DOE-HDBK-1012/1-92
JUNE 1992
DOE FUNDAMENTALS HANDBOOK
THERMODYNAMICS, HEAT TRANSFER,
AND FLUID FLOW
Volume 1 of 3
U.S. Department of Energy
FSC-6910
Washington, D.C. 20585
Distribution Statement A. Approved for public release; distribution is unlimited.
This document has been reproduced directly from the best available copy.
Available to DOE and DOE contractors from the Office of Scientific and Technical Information.
P. O. Box 62, Oak Ridge, TN 37831; (615) 576-8401.
Available to the public from the National Technical Information Service, U.S. Department of
Commerce, 5285 Port Royal Rd., Springfield, VA 22161.
Order No. DE92019789
THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW
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ABSTRACT
The Thermodynamics, Heat Transfer, and Fluid Flow Fundamentals Handbook was
developed to assist nuclear facility operating contractors provide operators, maintenance
personnel, and the technical staff with the necessary fundamentals training to ensure a basic
understanding of the thermal sciences. The handbook includes information on thermodynamics
and the properties of fluids; the three modes of heat transfer - conduction, convection, and
radiation; and fluid flow, and the energy relationships in fluid systems. This information will
provide personnel with a foundation for understanding the basic operation of various types of DOE
nuclear facility fluid systems.
Key Words: Training Material, Thermodynamics, Heat Transfer, Fluid Flow, Bernoulli's
Equation
THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW
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FOREWORD
The Department of Energy (DOE) Fundamentals Handbooks consist of ten academic
subjects, which include Mathematics; Classical Physics; Thermodynamics, Heat Transfer, and Fluid
Flow; Instrumentation and Control; Electrical Science; Material Science; Mechanical Science;
Chemistry; Engineering Symbology, Prints, and Drawings; and Nuclear Physics and Reactor
Theory. The handbooks are provided as an aid to DOE nuclear facility contractors.
These handbooks were first published as Reactor Operator Fundamentals Manuals in 1985
for use by DOE Category A reactors. The subject areas, subject matter content, and level of detail
of the Reactor Operator Fundamentals Manuals was determined from several sources. DOE
Category A reactor training managers determined which materials should be included, and served
as a primary reference in the initial development phase. Training guidelines from the commercial
nuclear power industry, results of job and task analyses, and independent input from contractors
and operations-oriented personnel were all considered and included to some degree in developing
the text material and learning objectives.
The DOE Fundamentals Handbooks represent the needs of various DOE nuclear facilities'
fundamentals training requirements. To increase their applicability to nonreactor nuclear facilities,
the Reactor Operator Fundamentals Manual learning objectives were distributed to the Nuclear
Facility Training Coordination Program Steering Committee for review and comment. To update
their reactor-specific content, DOE Category A reactor training managers also reviewed and
commented on the content. On the basis of feedback from these sources, information that applied
to two or more DOE nuclear facilities was considered generic and was included. The final draft
of each of these handbooks was then reviewed by these two groups. This approach has resulted
in revised modular handbooks that contain sufficient detail such that each facility may adjust the
content to fit their specific needs.
Each handbook contains an abstract, a foreword, an overview, learning objectives, and text
material, and is divided into modules so that content and order may be modified by individual DOE
contractors to suit their specific training needs. Each subject area is supported by a separate
examination bank with an answer key.
The DOE Fundamentals Handbooks have been prepared for the Assistant Secretary for
Nuclear Energy, Office of Nuclear Safety Policy and Standards, by the DOE Training Coordination
Program. This program is managed by EG&G Idaho, Inc.
THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW
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OVERVIEW
The Department of Energy Fundamentals Handbook entitled Thermodynamics, Heat
Transfer, and Fluid Flow was prepared as an information resource for personnel who are
responsible for the operation of the Department's nuclear facilities. A basic understanding of the
thermal sciences is necessary for DOE nuclear facility operators, maintenance personnel, and the
technical staff to safely operate and maintain the facility and facility support systems. The
information in the handbook is presented to provide a foundation for applying engineering
concepts to the job. This knowledge will help personnel more fully understand the impact that
their actions may have on the safe and reliable operation of facility components and systems.
The Thermodynamics, Heat Transfer, and Fluid Flow handbook consists of three modules
that are contained in three volumes. The following is a brief description of the information
presented in each module of the handbook.
Volume 1 of 3
Module 1 - Thermodynamics
This module explains the properties of fluids and how those properties are
affected by various processes. The module also explains how energy balances can
be performed on facility systems or components and how efficiency can be
calculated.
Volume 2 of 3
Module 2 - Heat Transfer
This module describes conduction, convection, and radiation heat transfer. The
module also explains how specific parameters can affect the rate of heat transfer.
Volume 3 of 3
Module 3 - Fluid Flow
This module describes the relationship between the different types of energy in a
fluid stream through the use of Bernoulli's equation. The module also discusses
the causes of head loss in fluid systems and what factors affect head loss.
THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW
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The information contained in this handbook is by no means all encompassing. An
attempt to present the entire subject of thermodynamics, heat transfer, and fluid flow would be
impractical. However, the Thermodynamics, Heat Transfer, and Fluid Flow handbook does
present enough information to provide the reader with a fundamental knowledge level sufficient
to understand the advanced theoretical concepts presented in other subject areas, and to better
understand basic system and equipment operations.



Department of Energy
Fundamentals Handbook
THERMODYNAMICS, HEAT TRANSFER,
AND FLUID FLOW
Module 1
Thermodynamics
Thermodynamics
TABLE OF CONTENTS
TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
THERMODYNAMIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Mass and Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Specific Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Density
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Specific Gravity
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Humidity
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Intensive and Extensive Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
TEMPERATURE AND PRESSURE MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . 6
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Temperature Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Pressure Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
ENERGY, WORK, AND HEAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
Specific Internal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
Specific P-V Energy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
Specific Enthalpy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Energy and Power Equivalences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
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TABLE OF CONTENTS
Thermodynamics
TABLE OF CONTENTS (Cont.)
THERMODYNAMIC SYSTEMS AND PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . .
26
Thermodynamic Systems and Surroundings
. . . . . . . . . . . . . . . . . . . . . . . . . . .
26
Types of Thermodynamic Systems
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Control Volume
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Thermodynamic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Cyclic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Reversible Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Irreversible Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Adiabatic Process
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
Isentropic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
Polytropic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
Throttling Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
CHANGE OF PHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
Classification of Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
Saturated and Subcooled Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
Moisture Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
Saturated and Superheated Vapors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
Constant Pressure Heat Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
Critical Point
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
Sublimation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
Triple Point
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
Condensation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
PROPERTY DIAGRAMS AND STEAM TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
Property Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
Pressure-Temperature (P-T) Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
Pressure-Specific Volume (P-v) Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Pressure-Enthalpy (P-h) Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
Enthalpy-Temperature (h-T) Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
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TABLE OF CONTENTS
TABLE OF CONTENTS (Cont.)
Temperature-Entropy (T-s) Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
Enthalpy-Entropy (h-s) or Mollier Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
Steam Tables
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
FIRST LAW OF THERMODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
SECOND LAW OF THERMODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Carnot’s Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
Diagrams of Ideal and Real Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
Power Plant Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
Heat Rejection
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
Typical Steam Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
Causes of Inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
COMPRESSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Boyle’s and Charles’ Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Ideal Gas Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
Compressibility of Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
Constant Pressure Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Constant Volume Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Effects of Pressure Changes on Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . 100
Effects of Temperature Changes on Fluid Properties
. . . . . . . . . . . . . . . . . . . . . 101
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
APPENDIX A Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
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LIST OF FIGURES
Thermodynamics
LIST OF FIGURES
Figure 1 Comparison of Temperature Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Figure 2 Pressure Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Figure 3
Intensive Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
Figure 4 Piston-Cylinder Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
Figure 5 Vapor Pressure Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
Figure 6 T-V Diagram Showing the Saturation Region
. . . . . . . . . . . . . . . . . . . . . . .
34
Figure 7 T-V Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
Figure 8 Pressure-Temperature Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
Figure 9 P-T Diagram for Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
Figure 10 P-v Diagram for Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Figure 11 P-h Diagram for Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
Figure 12 h-T Diagram for Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
Figure 13 T-s Diagram for Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
Figure 14 First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
Figure 15 Control Volume Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
Figure 16 Open System Control Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
Figure 17 Open System Control Volumes (Cont.) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Figure 18 Mulitple Control Volumes in Same System . . . . . . . . . . . . . . . . . . . . . . . . .
58
Figure 19 T-s Diagram with Rankine Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
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Thermodynamics
LIST OF FIGURES
LIST OF FIGURES (Cont.)
Figure 20 Typical Steam Plant Cycle
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
Figure 21 Carnot Cycle Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Figure 22 Real Process Cycle Compared to Carnot Cycle . . . . . . . . . . . . . . . . . . . . . .
75
Figure 23 Control Volume for Second Law Analysis
. . . . . . . . . . . . . . . . . . . . . . . . .
76
Figure 24 Expansion and Compression Processes on T-s Diagram . . . . . . . . . . . . . . . .
78
Figure 25 Expansion and Compression Processes on h-s Diagram . . . . . . . . . . . . . . . .
78
Figure 26 Steam Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
Figure 27 Comparison of Ideal and Actual Turbine Performances . . . . . . . . . . . . . . . . .
80
Figure 28 Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
Figure 29 Carnot Cycle vs. Typical Power Cycle Available Energy . . . . . . . . . . . . . . .
86
Figure 30 Ideal Carnot Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
Figure 31 Rankine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
Figure 32 Rankine Cycle with Real v.s. Ideal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
Figure 33 Rankine Cycle Efficiencies T-s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
Figure 34 h-s Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
Figure 35 Typical Steam Cycle
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
Figure 36 Steam Cycle (Ideal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
Figure 37 Steam Cycle (Real)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
Figure 38 Mollier Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
Figure 39 Ideal Gas Constant Values
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
Figure 40 Pressure-Volume Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
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Page v
HT-01
LIST OF FIGURES
Thermodynamics
LIST OF FIGURES (Cont.)
Figure A-1 Mollier Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
Figure A-2 Sample Steam Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
Figure A-3 Thermodynamic Properties of Mercury . . . . . . . . . . . . . . . . . . . . . . . . . . A-5
Figure A-4 Thermodynamic Properties of CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-7
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Page vi
Rev. 0
Thermodynamics
LIST OF TABLES
LIST OF TABLES
NONE
Rev. 0
Page vii
HT-01
REFERENCES
Thermodynamics
REFERENCES
VanWylen, G. J. and Sonntag, R. E., Fundamentals of Classical Thermodynamics
SI Version, 2nd Edition, John Wiley and Sons, New York, ISBN 0-471-04188-2.
Kreith, Frank, Principles of Heat Transfer, 3rd Edition, Intext Press, Inc., New
York, ISBN 0-7002-2422-X.
Holman, J. P., Thermodynamics, McGraw-Hill, New York.
Streeter, Victor, L., Fluid Mechanics, 5th Edition, McGraw-Hill, New York, ISBN
07-062191-9.
Rynolds, W. C. and Perkins, H. C., Engineering Thermodynamics, 2nd Edition,
McGraw-Hill, New York, ISBN 0-07-052046-1.
Meriam, J. L., Engineering Mechanics Statics and Dynamics, John Wiley and
Sons, New York, ISBN 0-471-01979-8.
Schneider, P. J. Conduction Heat Transfer, Addison-Wesley Pub. Co., California.
Holman, J. P., Heat Transfer, 3rd Edition, McGraw-Hill, New York.
Knudsen, J. G. and Katz, D. L., Fluid Dynamics and Heat Transfer, McGraw-Hill,
New York.
Kays, W. and London, A. L., Compact Heat Exchangers, 2nd Edition, McGraw-
Hill, New York.
Weibelt, J. A., Engineering Radiation Heat Transfer, Holt, Rinehart and Winston
Publish., New York.
Sparrow, E. M. and Cess, R. E., Radiation Heat Transfer, Brooks/Cole Publish.
Co., Belmont, California.
Hamilton, D. C. and Morgan, N. R., Radiant-Interchange Configuration Factors,
Tech. Note 2836, National Advisory Committee for Aeronautics.
HT-01
Page viii
Rev. 0
Thermodynamics
REFERENCES
REFERENCES (Cont.)
McDonald, A. T. and Fox, R. W., Introduction to Fluid mechanics, 2nd Edition,
John Wiley and Sons, New York, ISBN 0-471-01909-7.
Zucrow, M. J. and Hoffman, J. D., Gas Dynamics Vol.b1, John Wiley and Sons,
New York, ISBN 0-471-98440-X.
Crane Company, Flow of Fluids Through Valves, Fittings, and Pipe, Crane Co.
Technical Paper No. 410, Chicago, Illinois, 1957.
Esposito, Anthony, Fluid Power with Applications, Prentice-Hall, Inc., New
Jersey, ISBN 0-13-322701-4.
Beckwith, T. G. and Buck, N. L., Mechanical Measurements, Addison-Wesley
Publish Co., California.
Wallis, Graham, One-Dimensional Two-Phase Flow, McGraw-Hill, New York,
1969.
Kays, W. and Crawford, M. E., Convective Heat and Mass Transfer, McGraw-
Hill, New York, ISBN 0-07-03345-9.
Collier, J. G., Convective Boiling and Condensation, McGraw-Hill, New York,
ISBN 07-084402-X.
Academic Program for Nuclear Power Plant Personnel, Volumes III and IV,
Columbia, MD: General Physics Corporation, Library of Congress Card
#A326517, 1982.
Faires, Virgel Moring and Simmang, Clifford Max, Thermodynamics, MacMillan
Publishing Co. Inc., New York.
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Page ix
HT-01
OBJECTIVES
Thermodynamics
TERMINAL OBJECTIVE
1.0
Given operating conditions of a system, EVALUATE the thermodynamic state of the
system.
ENABLING OBJECTIVES
1.1
DEFINE the following properties:
a.
Specific volume
b.
Density
c.
Specific gravity
d.
Humidity
1.2
DESCRIBE the following classifications of thermodynamic properties:
a.
Intensive properties
b.
Extensive properties
1.3
DEFINE the thermodynamic properties temperature and pressure.
1.4
DESCRIBE the Fahrenheit, Celsius, Kelvin, and Rankine temperature scales including:
a.
Absolute zero temperature
b.
The freezing point of water at atmospheric pressure
c.
The boiling point of water at atmospheric pressure
1.5
CONVERT temperatures between the Fahrenheit, Celsius, Kelvin, and Rankine scales.
1.6
DESCRIBE the relationship between absolute pressure, gauge pressure, and vacuum.
1.7
CONVERT pressures between the following units:
a.
Pounds per square inch
b.
Inches of water
c.
Inches of mercury
d.
Millimeters of mercury
e.
Microns of mercury
1.8
DEFINE the following:
a.
Heat
b.
Latent heat
c.
Sensible heat
d.
Unit used to measure heat
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Thermodynamics
OBJECTIVES
ENABLING OBJECTIVES (Cont.)
1.9
DEFINE the following thermodynamic properties:
a.
Specific enthalpy
b.
Entropy
1.10 DESCRIBE the following types of thermodynamic systems:
a.
Isolated system
b.
Closed system
c.
Open system
1.11 DEFINE the following terms concerning thermodynamic systems:
a.
Thermodynamic surroundings
b.
Thermodynamic equilibrium
c.
Control volume
d.
Steady-state
1.12 DESCRIBE the following terms concerning thermodynamic processes:
a.
Thermodynamic process
b.
Cyclic process
c.
Reversible process
d.
Irreversible process
e.
Adiabatic process
f.
Isentropic process
g.
Throttling process
h.
Polytropic process
1.13 DISTINGUISH between intensive and extensive properties.
1.14 DEFINE the following terms:
a.
Saturation
b.
Subcooled liquid
c.
Superheated vapor
d.
Critical Point
e.
Triple Point
f.
Vapor pressure curve
g.
Quality
h.
Moisture content
1.15 DESCRIBE the processes of sublimation, vaporization, condensation, and fusion.
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HT-01
OBJECTIVES
Thermodynamics
ENABLING OBJECTIVES (Cont.)
1.16 Given a Mollier diagram and sufficient information to indicate the state of the fluid,
DETERMINE any unknown properties for the fluid.
1.17 Given a set of steam tables and sufficient information to indicate the state of the fluid,
DETERMINE any unknown properties for the fluid.
1.18 DETERMINE the change in the enthalpy of a fluid as it passes through a system
component, given the state of the fluid at the inlet and outlet of the component and either
steam tables or a Mollier diagram.
1.19
STATE the First Law of Thermodynamics.
1.20 Using the First Law of Thermodynamics, ANALYZE an open system including all
energy transfer processes crossing the boundaries.
1.21 Using the First Law of Thermodynamics, ANALYZE cyclic processes for a
thermodynamic system.
1.22 Given a defined system, PERFORM energy balances on all major components in the
system.
1.23 Given a heat exchanger, PERFORM an energy balance across the two sides of the heat
exchanger.
1.24
IDENTIFY the path(s) on a T-s diagram that represents the thermodynamic processes
occurring in a fluid system.
1.25
STATE the Second Law of Thermodynamics.
1.26 Using the Second Law of Thermodynamics, DETERMINE the maximum possible
efficiency of a system.
1.27 Given a thermodynamic system, CONDUCT an analysis using the Second Law of
Thermodynamics.
1.28 Given a thermodynamic system, DESCRIBE the method used to determine:
a.
The maximum efficiency of the system
b.
The efficiency of the components within the system
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Thermodynamics
OBJECTIVES
ENABLING OBJECTIVES (Cont.)
1.29 DIFFERENTIATE between the path for an ideal process and that for a real process on
a T-s or h-s diagram.
1.30 Given a T-s or h-s diagram for a system EVALUATE:
a.
System efficiencies
b.
Component efficiencies
1.31 DESCRIBE how individual factors affect system or component efficiency.
1.32 Apply the ideal gas laws to SOLVE for the unknown pressure, temperature, or volume.
1.33 DESCRIBE when a fluid may be considered to be incompressible.
1.34 CALCULATE the work done in constant pressure and constant volume processes.
1.35 DESCRIBE the effects of pressure changes on confined fluids.
1.36 DESCRIBE the effects of temperature changes on confined fluids.
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Thermodynamics
Intentionally Left Blank
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Page xiv
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Thermodynamics
THERMODYNAMIC PROPERTIES
THERMODYNAMIC PROPERTIES
Thermodynamic properties describe measurable characteristics of a substance.
A knowledge of
these properties
is essential
to
the understanding of
thermodynamics.
EO 1.1
DEFINE the following properties:
a.
Specific volume
b.
Density
c.
Specific gravity
d.
Humidity
EO 1.2
DESCRIBE the following classifications of
thermodynamic properties:
a.
Intensive properties
b.
Extensive properties
Mass and Weight
The mass (m) of a body is the measure of the amount of material present in that body. The
weight (wt) of a body is the force exerted by that body when its mass is accelerated in a
gravitational field. Mass and weight are related as shown in Equation 1-1.
wt =
(1-1)
mg
g
c
where:
wt
=
weight (lbf)
m
=
mass (lbm)
g
=
acceleration of gravity = 32.17 ft/sec2
gc
=
gravitational constant = 32.17 lbm-ft/lbf-sec2
Note that gc has the same numerical value as the acceleration of gravity at sea level, but is not
the acceleration of gravity. Rather, it is a dimensional constant employed to facilitate the use of
Newton’s Second Law of Motion with the English system of units.
The weight of a body is a force produced when the mass of the body is accelerated by a
gravitational acceleration.
The mass of a certain body will remain constant even if the
gravitational acceleration acting upon that body changes.
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Page 1
HT-01
THERMODYNAMIC PROPERTIES
Thermodynamics
According to Newton’s Second Law of Motion, force (F) = ma, where a is acceleration. For
example, on earth an object has a certain mass and a certain weight. When the same object is
placed in outer space, away from the earth’s gravitational field, its mass is the same, but it is
now in a "weightless" condition (that is, gravitational acceleration and, thus, force equal zero).
The English system uses the pound-force (lbf) as the unit of weight. Knowing that acceleration
has the units of ft/sec2 and using Newton’s second law, we can determine that the units of mass
are lbf-sec2/ft. For simplification, 1 lbf-sec2/ft is called a slug. The basic unit of mass in the
English system is the slug. However, the slug is an almost meaningless unit for the average
individual. The unit of mass generally used is the pound-mass (lbm). In order to allow lbm to
be used as a unit of mass, we must divide Newton’s second law by the gravitational constant (gc).


32.17 lbm
ft
lbf
sec2
g
c
Newton’s second law can be expressed by Equation 1-2.
(1-2)
F
ma
g
c
Use of the gravitational constant, gc, adapts Newton’s second law such that 1 lbf = 1 lbm at the
surface of the earth. It is important to note that this relationship is only true at the surface of the
earth, where the acceleration due to gravity is 32.17 ft/sec2. However, because all of our
discussions will be based upon experiences and observations on earth, we will use the lbm as the
unit of mass.
NOTE:
In Equation 1-2, acceleration "a" is often written as "g" because, in this case, the
acceleration is the gravitational acceleration due to the earth’s gravitational field
(g = 32.17 ft/sec2).
Example:
Using Equation 1-2, prove that 1 lbf = l lbm on earth.
Solution:
F
mg
g
c
1 lbf
(1 lbm) (32.17 ft/sec2)
32.17 (lbm
ft)
(lbf
sec2)
1 lbf
1 lbf (an equality)
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Thermodynamics
THERMODYNAMIC PROPERTIES
Specific Volume
The specific volume (ν) of a substance is the total volume (V) of that substance divided by the
total mass (m) of that substance (volume per unit mass).
It has units of cubic feet per
pound-mass (ft3/lbm).
(1-3)
ν
V
m
where:
ν
=
specific volume (ft3/lbm)
V
=
volume (ft3)
m
=
mass (lbm)
Density
The density (
) of a substance is the total mass (m) of that substance divided by the total
ρ
volume (V) occupied by that substance (mass per unit volume). It has units of pound-mass per
cubic feet (lbm/ft3). The density (
) of a substance is the reciprocal of its specific volume (ν).
ρ
(1-4)
ρ
m
V
1
ν
where:
=
density (lbm/ft3)
ρ
m
=
mass (lbm)
V
=
volume (ft3)
ν
=
specific volume (ft3/lbm)
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HT-01
THERMODYNAMIC PROPERTIES
Thermodynamics
Specific Gravity
Specific gravity (S.G.) is a measure of the relative density of a substance as compared to the
density of water at a standard temperature. Physicists use 39.2°F (4°C) as the standard, but
engineers ordinarily use 60°F. In the International System of Units (SI Units), the density of
water is 1.00 g/cm3 at the standard temperature. Therefore, the specific gravity (which is
dimensionless) for a liquid has the same numerical value as its density in units of g/cm3. Since
the density of a fluid varies with temperature, specific gravities must be determined and specified
at particular temperatures.
Humidity
Humidity is the amount of moisture (water vapor) in the air.
It can be expressed as absolute
humidity or relative humidity. Absolute humidity is the mass of water vapor divided by a unit
volume of air (grams of water/cm3 of air). Relative humidity is the amount of water vapor
present in the air divided by the maximum amount that the air could contain at that temperature.
Relative humidity is expressed as a percentage. The relative humidity is 100% if the air is
saturated with water vapor and 0% if no water vapor is present in the air at all.
Intensive and Extensive Properties
Thermodynamic properties can be divided into two general classes, intensive and extensive
properties. An intensive property is independent of the amount of mass. The value of an
extensive property varies directly with the mass. Thus, if a quantity of matter in a given state
is divided into two equal parts, each part will have the same value of intensive property as the
original and half the value of the extensive property. Temperature, pressure, specific volume,
and density are examples of intensive properties. Mass and total volume are examples of
extensive properties.
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Thermodynamics
THERMODYNAMIC PROPERTIES
Summary
The important information from this chapter is summarized below.
Thermodynamic Properties Summary
The following properties were defined:
•
Specific volume (ν) is the total volume (V) of a substance divided by the
total mass (m) of that substance.
•
Density (ρ) is the total mass (m) of a substance divided by the total
volume (V) occupied by that substance.
•
Specific gravity (S.G.) is a measure of the relative density of a substance
as compared to the density of water at a standard temperature.
•
Humidity is the amount of moisture (water vapor) in the air. It can be
measured in absolute or relative units.
The following classifications of thermodynamic properties were described:
•
Intensive properties are those that are independent of the amount of mass.
•
Extensive properties are those that vary directly with the mass.
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HT-01
TEMPERATURE AND PRESSURE MEASUREMENTS
Thermodynamics
TEMPERATURE AND PRESSURE MEASUREMENTS
Several types of temperature and pressure measurements are used during
discussions of thermodynamics. Operators must recognize the different types and
their interrelationships in order to understand thermodynamics.
EO 1.3
DEFINE the thermodynamic properties temperature
and pressure.
EO 1.4
DESCRIBE the Fahrenheit, Celsius, Kelvin, and
Rankine temperature scales including:
a.
Absolute zero temperature
b.
The freezing point of water at atmospheric pressure
c.
The boiling point of water at atmospheric pressure
EO 1.5
CONVERT temperatures between the Fahrenheit,
Celsius, Kelvin, and Rankine scales.
EO 1.6
DESCRIBE the relationship between absolute
pressure, gauge pressure, and vacuum.
EO 1.7
CONVERT pressures between the following units:
a.
Pounds per square inch
b.
Inches of water
c.
Inches of mercury
d.
Millimeters of mercury
e.
Microns of mercury
Temperature
Temperature is a measure of the molecular activity of a substance. The greater the movement
of molecules, the higher the temperature.
It is a relative measure of how "hot" or "cold" a
substance is and can be used to predict the direction of heat transfer.
Temperature Scales
The two temperature scales normally employed for measurement purposes are the Fahrenheit (F)
and Celsius (C) scales. These scales are based on a specification of the number of increments
between the freezing point and boiling point of water at standard atmospheric pressure. The
Celsius scale has 100 units between these points, and the Fahrenheit scale has 180 units. The
zero points on the scales are arbitrary.
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Thermodynamics
TEMPERATURE AND PRESSURE MEASUREMENTS
The freezing point of water was selected as the zero point of the Celsius scale. The coldest
temperature achievable with a mixture of ice and salt water was selected as the zero point of the
Fahrenheit scale. The temperature at which water boils was set at 100 on the Celsius scale and
212 on the Fahrenheit scale. The relationship between the scales is represented by the following
equations.
°F = 32.0 + (9/5)°C
(1-5)
°C = (°F - 32.0)(5/9)
(1-6)
It is necessary to define an absolute temperature scale having only positive values. The absolute
temperature scale that corresponds to the Celsius scale is called the Kelvin (K) scale, and the
absolute scale that corresponds to the Fahrenheit scale is called the Rankine (R) scale. The zero
points on both absolute scales represent the same physical state. This state is where there is no
molecular motion of individual atoms. The relationships between the absolute and relative
temperature scales are shown in the following equations.
°R = °F + 460
(1-7)
°K = °C + 273
(1-8)
Figure 1 Comparison of Temperature Scales
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Page 7
HT-01
TEMPERATURE AND PRESSURE MEASUREMENTS
Thermodynamics
The conversion of one temperature scale to another is sometimes required at nuclear facilities,
and the operator should be acquainted with the process. The following two examples will be
helpful.
Example 1: Temperature Scale Conversion
What is the Rankine equivalent of 80°C?
Solution:
°F
= (9/5) °C + 32
= (9/5)(80) + 32
= 176 °F
°R
= °F + 460
= 176 + 460
= 636 °R
Example 2: Temperature Scale Conversion
What is the Kelvin equivalent of 80°F?
Solution:
°C
= (5/9) (°F - 32)
= (5/9) (80 - 32)
= 26.7°C
°K = °C + 273
= 26.7 + 273
= 299.7 °K
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Thermodynamics
TEMPERATURE AND PRESSURE MEASUREMENTS
Pressure
Pressure is a measure of the force exerted per unit area on the boundaries of a substance (or
system). It is caused by the collisions of the molecules of the substance with the boundaries of
the system. As molecules hit the walls, they exert forces that try to push the walls outward. The
forces resulting from all of these collisions cause the pressure exerted by a system on its
surroundings. Pressure is frequently measured in units of lbf/in2 (psi).
Pressure Scales
When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia);
when measured relative to atmospheric pressure (14.7 psi), it is called gauge pressure (psig). The
latter pressure scale was developed because almost all pressure gauges register zero when open
to the atmosphere. Therefore, pressure gauges measure the difference between the pressure of
the fluid to which they are connected and that of the surrounding air.
If the pressure is below that of the atmosphere, it is designated as a vacuum. A perfect vacuum
would correspond to absolute zero pressure. All values of absolute pressure are positive, because
a negative value would indicate tension, which is considered impossible in any fluid. Gauge
pressures are positive if they are above atmospheric pressure and negative if they are below
atmospheric pressure. Figure 2 shows the relationships between absolute, gauge, vacuum, and
atmospheric pressures, as do Equations 1-9 and 1-10.
Figure 2 Pressure Relationships
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Page 9
HT-01
TEMPERATURE AND PRESSURE MEASUREMENTS
Thermodynamics
Pabs = Patm + Pgauge
(1-9)
Pabs = Patm - Pvac
(1-10)
Patm is atmospheric pressure, which is also called the barometric pressure. Pgauge is the gauge
pressure, and Pvac is vacuum. Once again, the following examples relating the various pressures
will be helpful in understanding the idea of gauge versus absolute pressures.
Example 1: Pressure Relationships
How deep can a diver descend in ocean water (density = 64 lbm/ft3) without damaging
his watch, which will withstand an absolute pressure of 80 psia? (P = density • height)
Solution:
Assume:
Patm
= 14.7 psia
Pabs
= Patm + Pgauge
80 psia = 14.7 + Pgauge
Pgauge
= (80 - 14.7) = 65.3 psig
Pgauge
= density
height = ρH
(65.3)(144 in2/ft2)
= (64 lbm/ft3)H
H
= (65.3)(144)/(64)
H
= 146.9 ft
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Thermodynamics
TEMPERATURE AND PRESSURE MEASUREMENTS
Example 2: Pressure Relationships
What is the absolute pressure at the bottom of a swimming pool 6 feet deep that is filled
with fresh water? Patm = 14.7 psia
Solution:
Pabs
= Patm + Pgauge
= 14.7 + ρH
= 14.7 + [(62.4 lbm/ft3)(6 ft)/(144 in.2/ft2)]
= 14.7 + 2.6
Pabs
= 17.3 psia
In addition to pounds per square inch, pressure can be measured with reference to the force that
exists in a column of fluid at a certain height. The most common of these are inches of water,
inches of mercury, millimeters of mercury, and microns of mercury. Conversion factors are listed
below.
14.7 psia = 408 inches of water
14.7 psia = 29.9 inches of mercury
1 inch of mercury = 25.4 millimeters of mercury
1 millimeter of mercury = 103 microns of mercury
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Page 11
HT-01
TEMPERATURE AND PRESSURE MEASUREMENTS
Thermodynamics
Summary
The important information from this chapter is summarized below.
Temperature and Pressure Scales Summary
The following properties were defined as follows.
•
Temperature is a measure of the molecular activity of a substance.
•
Pressure is a measure of the force per unit area exerted on the boundaries of a
substance (or system).
The relationship between the Fahrenheit, Celsius, Kelvin, and Rankine temperature scales
was described.
•
Absolute zero
= -460 °F or -273 °C
•
Freezing point of water = 32 °F or 0 °C
•
Boiling point of water
= 212 °F or 100 °C
Conversions between the different scales can be made using the following formulas.
•
°F = 32 + (9/5)°C
•
°C = (°F - 32)(5/9)
•
°R = °F + 460
•
°K = °C + 273
Relationships between absolute pressure, gauge pressure, and vacuum can be shown
using the following formulas.
•
Pabs
= Patm + Pgauge
•
Pabs
= Patm - Pvac
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Thermodynamics
TEMPERATURE AND PRESSURE MEASUREMENTS
Temperature and Pressure Scales Summary (Cont.)
Converting between the different pressure units can be done using the following
conversions.
•
14.7 psia
= 408 inches of water
•
14.7 psia
= 29.9 inches of mercury
•
1 inch of mercury = 25.4 millimeters of mercury
•
1 millimeter of mercury = 103 microns of mercury
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Page 13
HT-01
ENERGY, WORK, AND HEAT
Thermodynamics
ENERGY, WORK, AND HEAT
Heat and work are the two ways in which energy can be transferred across the
boundary of a system. One of the most important discoveries in thermodynamics
was that work could be converted into an equivalent amount of heat and that heat
could be converted into work.
EO 1.8
DEFINE the following:
a.
Heat
b.
Latent heat
c.
Sensible heat
d.
Units used to measure heat
EO 1.9
DEFINE the following thermodynamic properties:
a.
Specific enthalpy
b.
Entropy
Energy
Energy is defined as the capacity of a system to perform work or produce heat.
Potential Energy
Potential energy (PE) is defined as the energy of position. Using English system units, it is
defined by Equation 1-11.
(1-11)
PE
mgz
g
c
where:
PE
=
potential energy (ft-lbf)
m
=
mass (lbm)
z
=
height above some reference level (ft)
g
=
acceleration due to gravity (ft/sec2)
gc
=
gravitational constant = 32.17 ft-lbm/lbf-sec2
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Thermodynamics
ENERGY, WORK, AND HEAT
In most practical engineering calculations, the acceleration due to gravity (g) is numerically equal
to the gravitational constant (gc); thus, the potential energy (PE) in foot-pounds-force is
numerically equal to the product of the mass (m) in pounds-mass times the height (z) in feet
above some reference level.
Example:
Determine the potential energy of 50 lbm of water in a storage tank 100 ft above the
ground.
Solution:
Using Equation 1-11
PE
mgz
g
c
PE
(50 lbm) (32.17 ft/sec2) (100 ft)
32.17 ft lbm/lbf sec2
PE
5000 ft lbf
Kinetic Energy
Kinetic energy (KE) is the energy of motion. Using English system units, it is defined by
Equation 1-12.
(1-12)
KE
mv2
2g
c
where:
KE
=
kinetic energy (ft-lbf)
m
=
mass (lbm)
v
=
velocity (ft/sec)
gc
=
gravitational constant = 32.17 ft-lbm/lbf-sec2
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Example:
Determine the kinetic energy of 7 lbm of steam flowing through a pipe at a velocity of
100 ft/sec.
Solution:
Using Equation 1-12.
KE
mv2
2g
c
KE
(7 lbm) (100 ft/sec)2
2(32.17 ft lbm/lbf sec2)
KE
(7 lbm) (10,000 ft2/sec2)
(64.34 ft lbm/lbf sec2)
KE
1088 ft lbf
Specific Internal Energy
Potential energy and kinetic energy are macroscopic forms of energy. They can be visualized
in terms of the position and the velocity of objects. In addition to these macroscopic forms of
energy, a substance possesses several microscopic forms of energy. Microscopic forms of energy
include those due to the rotation, vibration, translation, and interactions among the molecules of
a substance. None of these forms of energy can be measured or evaluated directly, but
techniques have been developed to evaluate the change in the total sum of all these microscopic
forms of energy. These microscopic forms of energy are collectively called internal energy,
customarily represented by the symbol U. In engineering applications, the unit of internal energy
is the British thermal unit (Btu), which is also the unit of heat.
The specific internal energy (u) of a substance is its internal energy per unit mass. It equals the
total internal energy (U) divided by the total mass (m).
(1-13)
u
U
m
where:
u
=
specific internal energy (Btu/lbm)
U
=
internal energy (Btu)
m
=
mass (lbm)
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Example:
Determine the specific internal energy of 12 lbm of steam if the total internal energy is
23,000 Btu.
Solution:
Using Equation 1-13.
u
U
m
u
23,000 Btu
12 lbm
u
1916.67 Btu/lbm
Specific P-V Energy
In addition to the internal energy (U), another form of energy exists that is important in
understanding energy transfer systems. This form of energy is called P-V energy because it
arises from the pressure (P) and the volume (V) of a fluid. It is numerically equal to PV, the
product of pressure and volume. Because energy is defined as the capacity of a system to
perform work, a system where pressure and volume are permitted to expand performs work on
its surroundings. Therefore, a fluid under pressure has the capacity to perform work.
In
engineering applications, the units of P-V energy, also called flow energy, are the units of
pressure times volume (pounds-force per square foot times cubic feet), which equals foot-pounds
force (ft-lbf).
The specific P-V energy of a substance is the P-V energy per unit mass. It equals the total P-V
divided by the total mass m, or the product of the pressure P and the specific volume ν, and is
written as Pν.
(1-14)
Pν
PV
m
where:
P
=
pressure (lbf/ft2)
V
=
volume (ft3)
ν
=
specific volume (ft3/lbm)
V
m
m
=
mass (lbm)
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Example:
Determine the specific P-V energy of 15 lbm of steam at 1000 psi in an 18 ft3 tank.
Solution:
Using Equation 1-14
Pν
PV
m
Pν
(1000 lbf/in.2) (144 in.2/ft 2) (18 ft3)
15 lbm
Pν
172,800 ft lbf/lbm
Specific Enthalpy
Specific enthalpy (h) is defined as h = u + Pν, where u is the specific internal energy (Btu/lbm)
of the system being studied, P is the pressure of the system (lbf/ft2), and ν is the specific volume
(ft3/lbm) of the system. Enthalpy is usually used in connection with an "open" system problem
in thermodynamics. Enthalpy is a property of a substance, like pressure, temperature, and
volume, but it cannot be measured directly. Normally, the enthalpy of a substance is given with
respect to some reference value. For example, the specific enthalpy of water or steam is given
using the reference that the specific enthalpy of water is zero at .01°C and normal atmospheric
pressure. The fact that the absolute value of specific enthalpy is unknown is not a problem,
however, because it is the change in specific enthalpy (∆h) and not the absolute value that is
important in practical problems.
Steam tables include values of enthalpy as part of the
information tabulated.
Work
Kinetic energy, potential energy, internal energy, and P-V energy are forms of energy that are
properties of a system. Work is a form of energy, but it is energy in transit. Work is not a
property of a system. Work is a process done by or on a system, but a system contains no work.
This distinction between the forms of energy that are properties of a system and the forms of
energy that are transferred to and from a system is important to the understanding of energy
transfer systems.
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Work is defined for mechanical systems as the action of a force on an object through a distance.
It equals the product of the force (F) times the displacement (d).
W = Fd
(1-15)
where:
W
=
work (ft-lbf)
F
=
force (lbf)
d
=
displacement (ft)
Example:
Determine the amount of work done if a force of 150 lbf is applied to an object until it
has moved a distance of 30 feet.
Solution:
Using Equation 1-15
W = Fd
W = (150 lbf)(30 ft)
W = 4500 ft-lbf
In dealing with work in relation to energy transfer systems, it is important to distinguish between
work done by the system on its surroundings and work done on the system by its surroundings.
Work is done by the system when it is used to turn a turbine and thereby generate electricity in
a turbine-generator. Work is done on the system when a pump is used to move the working fluid
from one location to another. A positive value for work indicates that work is done by the
system on its surroundings; a negative value indicates that work is done on the system by its
surroundings.
Heat
Heat, like work, is energy in transit. The transfer of energy as heat, however, occurs at the
molecular level as a result of a temperature difference. The symbol Q is used to denote heat.
In engineering applications, the unit of heat is the British thermal unit (Btu). Specifically, this
is called the 60 degree Btu because it is measured by a one degree temperature change from 59.5
to 60.5°F.
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As with work, the amount of heat transferred depends upon the path and not simply on the initial
and final conditions of the system. Also, as with work, it is important to distinguish between
heat added to a system from its surroundings and heat removed from a system to its
surroundings. A positive value for heat indicates that heat is added to the system by its
surroundings. This is in contrast to work that is positive when energy is transferred from the
system and negative when transferred to the system. The symbol q is sometimes used to indicate
the heat added to or removed from a system per unit mass. It equals the total heat (Q) added
or removed divided by the mass (m). The term "specific heat" is not used for q since specific
heat is used for another parameter. The quantity represented by q is referred to simply as the
heat transferred per unit mass.
(1-16)
q
Q
m
where:
q
=
heat transferred per unit mass (Btu/lbm)
Q
=
heat transferred (Btu)
m
=
mass (lbm)
Example:
Determine the heat transferred per unit mass if 1500 Btu’s are transferred to 40 lbm of
water.
Solution:
Using Equation 1-16
q
Q
m
q
1500 Btu
40 lbm
q
37.5 Btu/lbm
The best way to quantify the definition of heat is to consider the relationship between the amount
of heat added to or removed from a system and the change in the temperature of the system.
Everyone is familiar with the physical phenomena that when a substance is heated, its
temperature increases, and when it is cooled, its temperature decreases. The heat added to or
removed from a substance to produce a change in its temperature is called sensible heat. The
units of heat are often defined in terms of the changes in temperature it produces.
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Another type of heat is called latent heat. Latent heat is the amount of heat added to or removed
from a substance to produce a change in phase. When latent heat is added, no temperature
change occurs. There are two types of latent heat. The first is the latent heat of fusion. This
is the amount of heat added or removed to change phase between solid and liquid. The second
type of latent heat is the latent heat of vaporization. This is the amount of heat added or
removed to change phase between liquid and vapor. The latent heat of vaporization is sometimes
called the latent heat of condensation.
Different substances are affected to different magnitudes by the addition of heat. When a given
amount of heat is added to different substances, their temperatures increase by different amounts.
The ratio of the heat (Q) added to or removed from a substance to the change in temperature
(∆T) produced is called the heat capacity (Cp) of the substance. The heat capacity of a substance
per unit mass is called the specific heat (cp) of the substance. The subscript p indicates that the
heat capacity and specific heat apply when the heat is added or removed at constant pressure.
(1-17)
Cp
Q
∆T
cp
Q
m∆T
cp
q
∆T
where:
Cp
=
heat capacity at constant pressure (Btu/°F)
cp
=
specific heat at constant pressure (Btu/lbm-°F)
Q
=
heat transferred (Btu)
q
=
heat transferred per unit mass (Btu/lbm)
m
=
mass (lbm)
∆T
=
temperature change (°F)
One lbm of water is raised 1°F and one Btu of heat is added. This implies that the specific heat
(cp) of water is one Btu/lbm-°F. The cp of water is equal to one Btu/lbm-°F only at 39.1°F.
By rearranging Equation 1-17 we obtain Q = mcp∆T, which is used to calculate latent heat. By
substituting mass flow rate in lbm/hr,
, for m, we obtain
. This equation is used
m˙
˙Q
m˙cp∆T
to calculate heat transfer in Btu/hr and will be useful in later chapters.
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Thermodynamics
Example:
How much heat is required to raise the temperature of 5 lbm of water from 50°F to
150°F? (Assume the specific heat (cp) for water is constant at 1.0 Btu/lbm-°F.)
Solution:
cp
=
Q
m∆T
Q = cpm∆T
Q = (1.0 Btu/lbm-°F)(5 lbm)(150°F - 50°F)
Q = (1.0 Btu/lbm-°F)(5 lbm)(100°F)
Q = 500 Btu
From the previous discussions on heat and work, it is evident that there are many similarities
between them. Heat and work are both transient phenomena. Systems never possess heat or
work, but either or both may occur when a system undergoes a change of energy state. Both heat
and work are boundary phenomena in that both are observed at the boundary of the system. Both
represent energy crossing the system boundary.
Entropy
Entropy (S) is a property of a substance, as are pressure, temperature, volume, and enthalpy.
Because entropy is a property, changes in it can be determined by knowing the initial and final
conditions of a substance. Entropy quantifies the energy of a substance that is no longer
available to perform useful work. Because entropy tells so much about the usefulness of an
amount of heat transferred in performing work, the steam tables include values of specific
entropy (s = S/m) as part of the information tabulated. Entropy is sometimes referred to as a
measure of the inability to do work for a given heat transferred. Entropy is represented by the
letter S and can be defined as ∆S in the following relationships.
(1-18)
∆S
∆Q
T
abs
(1-19)
∆s
∆q
T
abs
where:
S
=
the change in entropy of a system during some process (Btu/°R)
∆
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ENERGY, WORK, AND HEAT
Q
=
the amount of heat transferred to or from the system during the process
∆
(Btu)
Tabs
=
the absolute temperature at which the heat was transferred (°R)
∆s
=
the change in specific entropy of a system during some process
(Btu/lbm -oR)
∆q
=
the amount of heat transferred to or from the system during the process
(Btu/lbm)
Like enthalpy, entropy cannot be measured directly. Also, like enthalpy, the entropy of a
substance is given with respect to some reference value. For example, the specific entropy of
water or steam is given using the reference that the specific entropy of water is zero at 32°F.
The fact that the absolute value of specific entropy is unknown is not a problem because it is the
change in specific entropy (∆s) and not the absolute value that is important in practical problems.
Energy and Power Equivalences
The various forms of energy involved in energy transfer systems (such as potential energy,
kinetic energy, internal energy, P-V energy, work and heat) may be measured in numerous basic
units. In general, three types of units are used to measure energy: (1) mechanical units, such
as the foot-pound-force (ft-lbf); (2) thermal units, such as the British thermal unit (Btu); and (3)
electrical units, such as the watt-second (W-sec). In the mks and cgs systems, the mechanical
units of energy are the joule (j) and the erg, the thermal units are the kilocalorie (kcal) and the
calorie (cal), and the electrical units are the watt-second (W-sec) and the erg. Although the units
of the various forms of energy are different, they are equivalent.
Some of the most important experiments in science were those conducted by J. P. Joule in 1843,
who showed quantitatively that there was a direct correspondence between mechanical and
thermal energy. These experiments showed that one kilocalorie equals 4,186 joules. These same
experiments, when performed using English system units, show that one British thermal unit
(Btu) equals 778.3 ft-lbf. These experiments established the equivalence of mechanical and
thermal energy. Other experiments established the equivalence of electrical energy with both
mechanical and thermal energy. For engineering applications, these equivalences are expressed
by the following relationships.
1 ft-lbf = 1.286 x 10-3 Btu = 3.766 x 10-7 kW-hr
1 Btu = 778.3 ft-lbf = 2.928 x 10-4 kW-hr
1 kW-hr = 3.413 x 103 Btu = 2.655 x 106 ft-lbf
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There is one additional unit of energy encountered in engineering applications.
It is the
horsepower-hour (hp-hr). It is a mechanical unit of energy defined by the following relationship:
1 hp-hr = 1.980 x 106 ft-lbf
These relationships can be used to convert between the various English system units for the
various forms of energy.
Most computations involving the energy of the working fluid in an energy transfer system are
performed in Btu’s. Forms of mechanical energy (such as potential energy, kinetic energy, and
mechanical work) and other forms of energy (such as P-V energy) are usually given in
foot-pounds-force. These are converted to Btu’s by using 1 Btu = 778.3 ft-lbf.
This conversion factor is often used. In fact, a constant called the mechanical equivalent of heat,
usually denoted by the symbol J and sometimes referred to as Joule’s constant, is defined as:
.
J
778 ft lbf
Btu
Power is defined as the time rate of doing work.
It is equivalent to the rate of the energy
transfer. Power has units of energy per unit time. As with energy, power may be measured in
numerous basic units, but the units are equivalent. In the English system, the mechanical units
of power are foot-pounds-force per second or per hour (ft-lbf/sec or ft-lbf/hr) and horsepower
(hp). The thermal units of power are British thermal units per hour (Btu/hr), and the electrical
units of power are watts (W) or kilowatts (kW). For engineering applications, the equivalence
of these units is expressed by the following relationships.
1 ft-lbf/sec = 4.6263 Btu/hr = 1.356 x 10-3 kW
1 Btu/hr = 0.2162 ft-lbf/sec = 2.931 x 10-4 kW
1 kW = 3.413 x 103 Btu/hr = 737.6 ft-lbf/sec
Horsepower is related to foot-pounds-force per second (ft-lbf/sec) by the following relationship:
1 hp = 550.0 ft-lbf/sec
These relationships can be used to convert the English system units for power.
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Summary
The important information from this chapter is summarized below.
Energy, Work, and Heat Summary
•
Heat is described as energy in transit. This transfer occurs
on a molecular level as a result of temperature differences.
The unit of heat is the British thermal unit (Btu).
Latent heat
=
the amount of heat added or
removed to produce only a
phase change.
Sensible heat =
the heat added or removed
that causes a temperature
change.
•
The following properties were defined:
Specific enthalpy (h) is defined as h = u +
Pν, where u is the specific internal energy
(Btu/lbm) of the system being studied, P is
the pressure of the system (lbf/ft2), and ν is
the specific volume (ft3/lbm) of the system.
Entropy is sometimes referred to as a
measure of the inability to do work for a
given heat transferred.
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Thermodynamics
THERMODYNAMIC SYSTEMS AND PROCESSES
Defining an appropriate system can greatly simplify a thermodynamic analysis.
A thermodynamic system is any three-dimensional region of space that is bounded
by one or more surfaces. The bounding surfaces may be real or imaginary and
may be at rest or in motion. The boundary may change its size or shape. The
region of physical space that lies outside the selected boundaries of the system is
called the surroundings or the environment.
EO 1.10
DESCRIBE the following types of thermodynamic
systems:
a.
Isolated system
b.
Closed system
c.
Open system
EO 1.11
DEFINE the following terms concerning
thermodynamic systems:
a.
Thermodynamic surroundings
b.
Thermodynamic equilibrium
c.
Control volume
d.
Steady-state
EO 1.12
DESCRIBE the following terms concerning
thermodynamic processes:
a.
Thermodynamic process
b.
Cyclic process
c.
Reversible process
d.
Irreversible process
e.
Adiabatic process
f.
Isentropic process
g.
Throttling process
h.
Polytropic process
Thermodynamic Systems and Surroundings
Thermodynamics involves the study of various systems. A system in thermodynamics is nothing
more than the collection of matter that is being studied.