0420 2.1160
54 0.20646 0.01603 1480.6 22.073 1084.8 1.0014 0.4533 0.0439 2.1129
55 0.21414 0.01603 1430.3 23.074 1085.3 1.0012 0.4534 0.0459 2.1097
56 0.22206 0.01603 1381.9 24.075 1085.7 1.0011 0.4535 0.0478 2.1065
57 0.23024 0.01603 1335.4 25.077 1086.1 1.0009 0.4536 0.0497 2.1034
58 0.23868 0.01603 1290.6 26.077 1086.6 1.0008 0.4538 0.0517 2.1003
59 0.24740 0.01603 1247.5 27.078 1087.0 1.0006 0.4539 0.0536 2.0972
60 0.25639 0.01603 1206.1 28.079 1087.4 1.0005 0.4540 0.0555 2.0941
61 0.26567 0.01604 1166.2 29.079 1087.9 1.0004 0.4542 0.0575 2.0910
62 0.27524 0.01604 1127.7 30.079 1088.3 1.0002 0.4543 0.0594 2.0879
Temp.,
°F
t
Absolute
Pressure
pws, psia
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

Psychrometrics 1.11
63 0.28511 0.01604 1090.7 31.080 1088.7 1.0001 0.4545 0.0613 2.0849
64 0.29529 0.01604 1055.1 32.080 1089.2 1.0000 0.4546 0.0632 2.0818
65 0.30579 0.01604 1020.8 33.080 1089.6 0.9999 0.4547 0.0651 2.0788
66 0.31662 0.01604 987.77 34.080 1090.0 0.9998 0.4549 0.0670 2.0758
67 0.32777 0.01605 955.93 35.079 1090.5 0.9997 0.4550 0.0689 2.0728
68 0.33927 0.01605 925.25 36.079 1090.9 0.9996 0.4552 0.0708 2.0699
69 0.35113 0.01605 895.68 37.079 1091.3 0.9995 0.4553 0.0727 2.0669
70 0.36334 0.01605 867.19 38.078 1091.8 0.9994 0.4555 0.0746 2.0640
71 0.37592 0.01605 839.72 39.078 1092.2 0.9993 0.4556 0.0765 2.0610
72 0.38889 0.01606 813.23 40.077 1092.7 0.9992 0.4558 0.0784 2.0581
73 0.40224 0.01606 787.69 41.076 1093.1 0.9992 0.4559 0.0802 2.0552
74 0.41599 0.01606 763.06 42.075 1093.5 0.9991 0.4561 0.0821 2.0523
75 0.43015 0.01606 739.30 43.074 1094.0 0.9990 0.4563 0.0840 2.0495
76 0.44473 0.01606 716.38 44.073 1094.4 0.9990 0.4564 0.0859 2.0466
77 0.45973 0.01607 694.26 45.072 1094.8 0.9989 0.4566 0.0877 2.0438
78 0.47518 0.01607 672.92 46.071 1095.2 0.9988 0.4567 0.0896 2.0409
79 0.49108 0.01607 652.32 47.070 1095.7 0.9988 0.4569 0.0914 2.0381
80 0.50744 0.01607 632.44 48.069 1096.1 0.9987 0.4571 0.0933 2.0353
81 0.52427 0.01608 613.25 49.068 1096.5 0.9987 0.4572 0.0951 2.0325
82 0.54159 0.01608 594.72 50.066 1097.0 0.9986 0.4574 0.0970 2.0297
83 0.55940 0.01608 576.82 51.065 1097.4 0.9986 0.4576 0.0988 2.0270
84 0.57772 0.01608 559.54 52.064 1097.8 0.9985 0.4578 0.1007 2.0242
85 0.59656 0.01609 542.84 53.062 1098.3 0.9985 0.4579 0.1025 2.0215
86 0.61593 0.01609 526.71 54.061 1098.7 0.9984 0.4581 0.1043 2.0188
87 0.63585 0.01609 511.13 55.059 1099.1 0.9984 0.4583 0.1062 2.0160
88 0.65632 0.01609 496.07 56.058 1099.6 0.9984 0.4585 0.1080 2.0133
89 0.67736 0.01610 481.51 57.056 1100.0 0.9983 0.4586 0.1098 2.0107
90 0.69899 0.01610 467.45 58.054 1100.4 0.9983 0.4588 0.1116 2.0080
91 0.72122 0.01610 453.85 59.053 1100.9 0.9983 0.4590 0.1134 2.0053
92 0.74405 0.01611 440.70 60.051 1101.3 0.9983 0.4592 0.1152 2.0027
93 0.76751 0.01611 427.98 61.049 1101.7 0.9982 0.4594 0.1171 2.0000
94 0.79161 0.01611 415.68 62.048 1102.1 0.9982 0.4596 0.1189 1.9974
95 0.81636 0.01612 403.79 63.046 1102.6 0.9982 0.4598 0.1207 1.9948
96 0.84178 0.01612 392.28 64.044 1103.0 0.9982 0.4599 0.1225 1.9922
97 0.86788 0.01612 381.15 65.042 1103.4 0.9981 0.4601 0.1242 1.9896
98 0.89468 0.01612 370.38 66.041 1103.9 0.9981 0.4603 0.1260 1.9870
99 0.92220 0.01613 359.96 67.039 1104.3 0.9981 0.4605 0.1278 1.9845
100 0.95044 0.01613 349.87 68.037 1104.7 0.9981 0.4607 0.1296 1.9819
101 0.97943 0.01613 340.10 69.035 1105.1 0.9981 0.4609 0.1314 1.9794
102 1.0092 0.01614 330.65 70.033 1105.6 0.9981 0.4611 0.1332 1.9769
103 1.0397 0.01614 321.50 71.032 1106.0 0.9981 0.4613 0.1350 1.9743
104 1.0710 0.01614 312.63 72.030 1106.4 0.9981 0.4615 0.1367 1.9718
105 1.1032 0.01615 304.05 73.028 1106.9 0.9981 0.4617 0.1385 1.9693
106 1.1361 0.01615 295.73 74.026 1107.3 0.9981 0.4619 0.1403 1.9669
107 1.1699 0.01616 287.68 75.024 1107.7 0.9981 0.4621 0.1420 1.9644
108 1.2046 0.01616 279.88 76.022 1108.1 0.9981 0.4623 0.1438 1.9619
109 1.2401 0.01616 272.32 77.021 1108.6 0.9981 0.4625 0.1455 1.9595
110 1.2766 0.01617 264.99 78.019 1109.0 0.9981 0.4627 0.1473 1.9570
111 1.3140 0.01617 257.89 79.017 1109.4 0.9981 0.4629 0.1490 1.9546
Temp.,
°F
t
Absolute
Pressure
pws, psia
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

112 1.3523 0.01617 251.01 80.015 1109.8 0.9981 0.4632 0.1508 1.9522
113 1.3915 0.01618 244.34 81.013 1110.3 0.9981 0.4634 0.1525 1.9498
114 1.4318 0.01618 237.87 82.012 1110.7 0.9981 0.4636 0.1543 1.9474
115 1.4730 0.01618 231.60 83.010 1111.1 0.9982 0.4638 0.1560 1.9450
116 1.5153 0.01619 225.51 84.008 1111.5 0.9982 0.4640 0.1577 1.9427
117 1.5586 0.01619 219.62 85.006 1112.0 0.9982 0.4642 0.1595 1.9403
118 1.6030 0.01620 213.90 86.005 1112.4 0.9982 0.4644 0.1612 1.9380
119 1.6484 0.01620 208.35 87.003 1112.8 0.9982 0.4647 0.1629 1.9356
120 1.6949 0.01620 202.96 88.002 1113.2 0.9983 0.4649 0.1647 1.9333
121 1.7426 0.01621 197.74 89.000 1113.6 0.9983 0.4651 0.1664 1.9310
122 1.7914 0.01621 192.67 89.998 1114.1 0.9983 0.4653 0.1681 1.9287
123 1.8414 0.01622 187.75 90.997 1114.5 0.9983 0.4656 0.1698 1.9264
124 1.8925 0.01622 182.97 91.995 1114.9 0.9984 0.4658 0.1715 1.9241
125 1.9449 0.01623 178.34 92.994 1115.3 0.9984 0.4660 0.1732 1.9218
126 1.9985 0.01623 173.84 93.992 1115.7 0.9984 0.4662 0.1749 1.9195
127 2.0534 0.01623 169.47 94.991 1116.2 0.9985 0.4665 0.1766 1.9173
128 2.1096 0.01624 165.22 95.990 1116.6 0.9985 0.4667 0.1783 1.9150
129 2.1670 0.01624 161.10 96.988 1117.0 0.9986 0.4669 0.1800 1.9128
130 2.2258 0.01625 157.10 97.987 1117.4 0.9986 0.4672 0.1817 1.9106
131 2.2860 0.01625 153.22 98.986 1117.8 0.9986 0.4674 0.1834 1.9084
132 2.3475 0.01626 149.44 99.985 1118.3 0.9987 0.4677 0.1851 1.9061
133 2.4105 0.01626 145.77 100.98 1118.7 0.9987 0.4679 0.1868 1.9039
134 2.4749 0.01626 142.21 101.98 1119.1 0.9988 0.4682 0.1885 1.9018
135 2.5407 0.01627 138.74 102.98 1119.5 0.9988 0.4684 0.1902 1.8996
136 2.6081 0.01627 135.38 103.98 1119.9 0.9989 0.4686 0.1918 1.8974
137 2.6769 0.01628 132.10 104.98 1120.4 0.9989 0.4689 0.1935 1.8953
138 2.7473 0.01628 128.92 105.98 1120.8 0.9990 0.4691 0.1952 1.8931
139 2.8193 0.01629 125.83 106.98 1121.2 0.9990 0.4694 0.1969 1.8910
140 2.8929 0.01629 122.82 107.98 1121.6 0.9991 0.4697 0.1985 1.8888
141 2.9681 0.01630 119.90 108.98 1122.0 0.9991 0.4699 0.2002 1.8867
142 3.0450 0.01630 117.06 109.98 1122.4 0.9992 0.4702 0.2019 1.8846
143 3.1235 0.01631 114.29 110.98 1122.8 0.9993 0.4704 0.2035 1.8825
144 3.2038 0.01631 111.60 111.97 1123.3 0.9993 0.4707 0.2052 1.8804
145 3.2858 0.01632 108.99 112.97 1123.7 0.9994 0.4710 0.2068 1.8783
146 3.3696 0.01632 106.44 113.97 1124.1 0.9994 0.4712 0.2085 1.8762
147 3.4552 0.01633 103.97 114.97 1124.5 0.9995 0.4715 0.2101 1.8742
148 3.5426 0.01633 101.56 115.97 1124.9 0.9996 0.4718 0.2118 1.8721
149 3.6319 0.01634 99.216 116.97 1125.3 0.9997 0.4721 0.2134 1.8701
150 3.7231 0.01634 96.934 117.97 1125.7 0.9997 0.4723 0.2151 1.8680
151 3.8163 0.01635 94.714 118.97 1126.2 0.9998 0.4726 0.2167 1.8660
152 3.9114 0.01635 92.552 119.97 1126.6 0.9999 0.4729 0.2183 1.8640
153 4.0085 0.01636 90.448 120.97 1127.0 0.9999 0.4732 0.2200 1.8620
154 4.1076 0.01636 88.399 121.97 1127.4 1.0000 0.4735 0.2216 1.8599
155 4.2089 0.01637 86.405 122.97 1127.8 1.0001 0.4738 0.2232 1.8580
156 4.3122 0.01637 84.463 123.97 1128.2 1.0002 0.4741 0.2249 1.8560
157 4.4176 0.01638 82.571 124.97 1128.6 1.0003 0.4743 0.2265 1.8540
158 4.5253 0.01638 80.729 125.98 1129.0 1.0003 0.4746 0.2281 1.8520
159 4.6351 0.01639 78.934 126.98 1129.4 1.0004 0.4749 0.2297 1.8500
160 4.7472 0.01639 77.186 127.98 1129.8 1.0005 0.4753 0.2313 1.8481
Temp.,
°F
t
Absolute
Pressure
pws, psia
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

Psychrometrics 1.13
161 4.8616 0.01640 75.483 128.98 1130.2 1.0006 0.4756 0.2329 1.8461
162 4.9783 0.01640 73.824 129.98 1130.6 1.0007 0.4759 0.2346 1.8442
163 5.0973 0.01641 72.207 130.98 1131.1 1.0008 0.4762 0.2362 1.8423
164 5.2187 0.01642 70.632 131.98 1131.5 1.0009 0.4765 0.2378 1.8403
165 5.3426 0.01642 69.097 132.98 1131.9 1.0010 0.4768 0.2394 1.8384
166 5.4689 0.01643 67.600 133.98 1132.3 1.0011 0.4771 0.2410 1.8365
167 5.5978 0.01643 66.141 134.98 1132.7 1.0012 0.4775 0.2426 1.8346
168 5.7292 0.01644 64.720 135.99 1133.1 1.0013 0.4778 0.2442 1.8327
169 5.8632 0.01644 63.333 136.99 1133.5 1.0014 0.4781 0.2458 1.8308
170 5.9998 0.01645 61.982 137.99 1133.9 1.0015 0.4785 0.2474 1.8290
171 6.1390 0.01645 60.664 138.99 1134.3 1.0016 0.4788 0.2489 1.8271
172 6.2810 0.01646 59.379 139.99 1134.7 1.0017 0.4791 0.2505 1.8252
173 6.4258 0.01647 58.125 141.00 1135.1 1.0018 0.4795 0.2521 1.8234
174 6.5733 0.01647 56.903 142.00 1135.5 1.0019 0.4798 0.2537 1.8215
175 6.7237 0.01648 55.710 143.00 1135.9 1.0020 0.4802 0.2553 1.8197
176 6.8769 0.01648 54.547 144.00 1136.3 1.0021 0.4805 0.2569 1.8179
177 7.0331 0.01649 53.412 145.00 1136.7 1.0022 0.4809 0.2584 1.8160
178 7.1922 0.01650 52.305 146.01 1137.1 1.0023 0.4813 0.2600 1.8142
179 7.3544 0.01650 51.225 147.01 1137.5 1.0025 0.4816 0.2616 1.8124
180 7.5196 0.01651 50.171 148.01 1137.9 1.0026 0.4820 0.2631 1.8106
181 7.6879 0.01651 49.142 149.02 1138.3 1.0027 0.4824 0.2647 1.8088
182 7.8593 0.01652 48.138 150.02 1138.7 1.0028 0.4828 0.2663 1.8070
183 8.0339 0.01653 47.158 151.02 1139.1 1.0029 0.4831 0.2678 1.8052
184 8.2118 0.01653 46.201 152.03 1139.5 1.0031 0.4835 0.2694 1.8035
185 8.3930 0.01654 45.267 153.03 1139.9 1.0032 0.4839 0.2709 1.8017
186 8.5775 0.01654 44.355 154.03 1140.3 1.0033 0.4843 0.2725 1.7999
187 8.7653 0.01655 43.465 155.04 1140.7 1.0034 0.4847 0.2741 1.7982
188 8.9566 0.01656 42.596 156.04 1141.0 1.0036 0.4851 0.2756 1.7964
189 9.1514 0.01656 41.747 157.04 1141.4 1.0037 0.4855 0.2772 1.7947
190 9.3497 0.01657 40.918 158.05 1141.8 1.0038 0.4859 0.2787 1.7930
191 9.5515 0.01658 40.108 159.05 1142.2 1.0040 0.4863 0.2802 1.7912
192 9.7570 0.01658 39.317 160.06 1142.6 1.0041 0.4868 0.2818 1.7895
193 9.9662 0.01659 38.545 161.06 1143.0 1.0042 0.4872 0.2833 1.7878
194 10.179 0.01659 37.790 162.07 1143.4 1.0044 0.4876 0.2849 1.7861
195 10.396 0.01660 37.053 163.07 1143.8 1.0045 0.4880 0.2864 1.7844
196 10.616 0.01661 36.332 164.08 1144.2 1.0047 0.4885 0.2879 1.7827
197 10.841 0.01661 35.628 165.08 1144.6 1.0048 0.4889 0.2895 1.7810
198 11.069 0.01662 34.940 166.09 1144.9 1.0049 0.4894 0.2910 1.7793
199 11.301 0.01663 34.268 167.09 1145.3 1.0051 0.4898 0.2925 1.7777
200 11.538 0.01663 33.611 168.10 1145.7 1.0052 0.4903 0.2940 1.7760
201 11.778 0.01664 32.968 169.10 1146.1 1.0054 0.4908 0.2956 1.7743
202 12.023 0.01665 32.341 170.11 1146.5 1.0055 0.4912 0.2971 1.7727
203 12.271 0.01665 31.727 171.12 1146.9 1.0057 0.4917 0.2986 1.7710
204 12.525 0.01666 31.127 172.12 1147.3 1.0058 0.4922 0.3001 1.7694
205 12.782 0.01667 30.540 173.13 1147.6 1.0060 0.4927 0.3016 1.7678
206 13.044 0.01667 29.967 174.14 1148.0 1.0062 0.4931 0.3031 1.7661
207 13.310 0.01668 29.406 175.14 1148.4 1.0063 0.4936 0.3047 1.7645
208 13.581 0.01669 28.857 176.15 1148.8 1.0065 0.4941 0.3062 1.7629
Temp.,
°F
t
Absolute
Pressure
pws, psia
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

209 13.856 0.01669 28.321 177.16 1149.2 1.0066 0.4947 0.3077 1.7613
210 14.136 0.01670 27.796 178.17 1149.5 1.0068 0.4952 0.3092 1.7597
212 14.709 0.01671 26.781 180.18 1150.3 1.0071 0.4962 0.3122 1.7565
214 15.302 0.01673 25.809 182.20 1151.0 1.0075 0.4973 0.3152 1.7533
216 15.915 0.01674 24.879 184.21 1151.8 1.0078 0.4983 0.3182 1.7502
218 16.548 0.01676 23.988 186.23 1152.5 1.0082 0.4995 0.3211 1.7471
220 17.201 0.01677 23.135 188.25 1153.3 1.0085 0.5006 0.3241 1.7440
222 17.875 0.01679 22.317 190.27 1154.0 1.0089 0.5017 0.3271 1.7409
224 18.571 0.01680 21.534 192.29 1154.8 1.0093 0.5029 0.3300 1.7378
226 19.290 0.01681 20.783 194.31 1155.5 1.0096 0.5041 0.3330 1.7348
228 20.031 0.01683 20.063 196.33 1156.2 1.0100 0.5054 0.3359 1.7318
230 20.795 0.01684 19.373 198.35 1157.0 1.0104 0.5066 0.3388 1.7288
232 21.583 0.01686 18.710 200.37 1157.7 1.0108 0.5079 0.3418 1.7258
234 22.395 0.01687 18.074 202.40 1158.4 1.0112 0.5092 0.3447 1.7229
236 23.233 0.01689 17.464 204.42 1159.1 1.0116 0.5106 0.3476 1.7199
238 24.096 0.01691 16.878 206.45 1159.8 1.0120 0.5120 0.3505 1.7170
240 24.985 0.01692 16.316 208.47 1160.5 1.0125 0.5134 0.3534 1.7141
242 25.901 0.01694 15.775 210.50 1161.2 1.0129 0.5148 0.3563 1.7113
244 26.844 0.01695 15.256 212.53 1161.9 1.0133 0.5162 0.3592 1.7084
246 27.815 0.01697 14.757 214.56 1162.6 1.0138 0.5177 0.3620 1.7056
248 28.814 0.01698 14.277 216.59 1163.3 1.0142 0.5193 0.3649 1.7028
250 29.843 0.01700 13.816 218.62 1164.0 1.0147 0.5208 0.3678 1.7000
252 30.901 0.01702 13.373 220.65 1164.7 1.0152 0.5224 0.3706 1.6972
254 31.990 0.01703 12.946 222.68 1165.4 1.0156 0.5240 0.3735 1.6944
256 33.110 0.01705 12.535 224.72 1166.1 1.0161 0.5256 0.3763 1.6917
258 34.261 0.01707 12.140 226.75 1166.8 1.0166 0.5273 0.3792 1.6890
260 35.445 0.01708 11.760 228.79 1167.4 1.0171 0.5290 0.3820 1.6862
262 36.662 0.01710 11.394 230.83 1168.1 1.0176 0.5307 0.3848 1.6836
264 37.913 0.01712 11.041 232.87 1168.8 1.0181 0.5325 0.3876 1.6809
266 39.198 0.01714 10.702 234.90 1169.4 1.0186 0.5343 0.3904 1.6782
268 40.518 0.01715 10.374 236.94 1170.1 1.0192 0.5361 0.3932 1.6756
270 41.874 0.01717 10.059 238.99 1170.7 1.0197 0.5380 0.3960 1.6730
272 43.267 0.01719 9.7552 241.03 1171.4 1.0203 0.5399 0.3988 1.6704
274 44.697 0.01721 9.4621 243.07 1172.0 1.0208 0.5418 0.4016 1.6678
276 46.165 0.01722 9.1796 245.12 1172.7 1.0214 0.5438 0.4044 1.6652
278 47.671 0.01724 8.9070 247.16 1173.3 1.0219 0.5458 0.4071 1.6626
280 49.218 0.01726 8.6442 249.21 1173.9 1.0225 0.5478 0.4099 1.6601
282 50.804 0.01728 8.3905 251.26 1174.5 1.0231 0.5499 0.4127 1.6575
284 52.431 0.01730 8.1457 253.31 1175.2 1.0237 0.5520 0.4154 1.6550
286 54.100 0.01731 7.9094 255.36 1175.8 1.0243 0.5541 0.4182 1.6525
288 55.812 0.01733 7.6813 257.41 1176.4 1.0249 0.5562 0.4209 1.6500
290 57.567 0.01735 7.4610 259.47 1177.0 1.0255 0.5584 0.4236 1.6476
292 59.366 0.01737 7.2482 261.52 1177.6 1.0262 0.5606 0.4264 1.6451
294 61.210 0.01739 7.0426 263.58 1178.2 1.0268 0.5629 0.4291 1.6427
296 63.100 0.01741 6.8441 265.64 1178.8 1.0275 0.5652 0.4318 1.6402
298 65.037 0.01743 6.6521 267.70 1179.4 1.0281 0.5675 0.4345 1.6378
300 67.021 0.01745 6.4666 269.76 1180.0 1.0288 0.5699 0.4372 1.6354
Temp.,
°F
t
Absolute
Pressure
pws, psia
Btu/lb·°R
Specific Entropy,
Btu/lb·°R
Sat. Solid
vi
Sat. Vapor
vg
Sat. Solid
hi
Sat. Vapor
hg
Sat. Solid
cp,i
Sat. Vapor
cp,g
Sat. Solid
si
Sat. Vapor
sg
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Psychrometrics 1.15
The following properties are shown in Table 3:
t = temperature in degrees Fahrenheit based on ITS-90 and
expressed relative to absolute temperature T in degrees Rankine
by the following relation:
T = (°F +459.67)
pws = absolute pressure of water (solid, liquid, or vapor) at saturation
or sublimation temperature t, psia
vi = specific volume of saturated solid (ice), lb3/lb
vf = specific volume of saturated liquid (water), ft3/lb
vg = specific volume of saturated vapor (steam), ft3/lb
hi = specific enthalpy of saturated solid (ice), Btu/lb
hf = specific enthalpy of saturated liquid (water), Btu/lb kJ/kg
hg = specific enthalpy of saturated vapor (steam), Btu/lb
cp,i = specific isobaric heat capacity of saturated solid (ice), Btu/
(lb·°R)
cp,f = specific isobaric heat capacity of saturated liquid (water), Btu/
lb·°R
cp,g = specific isobaric heat capacity of saturated vapor (steam), Btu/
lb·°R
si = specific entropy of saturated solid (ice), Btu/lb·°R
sf = specific entropy of saturated liquid (water), Btu/lb·°R kJ/(kg·K)
sg = specific entropy of saturated vapor (steam), Btu/lb·°R
The water vapor saturation pressure is required to determine
a number of moist air properties, principally the saturation humid-
ity ratio. Values may be obtained from Table 3 or calculated from
formulas given by IPAWS R7-97(2012) and R14-08 (2011).
The saturation (sublimation) pressure over ice for the tem-
perature range of –148 to 32°F is given by
ln pws = C1/T + C2 + C3T + C4T2+ C5T3+ C6T4+ C7 ln T (5)
where
C1 = –1.021 416 5 E+04
C2 = –4.893 242 8 E+00
C3 = –5.376 579 4 E–03
C4 = 1.920 237 7 E–07
C5 = 3.557 583 2 E–10
C6 = –9.034 468 8 E–14
C7 = 4.163 501 9 E00
The saturation pressure over liquid water for the temperature range
of 32 to 392°F is given by
ln pws = C8/T + C9 + C10T + C11T2 + C12T3 + C13 ln T (6)
where
C8 = –1.044 039 7 E+04
C9 = –1.129 465 0 E+01
C10 = –2.702 235 5 E–02
C11 = 1.289 036 0 E–05
C12 = –2.478 068 1 E–09
C13 = 6.545 967 3 E+00
In both Equations (5) and (6),
pws = saturation pressure, psia
T = absolute temperature, °R = °F + 459.67
The coefficients of Equations (5) and (6) were derived from the
Hyland-Wexler equations, which are given in SI units. Because of
rounding errors in the derivations and in some computers’ calculat-
ing precision, results from Equations (5) and (6) may not agree pre-
cisely with Table 3 values.
The vapor pressure ps of water in saturated moist air differs neg-
ligibly from the saturation vapor pressure pws of pure water at the
same temperature. Consequently, ps can be used in equations in
place of pws with very little error:
ps = xws p
where xws is the mole fraction of water vapor in saturated moist air
at temperature t and pressure p, and p is the total barometric pressure
of moist air.
5. HUMIDITY PARAMETERS
Basic Parameters
Humidity ratio W (or mixing ratio) of a given moist air sample
is defined as the ratio of the mass of water vapor to the mass of dry
air in the sample:
W = Mw /Mda (7)
W equals the mole fraction ratio xw /xda multiplied by the ratio of
molecular masses (18.015268/28.966 = 0.621945):
W = 0.621945xw /xda (8)
Specific humidity  is the ratio of the mass of water vapor to
total mass of the moist air sample:
 = Mw /(Mw + Mda) (9a)
In terms of the humidity ratio,
 = W/(1 + W) (9b)
Absolute humidity (alternatively, water vapor density) dv is the
ratio of the mass of water vapor to total volume of the sample:
dv = Mw /V (10)
Density  of a moist air mixture is the ratio of total mass to total
volume:
 = (Mda + Mw)/V = (1/v)(1 + W) (11)
where v is the moist air specific volume, ft3/lbda, as defined by
Equation (24).
Humidity Parameters Involving Saturation
The following definitions of humidity parameters involve the
concept of moist air saturation:
Saturation humidity ratio Ws(t, p) is the humidity ratio of
moist air saturated with respect to water (or ice) at the same tem-
perature t and pressure p.
Relative humidity  is the ratio of the actual water vapor partial
pressure in moist air at the dew-point pressure and temperature to
the reference saturation water vapor partial pressure at the dry-bulb
pressure and temperature:
 = (pwv _ enh/pwvs _ ref |p,t) = [f(p, tdp)e(tdp)]/[ f(p, tdb)e(tdb)] (12)
Note that Equations (12) and (22) have been revised so that they
cover both the normal range of relative humidity where e(tdb)  p
and the extended range (e.g., atmospheric pressure drying kilns)
where e(tdb)  p. The definitions in earlier editions applied only to
the normal range.
Dew-point temperature td is the temperature of moist air satu-
rated at pressure p, with the same humidity ratio W as that of the
given sample of moist air. It is defined as the solution td( p, W) of the
following equation:
Ws ( p, td) = W (13)
Thermodynamic wet-bulb temperature t* is the temperature
at which water (liquid or solid), by evaporating into moist air at dry-
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bulb temperature t and humidity ratio W, can bring air to saturation
adiabatically at the same temperature t* while total pressure p is
constant. This parameter is considered separately in the section on
Thermodynamic Wet-Bulb and Dew-Point Temperature.
6. 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 per-
fect gas equation of state as follows:
Dry air: pdaV = nda RT (14)
Water vapor: pwV = nw RT (15)
where
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, 1545.349 ft·lbf /lb mol· °R
T = absolute temperature, °R
The mixture also obeys the perfect gas equation:
pV = nRT (16)
or
( pda + pw)V = (nda + nw)RT (17)
where p = pda + pw is the total mixture pressure and n = nda + nw is
the total number of moles in the mixture. From Equations (14)
to (17), the mole fractions of dry air and water vapor are, respec-
tively,
xda = pda /( pda + pw) = pda/p (18)
and
xw = pw /(pda + pw) = pw /p (19)
From Equations (8), (18), and (19), the humidity ratio W is
W = 0.621945 (20)
The saturation humidity ratio Ws is
Ws = 0.621945 (21)
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  is defined in Equation (12). Using the
second equality and eliminating the enhancement factors, which are
not applicable using the perfect gas assumption, gives
 = e(tdp)/e(tdb) (22)
Substituting Equation (21) for Ws into Equation (13),
 = (23)
where  is degree of saturation W/Ws, dimensionless.
Both  and  are zero for dry air and unity for saturated moist air.
At intermediate states, their values differ, substantially at higher
temperatures.
The specific volume v of a moist air mixture is expressed in
terms of a unit mass of dry air:
v = V/Mda = V/(28.966nda) (24)
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 (14)
and (24), with the relation p = pda + pw,
v = (25)
Using Equation (18),
v = (26)
In Equations (25) and (26), v is specific volume, T is absolute tem-
perature, p is total pressure, pw is partial pressure of water vapor, and
W is humidity ratio.
In specific units, Equation (26) may be expressed as
v = 0.370486(t + 459.67)(1 + 1.607858W )/p
where
v = specific volume, ft3/lbda
t = dry-bulb temperature, °F
W = humidity ratio, lbw/lbda
p = total pressure, psia
The enthalpy of a mixture of perfect gases equals the sum of the
individual partial enthalpies of the components. Therefore, the spe-
cific enthalpy of moist air can be written as follows:
h = hda + Whg (27)
where hda is the specific enthalpy for dry air in Btu/lbda and hg is the
specific enthalpy for saturated water vapor in Btu/lbw at the mix-
ture’s temperature. As an approximation,
hda  0.240t (28)
hg  1061 + 0.444t (29)
where t is the dry-bulb temperature in °F. The moist air specific
enthalpy in Btu/lbda then becomes
h = 0.240t + W(1061 + 0.444t) (30)
7. THERMODYNAMIC WET-BULB AND
DEW-POINT TEMPERATURE
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 adiabatic saturation, saturated air is expelled at a temper-
ature equal to that of the injected water. In this constant-pressure
process,
• Humidity ratio increases from initial value W to Ws*, correspond-
ing to saturation at temperature t*
• Enthalpy increases from initial value h to hs*, corresponding to
saturation at 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 specific enthalpy in Btu/lbw of water added at tem-
perature t*
pw
p pw
–
--------------
-
pws
p pws
–
----------------
-

1 1 
–
  pws p

 
–
----------------------------------------------
-
RT
28.966 p pw
–
 
-------------------------------------
RdaT
p pw
–
--------------
-
=
RT 1 1.607858W
+
 
28.966p
-------------------------------------------------
RdaT 1 1.607858W
+
 
p
------------------------------------------------------
-
=
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Psychrometrics 1.17
Therefore, if the process is strictly adiabatic, conservation of en-
thalpy at constant total pressure requires that
h + (Ws* – W)hw
* = hs
* (31)
Ws*, hw*, and hs* are functions only of temperature t* for a fixed
value of pressure. The value of t* that satisfies Equation (31) for
given values of h, W, and p is the thermodynamic wet-bulb
temperature.
A psychrometer consists of two thermometers; one thermome-
ter’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 adia-
batic saturation, which defines the thermodynamic wet-bulb tem-
perature, 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 (40) in Chapter 6]. Fortunately, only
small corrections must be applied to wet-bulb thermometer readings
to obtain the thermodynamic wet-bulb temperature.
As defined, thermodynamic wet-bulb temperature is a unique
property of a given moist air sample independent of measurement
techniques.
Equation (31) is exact because it defines the thermodynamic wet-
bulb temperature t*. Substituting the approximate perfect gas relation
[Equation (30)] for h, the corresponding expression for hs*, and the
approximate relation for saturated liquid water
h*
w  t* – 32 (32)
into Equation (31), and solving for the humidity ratio,
W = (33)
where t and t* are in °F. Below freezing, the corresponding equa-
tions are
h*
w  –143.35 – 0.48(32 – t*) (34)
W = (35)
A wet/ice-bulb thermometer is imprecise when determining
moisture content at 32°F.
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).
For perfect gases, this reduces to
pws(td) = pw = ( pW )/(0.621945 + W) (36)
where pw is the water vapor partial pressure for the moist air sam-
ple and pws(td) is the saturation vapor pressure at temperature td.
The saturation vapor pressure is obtained from Table 3 or by using
Equation (5) or (6). Alternatively, the dew-point temperature can
be calculated directly by one of the following equations (Peppers
1988):
Between dew points of 32 to 200°F,
td = C14 + C15 + C162 + C173 + C18( pw)0.1984 (37)
Below 32°F,
td = 90.12 + 26.142+ 0.89272 (38)
where
td = dew-point temperature, °F
 = ln pw
pw = water vapor partial pressure, psia
C14 = 100.45
C15 = 33.193
C16 = 2.319
C17 = 0.17074
C18 = 1.2063
8. NUMERICAL CALCULATION OF MOIST
AIR PROPERTIES
The following are outlines, citing equations and tables already
presented, for calculating moist air properties using perfect gas
relations. These relations are accurate enough for most engineer-
ing 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 Psy-
chrometric Charts.
SITUATION 1.
Given: Dry-bulb temperature t, Wet-bulb temperature t*, Pressure p
SITUATION 2.
Given: Dry-bulb temperature t, Dew-point temperature td, Pressure p
SITUATION 3.
Given: Dry-bulb temperature t, Relative humidity Pressure p
Moist Air Property Tables for Standard Pressure
Table 2 shows thermodynamic properties for standard atmo-
spheric pressure at temperatures from –80 to 200°F calculated using
the ASHRAE RP-1485 (Herrmann et al. 2009) research project
numerical model. Properties of intermediate moist air states can be
calculated using the degree of saturation :
Volume v = vda + vas (39)
Enthalpy h = hda + has (40)
These equations are accurate to about 662°F. At higher tempera-
tures, errors can be significant.
1093 0.556t*
–
 W*
s 0.240 t t*
–
 
–
1093 0.444t t*
–
+
---------------------------------------------------------------------------------------
-
1220 0.04t*
–
 W*
s 0.240 t t*
–
 
–
1220 0.444t 0.48t*
–
+
------------------------------------------------------------------------------------
-
To Obtain Use Comments
pws (t*) Table 3 or Equation (5) or (6) Sat. press. for temp. t*
Ws* Equation (21) Using pws(t*)
W Equation (33) or (35)
pws (t) Table 3 or Equation (5) or (6) Sat. press. for temp. t
Ws Equation (21) Using pws(t)
 Equation (23) Using pws(t)
v Equation (26)
h Equation (30)
pw Equation (36)
td Table 3 with Equation (36), (37), or (38)
pw = pws(td) Table 3 or Equation (5) or (6) Sat. press. for temp. td
W Equation (20)
pws(t) Table 3 or Equation (5) or (6) Sat. press. for temp. t
Ws Equation (21) Using pws (t)
 Equation (23) Using pws(t)
v Equation (26)
h Equation (30)
t* Equation (21) and (33) or (35)
with Table 3 or with Equation
(5) or (6)
Requires trial-and-error
or numerical solution
method
pws(t) Table 3 or Equation (5) or (6) Sat. press. for temp. t
pw Equation (22)
W Equation (20)
Ws Equation (21) Using pws(t)
v Equation (26)
h Equation (30)
td Table 3 with Equation (36),
(37), or (38)
t* Equation (21) and (33) or (35)
with Table 3 or with Equation
(5) or (6)
Requires trial-and-error
or numerical solution
method
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9. PSYCHROMETRIC CHARTS
A psychrometric chart graphically represents the thermody-
namic 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
five such psychrometric charts. Chart 1 is shown as Figure 1; the
others may be obtained through ASHRAE.
Charts 1, 2, and 3 are for sea-level pressure, Chart 4 is for 5000 ft
altitude (24.89 in. Hg), and Chart 5 is for 7500 ft altitude (22.65 in.
Hg). 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 Hyland and Wexler (1983a) and
ASHRAE research project RP-1485. 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, 4, 5 Normal temperature 32 to 120°F
Chart 2 Low temperature –40 to 50°F
Chart 3 High temperature 60 to 250°F
Charts 6 to 9 are for 400 to 600°F and cover altitudes sea level,
2500 ft, 5000 ft, and 7500 ft. They were produced by Nelson and
Sauer (2002) and are available as a download with Gatley (2013).
Psychrometric properties or charts for other barometric pres-
sures 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. Constructing
charts for altitude conditions has been discussed by Haines (1961),
Karig (1946), and Rohsenow (1946).
Comparison of charts 1 and 4 by overlay reveals the following:
• The dry-bulb lines coincide.
• Wet-bulb lines for a given temperature originate at the intersec-
tions of the corresponding dry-bulb line and the two saturation
curves, and they have the same slope.
• Humidity ratio and enthalpy for a given dry- and wet-bulb tem-
perature increase with altitude, but there is little change in relative
humidity.
• Volume changes rapidly; for a given dry-bulb and humidity ratio,
it is practically inversely proportional to barometric pressure.
The following table compares properties at sea level (chart 1) and
5000 ft (chart 4):
Figure 1 shows humidity ratio lines (horizontal) for the range
from 0 (dry air) to 0.03 lbw/lbda. Enthalpy lines are oblique lines
across the chart precisely parallel to each other.
Dry-bulb temperature lines are straight, not precisely parallel to
each other, and inclined slightly from the vertical position. Thermo-
dynamic wet-bulb temperature lines are oblique and in a slightly
different direction from enthalpy lines. They are straight but are not
precisely parallel to each other.
Relative humidity lines are shown in intervals of 10%. The sat-
uration curve is the line of 100% rh, whereas 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
region coincide with extensions of thermodynamic wet-bulb tem-
perature lines. If required, the fog region can be further expanded by
extending 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 shows use of the ASHRAE psychrometric chart to
determine moist air properties.
Example 1. Moist air exists at 100°Fdry-bulb temperature, 65°F thermody-
namic wet-bulb temperature, and 14.696 psia (29.921 in. Hg) 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 100°F dry-bulb temperature and 65°F thermodynamic wet-bulb tem-
perature lines. Read humidity ratio W = 0.00523 lbw /lbda.
The enthalpy can be found by using two triangles to draw a line
parallel to the nearest enthalpy line (30 Btu/lbda) through the state point
to the nearest edge scale. Read h = 29.80 Btu/lbda.
Dew-point temperature can be read at the intersection of W =
0.00523 lbw/lbda with the saturation curve. Thus, td = 40°F.
Relative humidity  can be estimated directly. Thus,  = 13%.
Specific volume can be found by linear interpolation between the
volume lines for 14.0 and 14.5 ft3/lbda. Thus, v = 14.22 ft3/lbda.
10. TYPICAL AIR-CONDITIONING PROCESSES
The ASHRAE psychrometric chart can be used to solve numer-
ous 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 14.696 psia.
Moist Air Sensible Heating or Cooling
Adding heat alone to or removing heat alone from moist air is
represented by a horizontal line on the ASHRAE chart, because 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
1q2 = (h2 – h1) (41)
Example 2. Moist air, saturated at 35°F, enters a heating coil at a rate of
20,000 cfm. Air leaves the coil at 100°F. Find the required rate of heat
addition.
Solution: Figure 3 schematically shows the solution. State 1 is
located on the saturation curve at 35°F. Thus, h1 = 13.01 Btu/lbda,
W1 = 0.00428 lbw/lbda, and v1 = 12.55 ft3/lbda. State 2 is located at
Chart No. db wb h W rh v
1 100 81 44.6 0.0186 45 14.5
4 100 81 49.8 0.0234 46 17.6
Fig. 2 Schematic of Device for Heating Moist Air
m
·
da
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the intersection of t = 100°F and W2 = W1 = 0.00428 lbw/lbda. Thus,
h2 = 28.77 Btu/lbda. The mass flow of dry air is
= (20,000  60)/12.55 = 95,620 lbda/h
From Equation (41),
1q2 = (95,620)(28.77 – 13.01) = 1,507,000 Btu/h
Moist Air Cooling and Dehumidification
Moisture condensation occurs when moist air is cooled to a tem-
perature 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 in Figure 4, the steady-flow energy and material
balance equations are
Thus,
(W1 – W2) (42)
1q2 = [(h1 – h2) – (W1 – W2)hw2] (43)
Example 3. Moist air at 85°F dry-bulb temperature and 50% rh enters a
cooling coil at 10,000 cfm and is processed to a final saturation condi-
tion at 50°F. Find the tons of refrigeration required.
Solution: Figure 5 shows the schematic solution. State 1 is located at
the intersection of t = 85°F and  = 50%. Thus, h1 = 34.62 Btu/lbda,
W1 = 0.01292 lbw/lbda, and v1 = 14.01 ft3/lbda. State 2 is located on
the saturation curve at 50°F. Thus, h2 = 20.30 Btu/lbda and W2 =
0.00766 lbw/lbda. From Table 3, hw2 = 18.07 Btu/lbw. The mass flow of
dry air is
= 10,000/14.01 = 713.8 lbda/min
From Equation (43),
1q2 = 713.8[(34.62 – 20.30) – (0.01292 – 0.00788)(18.07)]
= 10,154 Btu/min, or 50.77 tons of refrigeration
Adiabatic Mixing of Two Moist Airstreams
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:
Eliminating gives
(44)
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 seg-
ments, in the same ratio as the masses of dry air in the two streams.
Example 4. A stream of 5000 cfm of outdoor air at 40°F dry-bulb tempera-
ture and 35°F thermodynamic wet-bulb temperature is adiabatically
mixed with 15,000 cfm of recirculated air at 75°F 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: v1 = 12.65 ft3/lbda, and v2 = 13.68 ft3/lbda.
Therefore,
Fig. 3 Schematic Solution for Example 2
Fig. 4 Schematic of Device for Cooling Moist Air
m
·
da
m
·
da
h1 m
·
da
h2 q
1 2 m
·
w
hw2
+ +
=
m
·
da
W1 m
·
da
W2 m
·
w
+
=
m
·
w
m
·
da
=
m
·
da
Fig. 5 Schematic Solution for Example 3
m
·
da
m
·
da1
h1 m
·
da2
h2
+ m
·
da3
h3
=
m
·
da1
m
·
da2
+ m
·
da3
=
m
·
da1
W1 m
·
da2
W2
+ m
·
da3
W3
=
m
·
da3
h2 h3
–
h3 h1
–
----------------
-
W2 W3
–
W3 W1
–
--------------------
-
m
·
da1
m
·
da2
-----------
-
= =
Licensed
for
single
user.
©
2021
ASHRAE,
Inc.

2021 ASHRAE Handbook Fundamentals (I P).pdf

2021 ASHRAE Handbook Fundamentals (I P).pdf

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