2009 ASHRAE Handbook - Fundamentals (SI Edition)

599 Pages·2009·66.26 MB·English

2009 ASHRAE" HANDBOOK
FUNDAMENTALS
SI Edition
American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc.
1791 Tullie Circle, N.E., Atlanta, GA 30329
[phone] http :llwww.ashrae.org
G2009 by the American Society of Heating, Refrigerating and Air-conditioning Engineers,
Inc. All rights reserved.
DEDICATED TO THE ADVANCEMENT OF
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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 Internet Web site.
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,
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ISBN 978-1-933742-55-7
ISSN 1523-282
The paper for this book is both acid- and elemental-chlorine-fee and was
manufactured with pulp obtained from sources using sustainable forestry
practices. The printing used soy-based inks.
ASHRAE Research: Improving the Quality of Life
The American Society of Heating, Refrigerating and Air- annually, enabling ASHRAE to report new data about material
Conditioning Engineers is the world's foremost technical society in properties and building physics and to promote the application of
the fields of heating, ventilation, air conditioning, and refrigeration. innovative technologies.
Its members worldwide are individuals who share ideas, identify Chapters in the ASHRAE Handbook are updated through the
needs, support research, and write the industry's standards for test- experience of members of ASHRAE Technical Committees and
ing and practice. The result is that engineers are better able to keep through results of ASHRAE Research reported at ASHRAE meet-
indoor environments safe and productive while protecting and pre- ings and published in ASHRAE special publications and in
serving the outdoors for generations to come. ASHRAE Transactions.
One of the ways that ASHRAE supports its members' and indus- For information about ASHRAE Research or to become a mem-
try's need for information is through ASHRAE Research. Thou- ber, contact ASHRAE, 1791 Tullie Circle, Atlanta, GA 30329; tele-
sands of individuals and companies support ASHRAE Research phone: [phone]; www.ashrae.org.
Preface
The 2009 ASHRAE Handbook-Fundamentals covers basic prin- Chapter 20, Space Air Diffusion, has been completely rewritten to
ciples and data used in the HVAC&R industry. The ASHRAE Tech- harmonize with related chapters in other volumes, with major sec-
nical Committees that prepare these chapters strive not only to tions on fully mixed, partially mixed, stratified, and task/ambient
provide new information, but also to clarify existing information, systems and the principles behind their design and operation.
delete obsolete materials, and reorganize chapters to make the Hand- Chapter 21, Duct Design, has new data for round and rectangular
book more understandable and easier to use. An accompanying CD- fittings in agreement with the ASHRAE Duct Fitting Database, as
ROM contains all the volume's chapters in both I-P and SI units. well as new content on duct leakage requirements, spiral duct
This edition includes a new chapter (35), Sustainability, which roughness, and flexible duct pressure loss correction.
defines this concept for HVAC&R and describes the principles, Chapter 23, Insulation for Mechanical Systems, has added tables
design considerations, and detailed evaluations needed in designing from ASHRAE Standam'90.1-2007, and a new section on writing
sustainable HVAC&R systems. specifications.
Also new for this volume, chapter order and groupings have been Chapter 24, Airflow Around Buildings, has added a detailed dis-
revised for more logical flow and use. Some of the other revisions cussion on computational evaluation of airflow, plus new refer-
and additions to the volume are as follows: ences including updated versions of design standards and
manuals of practice.
Chapter 1, Psychrometrics, has new information on the composi-
Chapters 25, 26, and 27 carry new titles, reorganized as chapters
tion of dry air, and revised table data for thermodynamic proper-
on Heat, Air, and Moisture Control Fundamentals, Material Prop-
ties of water and moist air.
erties, and Examples, respectively, with updated content through-
Chapter 6, Mass Transfer, has added examples on evaluating diffu-
out.
sion coefficients, and on heat transfer and moisture removal rates.
Chapter 29, Refrigerants, has new content on stratospheric ozone
Chapter 7, Fundamentals of Control, includes new content on
depletion, global climate change, and global environmental char-
dampers, adaptive control, direct digital control (DDC) system
acteristics of refrigerants.
architecture and specifications, and wireless control.
Chapter 30, Thermophysical Properties of Refrigerants, has up-
Chapter 9, Thermal Comfort, has a new section on thermal com-
dateddatafor R-125, R-245fa, R-170, R-290, R-600, andR-600a.
fort and task performance, based on multiple new studies done in
Chapter 36, Measurement and Instruments, has revised content on
laboratory and office environments.
measurement of air velocity, infiltration, airtightness, and outdoor
Chapter 10, Indoor Environmental Health, was reorganized to
air ventilation, plus new information on particle image velocime-
describe hazard sources, health effects, exposure standards, and
try (PIV) and data acquisition and recording.
exposure controls. New and updated topics include mold, Legio-
nella, indoor air chemistry, thermal impacts, and water quality This volume is published, both as a bound print volume and in
standards. electronic format on a CD-ROM, in two editions: one using inch-
Chapter 14, Climatic Design Information, has new climate data pound (I-P) units of measurement, the other using the International
for 5564 stations (an increase of 1142 new stations compared to System of Units (SI).
2005 Fundamentals) on the CD-ROM accompanying this book. Corrections to the 2006,2007, and 2008 Handbook volumes can
A subset of data for selected stations is also included in the be found on the ASHRAE Web site at http://www,ashrae,orga nd in
printed chapter for convenient access. the Additions and Corrections section of this volume. Corrections
Chapter 15, Fenestration, has been revised to include new exam- for this volume will be listed in subsequent volumes and on the
ples of solar heat gain coefficient (SHGC) calculations, and new ASHRAE Web site.
research results on shading calculations and U-factors for various Reader comments are enthusiastically invited. To suggest im-
specialized door types. provements for a chapter, please comment using the form on the
Chapter 16, Ventilation and Infiltration, has new, detailed exam- ASHRAE Web site or, using the cutout page(s) at the end of this vol-
ples, updates from ASHRAE Standards 62.1 and 62.2, discussion ume's index, write to Handbook Editor, ASHRAE, 1791 Tullie Cir-
of relevant LEED8 aspects, and new information on airtightness cle, Atlanta, GA 30329, or fax [phone], or e-mail mowen@
and ventilation rates for commercial buildings. ashrae.org.
Chapter 18, Nonresidential Cooling and Heating Load Calcu-
lations, has been updated to reflect new ASHRAE research results
on climate data and on heat gains from office equipment, lighting, Mark S. Owen
and commercial cooking appliances. Editor
CONTENTS
Contributors vii
ASHRAE Technical Committees, Task Groups, and Technical Resource Groups ix
ASHRAE Research: Improving the Quality of Life X
Preface X
PRINCIPLES
Chapter 1. Psychrometrics (TC 1.1, Thermodynamics and Psychrometrics, TC 8.3, Absorption and Heat-
Operated Machines) 1 .1
2. Thermodynamics and Refrigeration Cycles (TC 1.1) 1.2
3. Fluid Flow (TC 1.3, Heat Transfer and Fluid Flow) 1.3
4. Heat Transfer (TC 1.3) 1.4
5. Two-Phase Flow (TC 1.3) 1.5
6. Mass Transfer (TC 1.3) 1.6
7. Fundamentals of Control (TC 1.4, Control Theory and Application) 1.7
8. Sound and Vibration (TC 2.6, Sound and Vibration Control) 1.8
INDOOR ENVIRONMENTAL QUALITY
Chapter 9. Thermal Comfort (TC 2.1, Physiology and Human Environment) 1.9
10. Indoor Environmental Health (Environmental Health Committee) 1.10
11. Air Contaminants (TC 2.3, Gaseous Air Contaminants and Gas Contaminant Removal
Equipment) 1.11
12. Odors (TC 2 .3) 1.12
13. Indoor Environmental Modeling (TC 4.10, Indoor Environmental Modeling) 1.13
LOAD AND ENERGY CALCULATIONS
Chapter 14. Climatic Design Information (TC 4.2, Climatic Information) 1.14
15. Fenestration (TC 4.5, Fenestration) 1.15
16. Ventilation and Infiltration (TC 4.3, Ventilation Requirements and Infiltration ) 1.16
17. Residential Cooling and Heating Load Calculations (TC 4.1, Load Calculation Data and
Procedures) 1.17
18. Nonresidential Cooling and Heating Load Calculations (TC 4.1) 1.18
19. Energy Estimating and Modeling Methods (TC 4.7, Energy Calculations) 1.19
HVAC DESIGN
Chapter 20. Space Air Diffusion (TC 5.3, Room Air Distribution) 1.20
21. Duct Design (TC 5.2, Duct Design) 1.21
22. Pipe Sizing (TC 6.1, Hydronic and Steam Equipment and Systems) 1.22
23. Insulation for Mechanical Systems (TC 1.8, Mechanical Systems Insulation) 1.23
24. Airflow Around Buildings (TC 4.3) 1.24
BUILDING ENVELOPE
Chapter 25. Heat, Air, and Moisture Control in Building Assemblies-Fundamentals
(TC 4.4, Building Materials and Building Envelope Performance) 1.25
26. Heat, Air, and Moisture Control in Building Assemblies-Material Properties (TC 4.4) 1.26
27. Heat, Air, and Moisture Control in Insulated Assemblies-Examples (TC 4.4) 1.27
MATERIALS
Chapter 28. Combustion and Fuels (TC 6.10, Fuels and Combustion) 1.28
29. Refrigerants (TC 3.1, Refrigerants and Secondary Coolants) 1.29
30. Thermophysical Properties of Refrigerants (TC 3.1) 1.30
3 1. Physical Properties of Secondary Coolants (Brines) (TC 3.1) 1.31
32. Sorbents and Desiccants (TC 8.12, Dessicant Dehumidification Equipment and Components) 1.32
33. Physical Properties of Materials (TC 1.3) 1.33
GENERAL
Chapter 34. Energy Resources (TC 2.8, Building Environmental Impacts and Sustainability) 1.34
35. Sustainability (TC 2.8) 1.35
36. Measurement and Instruments (TC 1.2, Instruments and Measurements) 1.36
37. Abbreviations and Symbols (TC 1.6, Terminology) 1. n
38. Units and Conversions (TC 1.6) 1.38
39. Codes and Standards 1.39
ADDITIONS AND CORRECTIONS 1.1
INDEX 1.1
Composite index to the 2006 Refrigeration, 2007 HVAC Applications, 2008 HVAC Systems and
Equipment, and 2009 Fundamentals volumes
Comment Pages
CHAPTER 2
THERMODYNAMICS AND REFRIGERATION CYCLES
THERMODYNAMICS ........... Theoretical Single-Stage Cycle Using Zeotropic
Stored Energy.. ...................... Refrigerant Mixture ................................................................ 2.9
Energy in Transition .............. .................................. 2.1
Second Law of Thermodynamics ..... ...................... 2.2
Equations of State ...................................................................... 2.3
Calculating Thermodynamic Properties ........
.................2 .6
or Azeotropic Mixture ............................................................. 2.7 Ammonia/Water Absorption Cycles ......................................... 2.18
Lorenz Refrigeration Cycle ................................................ Symbols .................................................................................... 2.19
TH ERMODYNAMICS is the study of energy, its transforma- Nuclear (atomic) energy derives from the cohesive forces hold-
tions, and its relation to states of matter. This chapter covers the in-g~ pr otons and neutrons together as the atom's nucleus.
application of thermodynamics to refrigeration cycles. The first part
reviews the first and second laws of thermodvnamics and oresents ENERGY IN TRANSITION
methods for calculating thermodynamic properties. The second and Heat Q is the mechanism that transfers energy across the bound-
third parts address compression and absorption refrigeration cycles, aries of systems with differing temperatures, always toward the
two common methods of thermal energy transfer. lower temperature. Heat is positive when energy is added to the sys-
tem (see Figure 1).
THERMODYNAMICS Work is the mechanism that transfers energy across the bound-
aries of systems with differing pressures (or force of any kind),
A thermodynamic system is a region in space or a quantity of always toward the lower pressure. If the total effect produced in the
matter bounded by a closed surface. The surroundings include system can be reduced to the raising of a weight, then nothing but
everything external to the system, and the system is separated from work has crossed the boundary. Work is positive when energy is
the surroundings by the system boundaries. These boundaries can removed from the system (see Figure 1).
be movable or fixed, real or imaginary. Mechanical or shaft work W is the energy delivered or ab-
Entropy and energy are important in any thermodynamic system. sorbed by a mechanism, such as a turbine, air compressor, or inter-
Entropy measures the molecular disorder of a system. The more nal combustion engine.
mixed a system, the greater its entropy; an orderly or unmixed con- Flow work is energy carried into or transmitted across the
figuration is one of low entropy. Energy has the capacity for pro- system boundary because a pumping process occurs somewhere
ducing an effect and can be categorized into either stored or outside the system, causing fluid to enter the system. It can be
transient forms. more easily understood as the work done by the fluid just outside
the system on the adjacent fluid entering the system to force or
STORED ENERGY push it into the system. Flow work also occurs as fluid leaves the
Thermal (internal) energy is caused by the motion of mole- system.
cules andor intermolecular forces.
Flow work (per unit mass) =pv (3)
Potential energy (PE) is caused by attractive forces existing
between molecules, or the elevation of the system.
where p is the pressure and v is the specific volume, or the volume
PE = mgz (1) displaied per unit mass evaluated at the inlet or exit.
A property of a system is any observable characteristic of the
where
system. The state of a system is defined by specifying the minimum
rn = mass
g = local acceleration of gravity
0
z = elevation above horizontal reference plane (IN)
Kinetic energy (KE) is the energy caused by the velocity ofmol- II wp ,
ecules and is expressed as II! I 1 1 ( OUT)
KE = m V 2/2 (2) ,
where V is the velocity of a fluid stream crossing the system boundary. m1 v1 Esysre~ vz
* mz f
Chemical energy is caused by the arrangement of atoms com-
posing the molecules.
I
___________z2 _______________________:
i__
____ DATUM LEVEL Q ______
The preparation of the first and second parts of this chapter is assigned to
TC 1.1, Thermodynamics and Psychrometrics. The third part is assigned to
TC 8.3, Absorption and Heat-Operated Machines. Fig. 1 Energy Flows in General Thermodynamic System
2.1
2.2 2009 ASHFUE Handbook-Fundamentals (SI)
set of independent properties. The most common thermodynamic cmin(u+ pv + 2V2 + gz1
properties are temperature T, pressure p, and specific volume v or
density p. Additional thermodynamic properties include entropy, in
stored forms of energy, and enthalpy. c
Frequently, thermodynamic properties combine to form other - moZl(fu + pv + -V2 2 + gz) out + Q - w (5)
properties. Enthalpy h is an important property that includes inter-
nal energy and flow work and is defined as
h=.u+pv (4)
where subscripts i andfrefer to the initial and final states, re-
where u is the internal energy per unit mass. spectively.
Each property in a given state has only one definite value, and Nearly all important engineering processes are commonly mod-
any property always has the same value for a given state, regardless
eled as steady-flow processes. Steady flow signifies that all quanti-
of how the substance arrived at that state.
ties associated with the system do not vary with time. Consequently,
A process is a change in state that can be defined as any change
c m(,+g+gz)
in the properties of a system. A process is described by specifying
the initial and final equilibrium states, the path (if identifiable), and
the interactions that take place across system boundaries during the all streams
process. entering
A cycle is a process or a series of processes wherein the initial
and final states of the system are identical. Therefore, at the conclu-
sion of a cycle, all the properties have the same value they had at the all streams
leaving
beginning. Refrigerant circulating in a closed system undergoes a
cycle. where h = u +pv as described in Equation (4).
A pure substance has a homogeneous and invariable chemical A second common application is the closed stationary system for
composition. It can exist in more than one phase, but the chemical which the first law equation reduces to
composition is the same in all phases.
If a substance is liquid at the saturation temperature and pressure, (7)
it is called a saturated liquid. If the temperature of the liquid is
lower than the saturation temperature for the existing pressure, it is SECOND LAW OF THERMODYNAMICS
called either a subcooled liquid (the temperature is lower than the The second law of thermodynamics differentiates and quantifies
saturation temperature for the given pressure) or a compressed liq- processes that only proceed in a certain direction (irreversible) from
uid (the pressure is greater than the saturation pressure for the given those that are reversible. The second law may be described in sev-
temperature). eral ways. One method uses the concept of entropy flow in an open
When a substance exists as part liquid and part vapor at the sat- system and the irreversibility associated with the process. The con-
uration temperature, its quality is defined as the ratio of the mass of cept of irreversibility provides added insight into the operation of
vapor to the total mass. Quality has meaning only when the sub- cycles. For example, the larger the irreversibility in a refrigeration
stance is saturated (i.e., at saturation pressure and temperature). cycle operating with a given refrigeration load between two fixed
Pressure and temperature of saturated substances are not indepen- temperature levels, the larger the amount of work required to oper-
dent properties. ate the cycle. Irreversibilities include pressure drops in lines and
If a substance exists as a vapor at saturation temperature and heat exchangers, heat transfer between fluids of different tempera-
pressure, it is called a saturated vapor. (Sometimes the term dry ture, and mechanical friction. Reducing total irreversibility in a
saturated vapor is used to emphasize that the quality is loo%.) cycle improves cycle performance, In the limit of no irreversibili-
When the vapor is at a temperature greater than the saturation tem- ties, a cycle attains its maximum ideal efficiency.
perature, it is a superheated vapor. Pressure and temperature of a In an open system, the second law of thermodynamics can be
superheated vapor are independent properties, because the temper- described in terms of entropy as
ature can increase while pressure remains constant. Gases such as
air at room temperature and pressure are highly superheated vapors.
FIRST LAW OF THERMODYNAMICS
where
The first law of thermodynamics is often called the law of con-
servation of energy. The following form of the first-law equation is dSsysten=r total change within system in time dt during process
?intisi = entropy increase caused by mass entering (incoming)
valid only in the absence of a nuclear or chemical reaction.
?im,s, = entropy decrease caused by mass leaving (exiting)
Based on the first law or the law of conservation of energy, for 6QiT = entropy change caused by reversible heat transfer between
any system, open or closed, there is an energy balance as system and surroundings at temperature T
dl = entropy caused by irreversibilities (always positive)
I
[N et amount of energy = [N et increase of stored Equation (8) accounts for all entropy changes in the system. Re-
added to system energy in system arranged, this equation becomes
or SQ = T[(Smese- &nisi) + dSsys- dl] (9)
In integrated form, if inlet and outlet properties, mass flow, and
[Energy in] - [Energy out] = [Increase of stored energy in system]
interactions with the surroundings do not vary with time, the general
Figure 1 illustrates energy flows into and out of a thermodynamic equation for the second law is
system, For the general case of multiple mass flows with uniform
properties in and out of the system, the energy balance can be
written
Thermodynamics and Refrigeration Cycles 2.3
In many applications, the process can be considered to operate Applying the second law to an entire refrigeration cycle shows
steadily withno change in time. The change in entropy ofthe system that a completely reversible cycle operating under the same con-
is therefore zero. The irreversibility rate, which is the rate of ditions has the maximum possible COP. Departure of the actual
entropy production caused by irreversibilities in the process, can be cycle from an ideal reversible cycle is given by the refrigerating
determined by rearranging Equation (1 0): efficiency:
The Carnot cycle usually serves as the ideal reversible refrigera-
Equation (6) can be used to replace the heat transfer quantity.
tion cycle. For multistage cycles, each stage is described by arevers-
Note that the absolute temperature of the surroundings with which
ible cycle.
the system is exchanging heat is used in the last term. If the temper-
ature of the surroundings is equal to the system temperature, heat is
EQUATIONS OF STATE
transferred reversibly and the last term in Equation (1 1) equals zero.
Equation (1 1) is commonly applied to a system with one mass The equation of state of a pure substance is a mathematical rela-
flow in, the same mass flow out, no work, and negligible kinetic or tion between pressure, specific volume, and temperature. When the
potential energy flows. Combining Equations (6) and (1 1) yields system is in thermodynamic equilibrium,
The principles of statistical mechanics are used to (1) explore the
fundamental properties of matter, (2) predict an equation of state
based on the statistical nature of a particular system, or (3) propose
In a cycle, the reduction of work produced by a power cycle (or
a functional form for an equation of state with unknown parameters
the increase in work required by a refrigeration cycle) equals the
that are determined by measuring thermodynamic properties of a
absolute ambient temperature multiplied by the sum of irreversibil-
substance. A fundamental equation with this basis is the virial
ities in all processes in the cycle. Thus, the difference in reversible
equation, which is expressed as an expansion in pressure p or in
and actual work for any refrigeration cycle, theoretical or real, oper-
reciprocal values of volume per unit mass v as
ating under the same conditions, becomes
THERMODYNAMIC ANALYSIS OF f! = 1 + (B/v) + (C/v2)+ (D/v3) + ... (20)
REFRIGERATION CYCLES RT
Refrigeration cycles transfer thermal energy from a region of low where coefficients B', C', D', etc., and B, C, D, etc., are the virial
temperature TR to one of higher temperature. Usually the higher- coefficients. B' and B are the second virial coefficients; C' and C
temperature heat sink is the ambient air or cooling water, at temper- are the third virial coefficients, etc. The virial coefficients are func-
ature To, the temperature of the surroundings. tions of temperature only, and values of the respective coefficients
The first and second laws of thermodynamics can be applied to in Equations (19) and (20) are related. For example, B'= BIRTand
individual components to determine mass and energy balances and C'= (C- B2)l(RT)z.
the irreversibility of the components. This procedure is illustrated in The universal gas constant R is defined as
later sections in this chapter.
Performance of a refrigeration cycle is usually described by a
coefficient of performance (COP), defined as the benefit of the
cycle (amount of heat removed) divided by the required energy
input to operate the cycle: where (pV), is the product of the pressure and the molar specific
volume along an isotherm with absolute temperature 7: The current
Useful refrigerating effect bestvalueofx is 8314.41 Jl(kgmo1.K). ThegasconstantRisequal
COP = Net energy supplied from external sources (14) to the universal gas constant R divided by the molecular mass Mof
the gas or gas mixture.
For a mechanical vapor compression system, the net energy sup- The quantity pvIRT is also called the compressibility factor Z,
plied is usually in the form of work, mechanical or electrical, and or
may include work to the compressor and fans or pumps. Thus,
Z = 1 + (Blv) + (C /v2) + (D/v3) + . '. (22)
COP = Q-evnp An advantage of the virial form is that statistical mechanics can
Wnet be used to predict the lower-order coefficients and provide physical
significance to the virial coefficients. For example, in Equation (22),
In an absorption refrigeration cycle, the net energy supplied is the term Blv is a function of interactions between two molecules,
usually in the form of heat into the generator and work into the C/v2be tween three molecules, etc. Because lower-order interactions
pumps and fans, or
are common, contributions of the higher-order terms are succes-
sively less. Thermodynamicists use the partition or distribution
Qevap function to determine virial coefficients; however, experimental val-
COP =
ues of the second and third coefficients are preferred. For dense
Qgen Wne,
+
fluids, many higher-order terms are necessary that can neither be sat-
In many cases, work supplied to an absorption system is very isfactorily predicted from theory nor determined from experimental
small compared to the amount of heat supplied to the generator, so measurements. In general, a truncated virial expansion of four terms
the work term is often neglected. is valid for densities of less than one-half the value at the critical
2.4 2009 ASHRAE Handbook-Fundamentals (SI)
point. For higher densities, additional terms can be used and deter- corresponding states provides useful approximations, and numer-
mined empirically. ous modifications have been reported. More complex treatments for
Computers allow the use of very complex equations of state in predicting properties, which recognize similarity of fluid properties,
calculating p-v-T values, even to high densities. The Benedict- are by generalized equations of state. These equations ordinarily
Webb-Rubin (B-W-R) equation of state (Benedict et al. 1940) and allow adjustment of the p-v-T surface by introducing parameters.
Martin-Hou equation (1 955) have had considerable use, but should One example (Hirschfelder et al. 1958) allows for departures from
generally be limited to densities less than the critical value. Stro- the principle of corresponding states by adding two correlating
bridge (1 962) suggested a modified Benedict-Webb-Rubin relation parameters.
that gives excellent results at higher densities and can be used for a
p-v-T surface that extends into the liquid phase. CALCULATING THERMODYNAMIC PROPERTIES
The B-W-R equation has been used extensively for hydrocarbons
Although equations of state provide p-v-T relations, thermo-
(Cooper and Goldfrank 1967):
dynamic analysis usually requires values for internal energy,
enthalpy, and entropy. These properties have been tabulated for
P = (RT/v)+ (B,RT- A, - C,/T2)/v2 + (bRT- a)/v3 many substances, including refrigerants (see Chapters 1, 30, and
33), and can be extracted from such tables by interpolating manu-
2 (-y/v2)
+ (aa)/v6+[ c(l +y/v )e ]/v3T2 (23) ally or with a suitable computer program. This approach is appro-
where the constant coefficients are A,, B,, C,, a, b, c, a, and y. priate for hand calculations and for relatively simple computer
models; however, for many computer simulations, the overhead in
The Martin-Hou equation, developed for fluorinated hydro-
memory or input and output required to use tabulated data can
carbon properties, has been used to calculate the thermodynamic
make this approach unacceptable. For large thermal system simu-
property tables in Chapter 30 and in ASHRAE Thermodynamic
lations or complex analyses, it may be more efficient to determine
Properties of Refrigerants (Stewart et al. 1986). The Martin-Hou
internal energy, enthalpy, and entropy using fundamental thermo-
equation is
dynamic relations or curves fit to experimental data. Some of these
RT A, + B2T+ C2e( -kT/ T,) A, + B3T+ C3e( -kT/ T,) relations are discussed in the following sections. Also, the ther-
p = -+ + modynamic relations discussed in those sections are the basis for
v-b 2 3 constructing tables of thermodynamic property data. Further in-
(V-b) (V-b)
formation on the topic may be found in references covering system
modeling and thermodynamics (Howell and Buckius 1992;
Stoecker 1989).
At least two intensive properties (properties independent of the
quantity of substance, such as temperature, pressure, specific vol-
where the constant coefficients are Ai, B,, C,, k, b, and a.
ume, and specific enthalpy) must be known to determine the
Strobridge (1 962) suggested an equation of state that was devel-
remaining properties. If two known properties are either p, v, or T
oped for nitrogen properties and used for most cryogenic fluids.
(these are relatively easy to measure and are commonly used in
This equation combines the B-W-R equation of state with an equa-
simulations), the third can be determined throughout the range of
tion for high-density nitrogen suggested by Benedict (1937). These
interest using an equation of state. Furthermore, if the specific
equations have been used successfully for liquid and vapor phases,
heats at zero pressure are known, specific heat can be accurately
extending in the liquid phase to the triple-point temperature and the
determined from spectroscopic measurements using statistical
freezing line, and in the vapor phase from 10 to 1000 K, with pres-
mechanics (NASA 1971). Entropy may be considered a function
sures to 1 GPa. The Strobridge equation is accurate within the
of T and p, and from calculus an infinitesimal change in entropy
uncertainty of the measuredp-v-T data:
can be written as
" 1 '
RnlT+n2+L+i+A p
T2 T4
Likewise, a change in enthalpy can be written as
+p3 ~ + Vi4+ex]Ap( -n1 6p 2
IT2 T3
Using the Gibbs relation Tds = dh - vdp and the definition of spe-
cific heat at constant pressure, cp = (dh/ST),, Equation (27) can be
rearranged to yield
The 15 coefficients of this equation's linear terms are determined
by a least-square fit to experimental data. Hust and McCarty (1967)
and Hust and Stewart (1 966) give further information on methods
and techniques for determining equations of state.
In the absence of experimental data, Van der Waals' principle of Equations (26) and (28) combine to yield (S~sldT7)~c J 7: Then,
corresponding states can predict fluid properties. This principle
using the Maxwell relation (8~Idp=)-~( d~/8T)E~q,u ation (26) may
relates properties of similar substances by suitable reducing factors
be rewritten as
(i,e,, the p-v-T surfaces of similar fluids in a given region are
assumed to be of similar shape). The critical point can be used to
define reducing parameters to scale the surface of one fluid to the
dimensions of another. Modifications of this principle, as suggested
by Kamerlingh Onnes, a Dutch cryogenic researcher, have been
used to improve correspondence at low pressures. The principle of This is an expression for an exact derivative, so it follows that
Thermodynamics and Refrigeration Cycles 2.5
If vapor pressure and liquid and vapor density data (all relatively
easy measurements to obtain) are known at saturation, then changes
in enthalpy and entropy can be calculated using Equation (37).
Integrating this expression at a fixed temperature yields Phase Equilibria for Multicomponent Systems
To understand phase equilibria, consider a container full of a liq-
uid made of two components; the more volatile component is des-
ignated i and the less volatile componentj (Figure 2A). This mixture
is all liquid because the temperature is low (but not so low that a
solid appears). Heat added at a constant pressure raises the mix-
where cpoi s the known zero-pressure specific heat, and dpT is used
ture’s temperature, and a sufficient increase causes vapor to form, as
to indicate that integration is performed at a fixed temperature. The
shown in Figure 2B. If heat at constant pressure continues to be
second partial derivative of specific volume with respect to temper-
added, eventually the temperature becomes so high that only vapor
ature can be determined from the equation of state. Thus, Equation
remains in the container (Figure 2C). A temperature-concentration
(31) can be used to determine the specific heat at any pressure.
(T-x)d iagram is useful for exploring details of this situation.
Using Tds = dh - vdp, Equation (29) can be written as
Figure 3 is a typical T-x diagram valid at a fixed pressure. The
kJpl
[ case shown in Figure 2A, a container full of liquid mixture with
dh = cpdT+ v-T - dp mole fraction xi,oa t temperature To,i s point 0 on the T- x diagram.
When heat is added, the temperature of the mixture increases. The
Equations (28) and (32) may be integrated at constant pressure to point at which vapor begins to form is the bubble point. Starting at
obtain point 0, the first bubble forms at temperature T, (point 1 on the dia-
gram). The locus of bubble points is the bubble-point curve, which
provides bubble points for various liquid mole fractions xi.
TI
and h(T,,P,) = h(TO?PO)+ JcpdT (34)
70
Integrating the Maxwell relation (ds/~?p=) -~( &/dT), gives an
equation for entropy changes at a constant temperature as
(35)
A ALL LIQUID B TWO-PHASE SUBSTANCE C ONLY VAPOR
(VAPORILIQUID)
x = mole fraction in liquid y = mole fraction in vapor
Likewise, integrating Equation (32) along an isotherm yields the
following equation for enthalpy changes at a constant temperature: Fig. 2 Mixture of i andj Components in
Constant-Pressure Container
MOLE FRACTION IN VAPOR y,
0 Y. Y, Y. 1
Internal energy can be calculated from u = h -pv. When entropy
or enthalpy are known at a reference temperature To and pressurepo,
values at any temperature and pressure may be obtained by combin-
ing Equations (33) and (35) or Equations (34) and (36).
Combinations (or variations) of Equations (33) through (36) can
be incorporated directly into computer subroutines to calculate
properties with improved accuracy and efficiency. However, these
equations are restricted to situations where the equation of state is
valid and the properties vary continuously. These restrictions are
violated by a change of phase such as evaporation and condensation,
which are essential processes in air-conditioning and refrigerating
devices. Therefore, the Clapeyron equation is of particular value;
for evaporation or condensation, it gives
(37)
0 x,3 52 x, 1
where MOLE FRACTION IN LlQUlDx
sfg = entropy of vaporization
hfg = enthalpy of vaporization Fig. 3 Temperature-Concentration (T-x) Diagram for
vfg = specific volume difference between vapor and liquid phases Zeotropic Mixture