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Thermodynamics for Chemical Engineers
Learn the basics of thermodynamics in this complete and practice-oriented introduction for students of chemical engineering
Thermodynamics is a vital branch of physics that focuses upon the interaction of heat, work, and temperature with energy, radiation, and matter. Thermodynamics can apply to a wide range of sciences, but is particularly important in chemical engineering, where the interconnection of heat and work with chemical reactions or physical changes of state are studied according to the laws of thermodynamics. Moreover, thermodynamics in chemical engineering focuses upon pure fluid and mixture properties, phase equilibrium, and chemical reactions within the confines of the laws of thermodynamics.
Given that thermodynamics is an essential course of study in chemical and petroleum engineering, Thermodynamics for Chemical Engineers provides an important introduction to the subject that comprehensively covers the topic in an easily-digestible manner. Suitable for undergraduate and graduate students, the text introduces the basic concepts of thermodynamics thoroughly and concisely while providing practice-oriented examples and illustrations. Thus, the book helps students bridge the gap between theoretical knowledge and basic experiments and measurement characteristics.
Thermodynamics for Chemical Engineers readers will also find:
- Practice-oriented examples to help students connect the learned concepts to actual laboratory instruments and experiments
- A broad suite of illustrations throughout the text to help illuminate the information presented
- Authors with decades working in chemical engineering and teaching thermodynamics
Thermodynamics for Chemical Engineers is the ideal resource not just for undergraduate and graduate students in chemical and petroleum engineering, but also for anyone looking for a basic guide to thermodynamics.
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Veröffentlichungsjahr: 2022
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Table of Contents
Cover
Title Page
Copyright
Preface
1 Introduction
1.1 Definition
1.2 Dimensions, Fundamental Quantities, and Units
1.3 Secondary or Derived Physical Quantities
1.4 SI Usage of Units and Symbols
1.5 Thermodynamic Systems and Variables
1.6 Zeroth Law
Problems for Chapter 1
2 Energy and the First Law
2.1 Introduction
2.2 Energy
2.3 First Law of Thermodynamics
2.4 Application of Solution Procedure to Simple Cases
2.5 Practical Application Examples
2.6 Differential Form
2.7 Inserting Time: Unsteady‐State Flow Process
2.8 Recap
Problems for Chapter 2
Reference
3 PVT Relations and Equations of State
3.1 Introduction
3.2 Graphical Representations
3.3 Critical Region
3.4 Tabular Representations
3.5 Mathematical Representations
3.6 Calculation of Volumes from EOS
3.7 Vapor Pressure and Enthalpy of Vaporization Correlations
3.8 Ideal Gas Enthalpy Changes: Applications
Problems for Chapter 3
References
4 Second Law of Thermodynamics
4.1 Introduction
4.2 General and Classical Statements of the Second Law
4.3 Heat Engines, Refrigerators, and Cycles
4.4 Implications of the Second Law
4.5 Efficiency
4.6 Specific Heat/Heat Capacity
4.7 Entropy Balance Equation for Open Systems
4.8 Availability and Maximum/Minimum Work
Problems for Chapter 4
5 Thermodynamic Relations
5.1 Introduction
5.2 Mathematics Review
5.3 Fundamental Thermodynamics Equation
5.4 Legendre Transforms
5.5 Maxwell Relations
5.6 Derivation of Thermodynamic Relationships
5.7 Open Systems: Chemical Potential
5.8 Property Change Calculations
5.9 Residual Properties
5.10 Property Changes Using Residual Functions
5.11 Generalized Correlations for Residual Functions
5.12 Two‐Phase Systems – Clapeyron Equation
Problems for Chapter 5
6 Practical Applications for Thermodynamics
6.1 Fluid Flow
6.2 Heat Engines and Refrigeration Units
Problems for Chapter 6
7 Solution Theory
7.1 Introduction
7.2 Composition Variables
7.3 Chemical Potential
7.4 Partial Molar Properties
7.5 General Gibbs–Duhem Equation
7.6 Differential Thermodynamic Properties in Open Systems in Terms of Measurables
7.7 Ideal Gas Mixtures
7.8 Fugacity and Fugacity Coefficient for Pure Substances
7.9 Equations for Calculating Fugacity
7.10 Application of Fugacity Equation to Gases and Liquids
7.11 Fugacity and Fugacity Coefficient in a Solution
7.12 Calculation of the Fugacity and Fugacity Coefficient in Solution
7.13 Ideal Solutions
7.14 Excess Properties. Activity Coefficients
7.15 Activity Coefficients with Different Standard States
7.16 Effect of Pressure on the Fugacity in Solution and Activity Coefficients Using the Lewis–Randall Rule
7.17 Property Change on Mixing
7.18 Excess Gibbs Energy Models
Problems for Chapter 7
References
8 Phase Equilibrium
8.1 Introduction
8.2 Equilibrium
8.3 Gibbs Phase Rule
8.4 Pure Components and Phase Equilibria
8.5 Different Phase Diagrams for Binary Mixtures at Vapor–Liquid Equilibrium (VLE)
8.6 Vapor/Liquid Equilibrium Relationship
8.7 Phase Calculations Using the Gamma–Phi Formulation
8.8 Phase Calculations Using the Phi–Phi Formulation
8.9 Modern Approach to Phase Equilibrium Calculations
8.10 Binary Liquid–Liquid Equilibrium (LLE)
8.11 Binary Vapor–Liquid–Liquid Equilibrium (VLLE)
8.12 Binary Vapor–Solid Equilibrium (VSE)
8.13 Binary Liquid–Solid Equilibrium (LSE)
Problems for Chapter 8
References
9 Chemical Reaction Equilibria
9.1 Introduction
9.2 Nature of Reactions
9.3 Chemical Reaction Stoichiometry
9.4 Extent of Reaction
9.5 Phase Rule for Reacting Systems
9.6 Principles of Reaction Equilibria
9.7 Understanding the Reaction Equilibria
9.8 Equilibrium Constant
9.9 Temperature Dependence of the Equilibrium Constant
9.10 Standard States
9.11 Applications to Different Types of Reactions
9.12 Multi‐reactions
9.13 Nonstoichiometric Solution
9.14 Equal Area Rule for Reactive Thermodynamic Equilibrium Calculations
Problems for Chapter 9
References
A Appendices
A.1 Instructions to Add an Add‐In Your Computer
A.2 Excel® LK CALC Add‐In
A.3 Excel® STEAM CALC Add‐In
A.4 Heat Capacity Equations for an Ideal Gas
A.5 Antoine Equation Constants
A.6 Heat Capacity Equations for liquids
A.7 Iterative Procedures for the Calculation of Vapor Liquid Equilibrium
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Units of the base units in the English Engineering System.
Table 1.2 SI prefixes.
Chapter 2
Table 2.1 Equations to calculate energies.
Table 2.2 Different forms for work.
Chapter 3
Table 3.1 Steam properties.
Table 3.2 Expressions for
a
and
b
in the Tsonopolous correlation.
Table 3.3 Values for the parameters of different EOS.
Table 3.4 Universal parameters for BACK.
Table 3.5 Characteristic parameters of the BACK EOS.
Table 3.6 Correction of the enthalpy for different conditions in a reaction...
Chapter 5
Table 5.1 Thermodynamic definitions of
P
,
V
,
T
, and
S
.
Table 5.2 Reduction of thermodynamic derivatives in terms of observables.
Chapter 6
Table 6.1 Comparing 100% efficient compressors.
Table 6.2 Comparing 100% and 75% efficient compressors.
Chapter 7
Table 7.1 Values for the parameter
α
in the NRTL model.
Table 7.2 Values of size and surface parameters.
Chapter 8
Table 8.1 Parameters for Eq. (8.77).
Chapter 9
Table P9.13.1 Critical constants and acentric factors.
Table P9.14.1 Wilson equation parameters for the liquid phase.
List of Illustrations
Chapter 1
Figure 1.1 A U‐tube glass manometer and its schematic diagram.
Figure 1.2 Dead‐weight gauge.
Figure 1.3 Secondary pressure measurement devices.
Figure 1.4 Secondary thermometers.
Chapter 2
Figure 2.1 Volumetric compression.
Figure 2.2 Flow of a constant volume of mass.
Figure 2.3 Flow sheet for solving problems with the first law of thermodynam...
Figure 2.4 Schematic representation of a compressor.
Figure 2.5 Condenser.
Figure 2.6 Heat exchanger.
Figure 2.7 Sketch of the system.
Figure 2.8 Diagram of an open system with unsteady flow.
Chapter 3
Figure 3.1
PρT
diagram for methane.
Figure 3.2 (a, b, c) Pressure–temperature diagrams.
Figure 3.3 (a, b) Pressure–volume (
PV
) diagrams.
Figure 3.4 Constant quality lines in a PV diagram.
Figure 3.5 Second virial coefficient of argon.
Figure 3.6 Third virial coefficient of argon.
Figure 3.8 Compressibility factor as a function of pressure (a) and as a fun...
Figure 3.8 Experimental PVT measurements and calculation of the second viria...
Figure 3.9 Phase diagram from the vdW EOS showing the vdW loops for argon.
Figure 3.10 Schematic diagram of the
PV
behavior of a cubic EOS.
Figure 3.11 Solver window.
Chapter 4
Figure 4.1 Diagram of an engine.
Figure 4.2 Schematic diagrams to prove equivalent between the statements of ...
Figure 4.3 Schematic diagrams of (a) heat engine and (b) refrigerator.
Figure 4.4
P
–
V
diagram for (a) a Carnot engine and (b) a Carnot refrigerator...
Figure 4.5 Carnot cycles using ideal gas and steam as a working fluid.
Figure 4.6 Cycles driving
S
with
G
.
Figure 4.7 Arrangement of two cycles to prove Proposition 2.
Figure 4.8 Arbitrary cycle separated into small Carnot cycles.
Figure 4.9 Arbitrary cycle with an irreversible path and a reversible path....
Figure 4.10 A general isolated system.
Figure 4.11 Engine.
Figure 4.12 Diagram of an open system.
Figure 4.13 Schematic diagram of a piston–cylinder.
Chapter 5
Figure 5.1 A function of exact differentials.
Figure 5.2 Function
y
= 3
x
2
.
Figure 5.3 Tangents at each point in the curve.
Figure 5.4 Nomograph to obtain the Maxwell relations.
Figure 5.5 A path between the real fluid and ideal gas.
Chapter 6
Figure 6.1 Different paths from a compressed liquid to the saturation liquid...
Figure 6.2 Enthalpy changes in an actual and an isentropic process.
Figure 6.3
PV
diagram for a compressor cycle.
Figure 6.4 Compressor
T
–
S
diagram.
Figure 6.5
T
–
S
plot for the Carnot cycle.
Figure 6.6 Schematic diagram of a vapor power plant.
Figure 6.7 Rankine cycle power plant.
Figure 6.8
T
–
S
plot for the Rankine cycle.
Figure 6.9 Comparison between Rankine and Carnot cycles.
Figure 6.10
T
–
S
diagram of a reheat Rankine cycle.
Figure 6.11 Rankine cycle with reheating.
Figure 6.12 Rankine cycle with regeneration.
Figure 6.13
T
–
S
diagram for the regeneration cycle.
Figure 6.14 Drawing from the patent granted to N. Otto.
Figure 6.15 Schematic of the start and the four strokes in a piston.
Figure 6.16 Schematic
P
–
V
diagram of the Otto engine cycle.
Figure 6.17
P
–
V
and
T
–
S
diagrams for the air standard cycle (idealized Otto ...
Figure 6.18 Effect of the compression ratio and
γ
ig
in the efficiency o...
Figure 6.19 Patent #608,845 for the diesel engine.
Figure 6.20
P
–
V
and
T
–
S
diagram for the air standard cycle (idealized diesel...
Figure 6.21 Simple schematic diagram for a turbine.
Figure 6.22 Simplified Brayton cycle.
Figure 6.23 Carnot refrigerator cycle.
Figure 6.24 Carnot cycle for an irreversible refrigerator.
Figure 6.25 Vapor compression refrigeration.
Figure 6.26 Vapor compression cycle on a ln
P
–
H
diagram using refrigerant R‐...
Figure 6.27 Vapor compression refrigeration with a turbine.
Figure 6.28 Schematic diagram of an air refrigeration cycle.
Figure 6.29 Schematic of an absorption refrigeration cycle.
Figure 6.30 Diagram with an engine and a refrigerator.
Figure 6.31 Heat pump diagram.
Figure 6.32 Cooling process for liquefaction.
Figure 6.33 Diagram for the Linde liquefaction process.
Figure 6.34
T
–
S
diagram for the Linde liquefaction process.
Figure 6.35 Diagram for the Claude liquefaction process.
Figure 6.36
T
–
S
diagram for air and paths of the Claude liquefaction process...
Figure 6.37 100% efficient, adiabatic compression of an ideal gas.
Figure 6.38 75% efficient, adiabatic compression of an ideal gas.
Figure 6.39 100% efficient, isothermal compression of an ideal gas.
Figure 6.40 75% efficient, isothermal compression of an ideal gas.
Figure 6.41 100% efficient, adiabatic compression of a real gas (GERG).
Figure 6.42 100% efficient, isothermal compression of a real gas (GERG).
Figure 6.43 100% efficient, adiabatic compression of a real gas (PR).
Figure 6.44 100% efficient, isothermal compression of a real gas (PR).
Figure 6.45 75% efficient, adiabatic compression of an ideal gas.
Figure 6.46 75% efficient, isothermal compression of an ideal gas.
Figure 6.47 75% efficient, adiabatic compression of a real gas (GERG).
Figure 6.48 75% efficient, isothermal compression of a real gas (GERG).
Figure 6.49 75% efficient, adiabatic compression of a real gas (PR).
Figure 6.50 75% efficient, isothermal compression of a real gas (PR).
Chapter 7
Figure 7.1 Graphical representation of the partial molar properties.
Figure 7.2 Selected state points to calculate the fugacity.
Figure 7.3 Representation of the Lewis–Randall Rule and Henry Law.
Figure 7.4 Schematic diagram of a mixing process.
Chapter 8
Figure 8.1 Different types of equilibrium states in the entropy surface: (a)...
Figure 8.2 System of constant energy, volume, and moles.
Figure 8.3 Maxwell equal area rule.
Figure 8.4 Phase diagram for pressure vs composition.
Figure 8.5 Phase equilibrium
P
–
x
,
y
diagram for a binary mixture at differen...
Figure 8.6 Phase diagram of temperature vs composition.
Figure 8.7 Phase diagrams for binary mixtures.
T
–
x
,
y
:
(a) minimum boi...
Figure 8.8
P
–
T
diagram showing the phase envelopes of a binary mixture.
Figure 8.9 Phase envelope with retrograde condensation.
Figure 8.10 Different
x–y
diagrams at atmospheric pressure.
Figure 8.11 Phase equilibria calculations in a
P
–
x
,
y
diagram.
Figure 8.12 Flash separator.
Figure 8.13
K
‐values for hydrocarbon at low temperature adapted for SI units...
Figure 8.14
K
‐values for hydrocarbon at high temperature adapted for SI unit...
Figure 8.15 Gibbs energy as a function of composition: (a) single phase and ...
Figure 8.16 Equal area rule for binary mixture two‐phase separation: (a) der...
Figure 8.17 Tangent plane equation vs the derivative of the Gibbs energy.
Figure 8.18 Equilibrium compositions in a two‐phase, ternary system.
Figure 8.19 Liquid–liquid equilibrium in a
P
–
x
and
T
–
x
diagram. (a) with Low...
Figure 8.20 Solubility diagrams: (a) with LCST, (b) with LCST and UCSP, (c) ...
Figure 8.21
vs
x
1
.
Figure 8.22
vs
x
1
.
Figure 8.23
A
12
or
A
21
vs
T
.
Figure 8.24
T
vs
x
1
.
Figure 8.25 Temperature–pressure–composition diagram showing VLE, LLE, and V...
Figure 8.26 Temperature–composition and pressure–composition diagrams for a ...
Figure 8.27 Temperature–composition and pressure–composition diagrams for a ...
Figure 8.28
T
vs
y
1
.
Figure 8.29
y
1
vs
P
.
Figure 8.30 Different Liquid–Solid Equilibrium for miscible components (a)–(...
Figure 8.31
T
vs
x
1
.
Chapter 9
Figure 9.1 Gibbs energy vs the extent of the reaction.
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Begin Reading
A Appendices
Index
End User License Agreement
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Thermodynamics for Chemical Engineers
Kenneth R. HallGustavo A. Iglesias-Silva
Authors
Prof. Kenneth Richard Hall ret.Texas A&M UniversityBryan Research & Engineering77845 College Station, TXUnited States
Prof. Gustavo Arturo Iglesias‐SilvaNational Technological Institute of Mexico ‐ Technological Institute of CelayaChemical Engineering30810 Celaya, GuanajuatoMexico
Cover Image: © piranka/Getty Images
All books published by WILEY‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing‐in‐Publication DataA catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2022 WILEY‐VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978‐3‐527‐35030‐8ePDF ISBN: 978‐3‐527‐83678‐9ePub ISBN: 978‐3‐527‐83679‐6
Preface
This book covers our experiences as instructors teaching thermodynamics in undergraduate‐ and graduate‐level courses. Our years of teaching have indicated to us that many students have problems understanding many concepts of thermodynamics. Our intention with this book is to present the subjects in a manner that enables the reader to assimilate them as quickly as possible. This book is primarily a textbook for the usual two thermodynamic courses that appear in chemical engineering curricula, but it can also be useful in careers that require a sense of thermodynamics.
The first chapter contains introductory material to familiarize students with the notation, definitions, and variables used in thermodynamics The second chapter deals with the first law of thermodynamics by introducing a general equation applying to open and closed systems to enable students to analyze energy transfer problems. The third chapter introduces the PVT behavior of pure substances. The fourth and fifth chapters discuss the second law of thermodynamics and the necessary mathematical formality to calculate thermodynamic properties, respectively. Chapter 6 introduces practical applications of thermodynamics. Chapter 7 introduces to the students to all the concepts necessary to compute equilibrium problems. Chapter 8 introduces calculation of physical equilibrium among phases and includes new procedures for the calculation of equilibrium based upon the Gibbs energy. Finally, Chapter 9 discusses chemical equilibrium.
The authors acknowledge the many students that offered their comments and criticisms during their thermodynamic courses. These observations have encouraged the authors to write this textbook. In addition, the authors thank Prof. J. C. Holste for making available to us many problem statements that he has developed during his teaching career at Texas A&M University.
College Station Texas, USAApril 2022
Kenneth R. Hall
Gustavo A. Iglesias‐Silva
1Introduction
1.1 Definition
Welcome to a new world, one without time! This is the world of thermodynamics, and it is the world we shall study in this course. Thermodynamics is an engineering/science field of study that is an exceptionally powerful tool for solving difficult problems with relatively little effort. For example, consider a glass of water that over the course of a day is heated, cooled, stirred, boiled, and frozen. How could we find the final condition of the water as represented by its characteristics knowing only the initial condition? It would be necessary to know the position and momentum of each molecule of water as a function of time and integrate from the initial time to the final time. Given that the water may contain 1025 molecules, this problem poses a prohibitively difficult task. However, with thermodynamics, we can translate this problem from a time domain to a timeless domain. In that new domain, we can solve the problem by knowing only a few things (less than five) about the water. Surely, you would rather tackle the latter problem than the former one. The translational procedure to move between the real world and the thermodynamic world is the application of the laws of thermodynamics. These are observations for which we have found no contradictions. The means for translation is mathematics. This process/procedure will become obvious as we progress through the course.
What is thermodynamics? The original Greek words from which we derive the name are thermos = heat and dynamos = power. This analysis would imply that thermodynamics is a study of heat power. Indeed, early thermodynamisists studied extracting energy transferred as work from energy transferred as heat. However, thermodynamics is a much richer and broader topic than that. The topic has very few concepts combined with formal elegance. Therefore, thermodynamics in a broader sense is a mathematical description of the real world using its physical properties.
Thermodynamics comes in two “flavors”: classical and statistical. Classical thermodynamics derives from macroscopic observations. Statistical thermodynamics derives from microscopic models. A modern bridge between the two is computer simulation that uses numerical techniques to apply principles of statistical thermodynamics to macroscopic problems to increase understanding. This course considers classical thermodynamics, but, when appropriate, introduces the concepts of statistical thermodynamics to provide deeper understanding.
1.2 Dimensions, Fundamental Quantities, and Units
Thermodynamics has simple mathematics, but the concepts are usually more demanding for students. It is important to recall several important definitions before beginning a course in thermodynamics to emphasize the importance of concepts. Therefore, let us define some common concepts that are useful in thermodynamics.
The numbers are meaningless without the correct specification of what they represent. For example, it does not make sense to say I reduced my weight by three or the distance that I walk every day is five. We must state that we have reduced our weight by 3 lb or 3 kg, and we traveled 5 mi or 5 km. These specifications are units. The product of a number and a unit can express any physical quantity. The number multiplying the unit is the numerical value of the quantity expressed in that unit, that is
where {A} is the numerical value or magnitude of A when expressing the value of A with units [A]. For example, if you weigh 60 kg, then {A} = 60 and [A] is kilograms. Generally, in figures and tables, we see the labels A/[A], which indicate numerical values according to Eq. (1.1). Thus, the axis of a graph or the heading of a column in a table should be “m kg−1,” denoting the mass measured in kilograms instead of “m (kg)” or “Mass (kg).”
Many units exist for different physical quantities, so it is convenient to introduce a general designation for a single class of units. Then, all the units employed for a particular physical property have the same dimension and use a separate symbol for it. The concept dimension is the name of a class of units, and a particular unit is an individual member of this class. The use of dimensions requires establishing a scale of measure with specific units. The International System of Units (SI: Systeme International) sets these units by international agreement. The SI establishes seven base units for seven base physical quantities that do not depend upon any other physical property (such as the length of the King's foot, the mass of a 90% platinum and 10% iridium bar, or suchlike).
The SI is a system of units for which
the unperturbed ground‐state hyperfine transition frequency of the cesium atom, Δ
v
Cs
, is 9 192 631 770 Hz
the speed of light under vacuum,
c
, is 299 792 458 m/s
the Planck constant,
h
, is 6.62607015 × 10
−34
J s
the elementary charge,
e
, is 1.602176634 × 10
−
19
C
the Boltzmann constant,
k
, is 1.380649 × 10
−23
J/K
the Avogadro constant,
N
A
, is 6.02214076 × 10
23
mol
−1
the luminous efficacy of monochromatic radiation of frequency 540 × 10
12
Hz and
K
cd
is 683 lm/W
in which Hz (hertz), J (joule), C (coulomb), lm (lumen), and W (watt) have relationships to the following units: s (second), m (meter), kg (kilogram), A (ampere), K (kelvin), mol (mole), and cd (candela): Hz = s−1, J = kg m2/s2, C = A s, lm = cd m2, m−2 = cd sr, and W = kg m2/s3.
Table 1.1 Units of the base units in the English Engineering System.
Physical property
Unit
Symbol
Length
Foot
ft
Mass
Pound‐mass
lbm, #m
Time
Second
sec
Electric current
Ampere
amp
Temperature
Rankine
°R
Amount of substance
Pound‐mole
lbmol, # mole
Luminous intensity
Foot‐candles
ft Cd
The base units of the SI are as follows:
Time (
t
) is a measure of the separation of events. The SI unit of time is second (s), and it comes directly from Δ
v
Cs
defined above in terms of Hz, which is s
−1
.
Length (
l
) is a measure of the separation of points in space. Meter, m, is the fundamental unit of length defined as the length of the path traveled by light under vacuum during a time interval of 1/299 792 458 of a second.
Mass (m) is a measure of the amount of an object. Kilogram, kg, comes from Planck's constant expressed in J s, which equals kg m
2
/s with m and s defined under time and length.
Ampere (A) is the SI unit for electric current, and it comes from the elementary charge,
e
, expressed in C (=A s) with s defined under time.
Thermodynamic temperature (
T
) measures the “hotness” of an object and reflects the motion of its molecules. The unit of thermodynamic temperature is kelvin (K), and it comes from the Boltzmann constant expressed in J/K or kg m
2
/(s
2
K) (kg, m, and s already have definitions).
The amount of substance is mole (
n
) in SI. It comes directly from
N
A
(Avogadro's number).
The SI unit for luminous intensity in a given direction is candela (cd) defined by the luminous efficacy of monochromatic radiation of frequency expressed in lm/W.
Other systems of units exist, such as the English Engineering System (used sparingly throughout the world primarily in the United States and a few small political entities). The primary dimensions are force, mass, length, time, and temperature. The units for force and mass are independent. Table 1.1 contains the base units in this system.
A prefix added to any unit can produce an integer multiple of the base unit. For example, a kilometer denotes one thousand meters, and a millimeter denotes one thousandth of a meter: For example, 1 km = 1 × 103 m and 1 mm = 1 × 10−3 m. Table 1.2 contains the accepted prefixes for use with SI units.
Table 1.2 SI prefixes.
Name
Symbol
Factor
Name
Symbol
Factor
yotta
Y
10
24
deci
d
10
–1
zetta
Z
10
21
centi
c
10
–2
exa
E
10
18
milli
m
10
–3
peta
P
10
15
micro
μ
10
–6
tera
T
10
12
nano
n
10
–9
giga
G
10
9
pico
p
10
–12
mega
M
10
6
femto
f
10
–15
kilo
k
10
3
atto
a
10
–18
hecto
h
10
2
zepto
z
10
–21
deka
da
10
1
yocto
y
10
–24
1.3 Secondary or Derived Physical Quantities
All other quantities derive from base quantities by multiplication and division. These quantities have units that are a combination of the base units according to the algebraic relations of the corresponding physical quantities. Some derived physical properties are area, volume, force, pressure, etc.
Area is a measure of the surface of an object. It is two dimensional and in terms of dimensional symbols is L2. The units employed to represent the area are square meters in the SI system or square feet in the English system.
Volume is the space occupied by an object and in terms of dimensions is the product of the lengths associated with the object: L × L × L = L3. The SI unit for volume is the cubic meter. The volume of a substance depends upon the amount of the material, but a specific volume and molar volume (m3/kg or m3/mol) are independent of the amount of the material. The reciprocal of the specific volume is the density. Obviously, an object can have a total volume (the amount of space it occupies) and a specific or molar volume that applies to any sized object. In this text, we use capital letters to denote the molar properties of a substance, so a total property would be the molar property multiplied by the number of moles. For example, the total volume is
The specific volume (volume per mass) is (nV)/m = V/M, where M is the molar mass (or molecular weight) and the molar volume is V (volume per mole).
Force induces motion or change. Newton's laws describe the action of forces in causing motion. Newton's second law states that force is the product of mass m and its acceleration a,
Thus, force = (mass)(length)/(time)2. The SI unit for force is newton (N), and according to the above equation, it is the force required to accelerate a mass of 1 kg at a rate of 1 m/s2. Therefore,
In the English Engineering System, the unit of force is pound force (lbf), and 1 lb force imparts an acceleration of 32.1740 ft/s2 to a mass of 1 lb. In this system, force is an independent dimension that requires a proportionality constant to be consistent with the definition Eq. (1.3)
Thus,
and 1 lbf = 4.4482216 N. In this system of units, confusion exists between the terms mass and weight, and often, they are used synonymously. For example, when we buy meat by weight, we are interested in the amount of meat. Likewise, when we measure our body weight, we want to know the amount of fat or muscle present. Scales measure force. Weight refers to the force exerted upon an object by virtue of its position in a gravitational field. In most circumstances, this ambiguity is not a problem because the weight of an object is directly proportional to its mass (see Eq. (1.3)), and on Earth, the proportionality constant is the gravitational acceleration, which is essentially constant. We conclude that the mass of an object does not change, but its weight does depend on the gravitational field surrounding the object.
Example 1.1
An alien weighs 102 N on his planet and 700 N on Earth. The gravitational acceleration on Earth is approximately 9.802 m/s2. What is the gravitational acceleration of the alien's planet? From the following table (moons are in italics), can you infer from which planet or moon this alien comes?
Planet/moons
Approximate gravitational acceleration (m/s
2
)
Planets/moons
Approximate gravitational acceleration (m/s
2
)
Mercury
3.70
Saturn
11.19
Venus
8.87
Titan
1.36
Moon
1.63
Uranus
9.01
Mars
3.73
Titania
0.38
Jupiter
25.93
Oberon
0.35
Io
1.79
Neptune
11.28
Europa
1.31
Triton
0.78
Ganymede
1.43
Pluto
0.61
Callisto
1.24
Solution
First, we calculate the mass of the alien using the information from Earth:
Because the mass is independent of the location, on its native planet or moon
Most likely, the alien comes from the moon of Jupiter: Ganymede.
Pressure is the force applied over an area. In the SI system, the unit of force is newton and that for area is square meters, so the unit of pressure is N/m2. This unit is called pascal, and its symbol is Pa. In the English Engineering System, the usual pressure unit is pound force per square inch (psi). If an object rests on a surface, the force pressing on the surface is its weight. However, in different positions, the area in contact can be different, and it can exert different pressures. Pressure is an observable and it is not a function of mass.
We use various terms for pressure:
Atmospheric pressure,
P
atm
, is the pressure caused by the weight of the Earth's atmosphere on an object. We might find this pressure called “barometric” pressure. The standard atmosphere (atm) is a unit of pressure equal to 101.325 kPa.
Absolute pressure,
P
abs
, is the total pressure. An absolute pressure of 0 is perfect vacuum. All thermodynamic calculations must use absolute pressure.
Gauge or manometric pressure,
P
man
, is the pressure relative to atmospheric pressure,
P
man
=
P
abs
−
P
atm
.
Vacuum is a gauge pressure that is below the atmospheric pressure. It reports a positive number for vacuum.
We calculate the absolute pressure by adding the atmospheric pressure to the gauge pressure:
Many pressure measurement techniques are available. First, we must define primary and secondary measurement standards. A primary standard is a measurement device for which the theoretical relation between the measured physical property and the desired quantity (pressure in this case) is known exactly. A secondary standard is a measurement device for which the theoretical relation between the measured physical property and the desired quantity (pressure, temperature, etc.) is not known exactly. Secondary measurement devices must have calibrations against the primary standards.
First, let us consider manometers and dead‐weight gauges. These are primary pressure devices commonly used in engineering. Figure 1.1 shows a manometer and its schematic diagram. Manometers measure differential pressures. The differential equation that expresses pressure is
Figure 1.1 A U‐tube glass manometer and its schematic diagram.
where ρ is the density of the fluid and g is the local acceleration of gravity. If the density is constant, the integration of the Eq. (1.8) is
In Figure 1.1, a force pushes on the fluid in position 1 and the atmospheric pressure acts against the fluid in position 2, then
This equation indicates that the hydraulic pressure (gauge pressure) is ρgh. This effect also is the pressure that a vertical column of fluid exerts at its base caused by gravity
Applying Newton's law and the definition of pressure,
in which ρ is the mass density (mass per volume). Equation (1.11) is the theoretical relation for pressure as a function of height and density of a fluid in a manometer. For very precise measurement of pressure with a manometer, the density of the measuring fluid must be corrected for its thermal expansion and for the height measuring device in a gravitational field.
Calibration of commercial mercury manometers uses the density at 0 °C, and the measuring scale (usually brass) has zero correction at either 70 or 77 °F. Because these devices measure distances, units of pressure exist such as mm Hg, in of H2O, etc. Torr is the pressure equal to 1 mm of mercury at 0 °C in a standard gravitational field. One torr equals 133.322 Pa. The overall uncertainty in a manometer is approximately 8.1 × 10−5 Pa. Manometers are useful and practical for measurements from 10−3 to 2 atm.
Another primary standard is the dead‐weight gauge. Figure 1.2 depicts such a gauge along with a schematic. In this case, masses impose the downward force on the plate and piston (with a known cross‐sectional area).
Figure 1.2 Dead‐weight gauge.
The theoretical relationship for this device comes from a force balance between the working fluid (oil or air) and the weights:
in which P is the pressure; A is the cross‐sectional area of the piston; m is the mass of the piston, pan, and load; and g is the local gravitational acceleration. Therefore,
The ultimate accuracy for the best dead‐weight gauges is about 1 part in 30 000 with a precision of 1 part in 20 000. Dead‐weight gauges are the instrument of choice for the measurement of highest accuracy or for calibrating other pressure gauges. The secondary pressure devices are pressure transducers, bourdon tubes, and differential pressure indicators (DPIs) (Figure 1.3).
Figure 1.3 Secondary pressure measurement devices.
Example 1.2
Calculate the pressure that the atmosphere exerts on the head of a man who is 1.75 m tall and who is on top of a mountain that is 1000 m high. The temperature is 10 °C. Assume that the pressure at the sea level is 101 kPa, g = 9.80665 m/s2, and the density of air in kg/m3 is a function of temperature (but not pressure) given by
Solution
Using Eq. (1.9).
Example 1.3
A dead‐weight gauge has the following specifications:
Piston diameter = 2.5 cm
Pan mass = 415 g
Cylinder mass = 500 g
Masses: #1: 100 g, #2: 500 g, #3: 1 kg, #4: 3 kg, and #5: 5 kg
An experimenter uses two #1, one #2, one #4, and 1 #5 masses to balance the gauge with the pressure of the system. What is the gauge pressure if the local acceleration of gravity is 9.805 m/s2?
Solution
The total mass (pan plus weights) is
Using Eq. (1.13)
Temperature from statistical thermodynamics is a variable that describes how atoms or molecules distribute among the quantum energy levels available to them. In classical thermodynamics, the definition of temperature comes from the second law of thermodynamics, while its measurement comes from the zeroth law. Temperature is an observable and not a function of mass.
Now, imagine that you are a Neanderthal, and you have many hot stones. How can you tell a person of your tribe which stone is the hottest and then the next hottest? Probably, you can use different tones and sounds to solve the problem, but if you come upon a different tribe, and you want to explain the hotness, these sounds may not mean anything to them. Therefore, it is necessary to create a system for measuring the temperature that is the same for everyone. Temperature scales are the solution. We define these scales by using a primary thermometer to determine temperatures corresponding to the observed physical behavior, i.e. triple points, boiling points, and melting points. Like the primary pressure device, a primary thermometer is one for which a known relationship exists between some physical property and the absolute temperature. The examples of primary thermometers are gas thermometer, acoustic thermometer, noise thermometer, and total radiation thermometer. The relationship for the gas thermometer is
where V is the molar volume, P is the pressure, and R = 8.3144621 J/(mol K) is the universal gas constant (the gas constant is not actually a constant, rather it is an experimental number subject to change, but “constant” at any given time). It is convenient to use a reference point temperature
The common reference temperature is the triple point of water (273.16 K). Primary thermometers are difficult to use and expensive, so their use is primarily to establish temperature scales and to calibrate secondary thermometers. The Kelvin and Celsius scales are by international agreement defined numerically by two points: absolute zero (0 K) and the triple point of water. At absolute zero, all kinetic motion of particles ceases, and the molecules and atoms are in their ground states. Gas thermometry establishes the Kelvin scale.
In the Celsius scale, the freezing point of water is 0 °C, and the boiling point of water at atmospheric pressure is 100 °C. Every unit is a degree Celsius. The name of this temperature scale comes from the Swedish astronomer Anders Celsius (1701–1744), who developed the temperature scale two years before his death. The mathematical relationship between the Kelvin and Celsius scales is
In addition to the Kelvin and Celsius scales, two other scales exist in the English Engineering System: Rankine and Fahrenheit. The Rankine scale is an absolute temperature scale like the Kelvin scale. The relationship between them is
A direct relation exists between the Fahrenheit and Rankine temperatures
and between the Fahrenheit and Celsius scales
Because primary thermometers are not useful for practical purposes, we use secondary thermometers for such applications. Examples of secondary thermometers are glass thermometers, thermistors, platinum resistance thermometers (PLTs), bimetallic strips, and thermocouples. These devices require calibration using an internationally recognized temperature scale based on primary thermometers and fixed points. PLTs also find use as transfer standards. Their calibration uses a primary thermometer to calibrate other temperature‐measuring devices. The primary scale is the International Temperature Scale of 1990 (ITS‐90) with its addendum the Provisional Low Temperature Scale of 2000 (PLTS‐2000). ITS‐90 contains seventeen fixed points and four temperature instruments. The temperatures range from 0.65 to 10000 K using a gas thermometer and a PRT. Below 0.65 K, the PLTS‐2000 scale uses Johnson noise and nuclear orientation thermometers. Figure 1.4 depicts secondary thermometers.
Figure 1.4 Secondary thermometers.
Example 1.4
An experimentalist has problems with a PLT giving incorrect temperatures. He knows that the electrical resistance of a wire is a function of temperature
in which α is the temperature coefficient of resistance and R0 and T0 are reference resistance and reference temperature (triple point of water), respectively. The manufacturer says that the thermometer has a calibrated standard resistance of 10.5 Ω at 0.01 °C. The experimentalist measures a resistance of 12.94 Ω at 75 °C. Is the manufacturer correct? Assume α = 3.92 × 10−3 °C−1.
Solution
Find the R0:
Either the manufacturer is wrong, or the experimenter has a faulty resistance measurement.
It is possible to perform dimensional analysis in SI because any derived unit A can be expressed in terms of the SI base units by
in which the exponents α, β, γ, … and the factors ak are numbers. The dimension of A is
where L, M, T, I, θ, N, and J are the dimensions of the SI base units and α, β, γ, … are the dimensional exponents. The general SI‐derived unit of A is mα kgβ sγ Aδ Kε molζ cdη, which is obtained by replacing the dimensions of the SI base quantities with the symbols for the corresponding base units. For dimensionless quantities, the exponents are zero and dim A = 1. This quantity does not have units (symbols) because its unit is 1 (the exponents are zero).
Example 1.5
Consider an object of mass m that moves uniformly a distance l in a time t. If the total kinetic energy is , express the velocity and the energy in terms of their symbols and express their dimensions.
Solution
Symbols mass = m, length = l, and time = t.
For the velocity: and the kinetic energy is (nEk) = ml2t−2/2.
For the dimensions:
and the dimensional exponents are 1 and −1.
dim(
nE
k
) = ML
2
T
−2
and the dimensional exponents are 1, 2, and −2.
The SI‐derived unit of the kinetic energy is then kg m2/s2 named joule with the symbol J.
1.4 SI Usage of Units and Symbols
Several rules exist for using SI units and symbols. The most important are:
Roman type (not italics or bold) denotes unit symbols regardless of the type used in the surrounding text.
The unit symbols are lowercase except when the name of the symbol derives from a proper name. The unit name is in lowercase, but the symbol may be upper case, e.g. meter (m), kelvin (K), pascal (Pa), and second (s).
Plurals used if indicated by normal grammar rules are henries and seconds. Lux, hertz, and siemens are the same for plural and singular. Unit symbols do not change when plural.
A space appears between the numerical value and the unit or symbol, e.g. 10 Hz and 15 MPa. A period does not follow unit symbols unless at the end of a sentence.
Raised dots or a space indicate products of symbols. Slashes, a horizontal line, or negative exponents denote quotients of symbols. No more than one slash should appear in any expression. For example,
Unit symbols and unit names do not appear together, e.g. meter per second, m/s, and m s
−1
are correct while meter/s, meter per s, and meter s
−1
are incorrect.
Unit symbols or names do not have abbreviations, e.g. sec for s or seconds, sq mm for mm
2
or square millimeter, and cc for cm
3
or cubic centimeter. If the name of a unit appears, it must be written out in full.
Conventions also exist for the use of the prefixes in
Table 1.2
. The following rules apply to prefix names, and symbols follow the first rule of the unit symbols (roman type not italics or bold) regardless of the type used in the surrounding text, the prefix name can be attached to a unit name without a space, which also applies to a prefix symbol attached to the unit symbol, e.g. mm (millimeter), TΩ (teraohm), and GHz (gigahertz).
The union of a prefix and a unit symbol is a new, inseparable symbol that indicates a multiple or sub‐multiple of the unit that follows all the rules for SI units. The prefix name is also inseparable from the unit name forming a single word when attached to each other, e.g. cm
3
, μs
−1
, megapascal, and microliter.
Prefix names and symbols cannot appear more than once, e.g. nm (nanometer) is correct but not mμm (“millimicrometer”).
It is not desirable to use multiple prefixes in a derived unit formed by a division. It is preferable to reduce the prefixes to a minimum, e.g. it is correct to write 10 kW/ms, but it is preferable to write 10 MW/s because it contains only one prefix. This rule also applies to the product of units with prefixes, e.g. 10 kV s is preferable to 10 MV ms. When working with units that involve the kilogram, it is always preferable to use kg rather than g.
Prefix symbols or names cannot appear alone, for example, 5 M.
The kilogram is the only SI unit with a prefix as part of its name and symbol. The prefixes in
Table 1.2
are applicable to the unit gram and the unit symbol g. For instance, 10
−6
kg = 1 μg is acceptable but not 10
−6
kg = 1 μkg (1 microkilogram).
The prefix symbols and names are acceptable for use with the unit symbol °C and the unit name degree Celsius. The examples are 12 m °C (12 millidegrees Celsius).
SI prefix symbols and prefix names may be used with the unit symbols and names: L (liter), t (metric ton), eV (electronvolt), u (unified atomic mass unit), and Da (dalton). However, although submultiples of liter, such as mL (milliliter) and dL (deciliter), are common, multiples of liter, such as kL (kiloliter) and ML (megaliter), are not. Similarly, although multiples of metric tonne such as kt (kilometric ton) are common, submultiples such as mt (millimetric ton) are not. The examples of the use of prefix symbols with eV and u are 80 MeV (80 megaelectronvolts) and 15 nu (15 nanounified atomic mass units), respectively.
1.5 Thermodynamic Systems and Variables
A system is a volume of space set aside to study. A boundary is a physical or imaginary surface (mathematical sense) that separates the system from the remainder of the universe. Everything outside the system is its surroundings. Three classes of systems exist depending on mass and energy transfer:
Isolated system
is one that has no mass or energy crossing its boundary
Closed system
is one that permits energy, but not mass, to cross its boundaries
Open system
is one that permits energy and mass to cross its boundaries
The state is the condition of the system. Its physical properties determine the state of a system. A property is a characteristic. An open system is in steady state if its properties vary with position but not with time. When the properties of any system vary with neither position nor time, the system is in equilibrium.
Application of thermodynamics is possible when the system consists of one or more parts with spatially uniform properties. Each of these parts is a phase. Many events can happen in a system. This sequence of events is a process. In thermodynamics, the process is reversible if the system can return from its final state to its initial state without finite changes in the surroundings. If the system requires finite changes in the surroundings to return from its final state to its initial state, the process is irreversible.
In classical thermodynamics, we utilize the physical properties mentioned in Sections 1.2 and 1.3. They fall into two groups:
Intensive properties do not depend on the amount of the material in the object. They are point functions, so they exist at each point within the system and can vary from point to point (if the system is not at equilibrium). They are not additive. The examples of these properties are pressure, temperature, density, and specific volume. Consider a pure component in a closed system that contains a single phase at equilibrium. For such a system, any intensive variable depends upon two other intensive variables,
For example, if we know the density and temperature of a pure substance, then we know other properties such as pressure and surface tension. In the case of mixtures, the intensive property depends upon the two intensive variables and the composition of the mixture. A pure component is a special case of a mixture with a composition of 100% of the component.
Extensive properties are those that depend upon the amount of the material in the object. They are additive; that is, the value of the property for the object is the sum of the values of all its constituent parts. The examples are total volume, mass, length, and area. Again, for a pure component in a closed system with a single equilibrium phase, any extensive property is a function of two intensive properties plus the amount of the material
in which m is the mass of the system. Equation (1.21) enables the definition of a specific property
All specific properties are intensive properties.
1.6 Zeroth Law
The statement of the law is: The initial law of thermodynamics we shall investigate is the zeroth law (discovered after the first and second laws, hence the zeroth law). It has but one function: it enables construction of thermometers. The statement of the law is as follows:
Two systems separatelyin thermal equilibrium with a third system are in thermal equilibrium with each other.
Mathematically, this statement is
We can solve each equation for one variable, e.g. PB
Thus, f1 = f2 and A and C are in equilibrium with B. If A and C are in equilibrium with B, then by the zeroth law, they are in equilibrium with each other and
This implies that f1 and f2 contain VB in such a manner that it cancels exactly, e.g.
If this is the case, then
or
When we study the second law of thermodynamics, this final equation establishes the empirical temperature and the definition of the absolute temperature. Absolute thermodynamic temperature is a mathematical function that depends upon two variables, commonly pressure and molar volume.
Problems for Chapter 1
1.1
What thermodynamic variable results from the zeroth law of thermodynamics?
1.2
A European data sheet provides a pressure specification of 350 kg
f
/cm
2
. Convert this pressure to units of atmospheres. (This pressure unit was widely used in both research and practical applications for many years and persists today even though it is not an accepted SI unit.) The kg
f
unit is defined analogously to the lb
f
unit using the same value for the acceleration due to gravity but in appropriate SI units.
1.3
If the density of the gasoline fluctuates between 650 and 870 kg/m
3
, what is the minimum and maximum volume that 10000 kg occupies in a cylindrical steel tank? What is the mass of gasoline? What is the minimum and maximum height of the tank if its diameter is 1 m. Calculate the mass of the two tanks if the density of steel is 7850 kg/m
3
.
1.4
A black and white cat that weighs 5 kg kneads the stomach of its owner with its two front paws. What is the pressure that it exerts upon his owner's stomach? Consider that the paws are circular with a diameter of 1.8 cm.
1.5
A diver plunges vertically into the sea until reaching a depth of 100 m. To decompress, he must reduce his pressure by 122.625 kPa and rest for one minute; to do so, he must climb a certain distance. What pressure does the diver endure at the end? How many minutes should he rest? The density of water is 1 g/cm
3
, g = 9.81 m/s
2
.
1.6
Calculate the force caused by pressure acting on a horizontal hatch of 1 m diameter for a submarine submerged 600 m from the surface. What is the force if the submarine is on the surface of water?
1.7
The municipal water service fills a house cistern with a mass flow rate of 10 kg/s. The dimensions of the cistern are 7 m long by 1.2 m wide and 1.5 m high. Convert the mass flow rate to volumetric flow rate in l/min. How long does it take to fill the cistern? Consider the density of water equal to 1000 kg/m
3
.
1.8
At which temperature is the Celsius scale three times the Kelvin scale? Also, at which temperature is the Celsius scale three times the Fahrenheit scale?
1.9
A pressurized tank filled with gas has a leak through a hole with a 0.4 mm diameter. An engineer finds a quick temporary solution to put a weight on the hole, so the gas does not escape. What is the mass of the weight that the engineer must put on the hole if the pressure inside of the tank is 2750 kPa?
1.10
An American travels by car to México. Suddenly, he notices that the speed limit signs say 90 km/h in the country and is 60 km/h in the city. Unfortunately, his car speedometer shows the speed in miles per hour. He is driving the car at 70 the speed limit in most highways in America and at 40 in the city. Is he violating the law? A mile is 1609 m.
1.11
What is the total mass and weight of an oak barrel containing 59 gal of Cabernet Sauvignon wine? The mass of the barrel is 110 kg. The density of the wine is 0.985 g/cm
3
.
1.12
Shock‐compression experiments on diamond have reported the melting temperature of carbon at a pressures of up to 1.1 TPa (6
11
Mbar). Convert the pressure into atm, psia, MPa, and inches of Hg.
1.13
An equation of state presents the pressure as a function of temperature and molar volume. A simple equation is
The unit of P is MPa, and the value of R is 8.314. What units should R, a, and b have if the volume is cm3/mol and T is in kelvins?
1.14
What is the pressure in atm at point B in the following diagram if an open container contains oil with a density of 0.845 g/cm
3
?
1.15
If a mercury barometer reads 27 in. of mercury, what is the pressure in atm? Is this device measuring absolute pressure? The density of mercury is 13 590 kg/m
3
.
1.16
Find the expression for the difference pressure between
P
2
and
P
1
for a manometer containing three different fluids:
1.17
A manometer can measure pressure differences of a fluid flowing through an orifice as shown in the figure below. The expression for measuring the pressure differences is
Find the expression for the difference in pressure between P2 and P1. The density of the liquid in the manometer is ρl
1.18
A pressure gauge is connected in the same tank as a lamp oil manometer. If the display of the gauge reads 5 kPa, what is the height of oil in the manometer? Consider the density of the oil to be 0.81 g/cm
3
.
