thermodynamics i mecn 4201

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Thermodynamics I Inter Thermodynamics I Inter - Bayamon - Bayamon Lecture Lecture 1 1 Thermodynamics I Thermodynamics I MECN 4201 MECN 4201 Professor: Dr. Omar E. Meza Castillo Professor: Dr. Omar E. Meza Castillo [email protected] http://facultad.bayamon.inter.edu/omeza Department of Mechanical Engineering Department of Mechanical Engineering Inter American University of Puerto Rico Inter American University of Puerto Rico Bayamon Campus Bayamon Campus

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Thermodynamics I MECN 4201. Professor: Dr. Omar E. Meza Castillo [email protected] http://facultad.bayamon.inter.edu/omeza Department of Mechanical Engineering Inter American University of Puerto Rico Bayamon Campus. Course Information. - PowerPoint PPT Presentation

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LectureLecture

11Thermodynamics IThermodynamics I

MECN 4201 MECN 4201

Professor: Dr. Omar E. Meza CastilloProfessor: Dr. Omar E. Meza [email protected]

http://facultad.bayamon.inter.edu/omeza

Department of Mechanical EngineeringDepartment of Mechanical Engineering

Inter American University of Puerto RicoInter American University of Puerto Rico

Bayamon CampusBayamon Campus

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Catalog DescriptionCatalog Description: : Analysis of the basic concepts of Analysis of the basic concepts of thermodynamics. Includes the study of the properties of thermodynamics. Includes the study of the properties of pure substances and the equation of the ideal state of pure substances and the equation of the ideal state of gas. Analysis of the transfer of energy by heat, work and gas. Analysis of the transfer of energy by heat, work and mass. Application of the first and second law of mass. Application of the first and second law of thermodynamics. Analysis of the Carnot Cycle and thermodynamics. Analysis of the Carnot Cycle and entropy.entropy.

Prerequisites: Prerequisites: PHYS 3312 – Physics for Engineers IIPHYS 3312 – Physics for Engineers IICHEM 2115 – General Chemistry for Engineers.CHEM 2115 – General Chemistry for Engineers.

Course Text: Course Text: Cengel, Y. A. (2008). Cengel, Y. A. (2008). Introduction to Introduction to Thermodynamics and Heat TransferThermodynamics and Heat Transfer. 2nd. 2nd ed. McGraw-Hill.ed. McGraw-Hill.

Absences:Absences: On those days when you will be absent, find On those days when you will be absent, find a friend or an acquaintance to take notes for you or visit a friend or an acquaintance to take notes for you or visit Blackboard. Blackboard. Do not call or send an e-mail the instructor Do not call or send an e-mail the instructor and ask what went on in class, and what the homework and ask what went on in class, and what the homework assignment is.assignment is.

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Course InformationCourse Information

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Homework assignments:Homework assignments: Homework problems will be Homework problems will be assigned on a regular basis. Problems will be solved assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on any white paper using the Problem-Solving Technique on any white paper with no more than one problem written on one sheet of with no more than one problem written on one sheet of paper. Homework will be collected when due, with your paper. Homework will be collected when due, with your name written legibly on the from of the title page. It is name written legibly on the from of the title page. It is graded on a 0 to 100 points scale. Late homework (any graded on a 0 to 100 points scale. Late homework (any reason) reason) will not be acceptedwill not be accepted.. Problem-Solving Technique:Problem-Solving Technique:

A.A. KnownKnown

B.B. FindFind

C.C. AssumptionsAssumptions

D.D. SchematicSchematic

E.E. Analysis, andAnalysis, and

F.F. ResultsResults

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Course InformationCourse Information

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Quiz: Quiz: There are four or more partial quizes during the semester.

Partial Exams and Final Exam: Partial Exams and Final Exam: There are three partial exams during the semester, and a final exam at the end of the semester.

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Course InformationCourse Information

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on Course GradingCourse Grading

The total course grade is comprised of homework assignments, quizes, partial exams, and final exam as follows: Homework (6 or more ) 20% Quiz (4 or more) 20% Partial Exam (3) 20% Final Exam 25% Final Project 15%

100% Cheating: Cheating: You are allowed to cooperate on homework

by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from others will be considered academic misconduct and will get no points.

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Most Course Material (Course Notes, Handouts, Homework, Final Project, and Communications) on Web Page

Power Point Lectures will posted every week or two Office Hours: Tuesday and Thursday @ 5:50 to 7:20 PM Email: [email protected]

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Course MaterialsCourse Materials

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Introduction and Overview Basic Concepts of Thermodynamics Properties of Pure Substances Energy Transfer by Heat, Work and Mass The First Law of Thermodynamics for Closed

System The First Law of Thermodynamics for Open

System The Second Law of Thermodynamics Entropy.

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Course OutlineCourse Outline

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IntroductionIntroduction

Introduction to Introduction to ThermodynamicsThermodynamics

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To explain the fundamental concepts of To explain the fundamental concepts of thermodynamics such as system, state, thermodynamics such as system, state, equilibrium, process, and cycleequilibrium, process, and cycle

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Course ObjectiveCourse Objective

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on IntroductionIntroduction

What is Thermodynamics?What is Thermodynamics?Thermodynamics can be defined as the Thermodynamics can be defined as the science of science of energyenergy. The name thermodynamics stem from the . The name thermodynamics stem from the Greek words: Greek words: THERMETHERME (heat) and (heat) and DYNAMISDYNAMIS (power). (power). Initially at early 1900’s: the capacity of heat to Initially at early 1900’s: the capacity of heat to produce produce workwork. . Today the scope is larger including all Today the scope is larger including all aspect of energy and its transformation. Engineers aspect of energy and its transformation. Engineers are interested to studyare interested to study System <-> SurroundingSystem <-> Surrounding..Involves the study of Involves the study of work and heat work and heat interactions with interactions with matter and its propertiesmatter and its propertiesTwo important concepts in Thermodynamics are Two important concepts in Thermodynamics are Energy Energy and Entropy.and Entropy.Energy is always conserved.Energy is always conserved.Entropy determines whether a process is Entropy determines whether a process is possible, i.e. a possible, i.e. a process which process which produces produces entropy is entropy is possible, one that possible, one that destroys destroys entropy is entropy is impossible.impossible.

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on Thermodynamics and EnergyThermodynamics and Energy

Why do Engineers study Thermodynamics?Why do Engineers study Thermodynamics?

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on IntroductionIntroduction

Applications: Thermodynamics in Engineering Applications: Thermodynamics in Engineering SystemsSystems Power GenerationPower Generation Refrigeration and Heat PumpsRefrigeration and Heat Pumps Internal Combustion EnginesInternal Combustion Engines HVAC SystemsHVAC Systems Jet PropulsionJet Propulsion Supersonic FlowsSupersonic Flows Fuel CellsFuel Cells Reacting and non-Reacting ProcessesReacting and non-Reacting Processes

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on IntroductionIntroduction

One of the greatest inventions ever – the One of the greatest inventions ever – the Steam Engine!Steam Engine!

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on IntroductionIntroduction

How one invention changed the worldHow one invention changed the world

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Basic ConceptsBasic Concepts

ThermodynamicsThermodynamics

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on Importance of Dimensions and UnitsImportance of Dimensions and Units

Engineering UnitsEngineering UnitsThree systems:Three systems: SI SI (from Le Système International d’ (from Le Système International d’ Unités) SUnités) System ystem

of Units [M,L,t,T] – force is a secondary unitof Units [M,L,t,T] – force is a secondary unit British Gravitational System [F,L,t,T] – force is a British Gravitational System [F,L,t,T] – force is a

primary unitprimary unit English Engineering System [F,M,L,t,T] - both English Engineering System [F,M,L,t,T] - both

mass and force are primary unitsmass and force are primary units

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on Importance of Dimensions and UnitsImportance of Dimensions and Units

English Engineering UnitsEnglish Engineering Units When is a pound not a pound?When is a pound not a pound?

In English Engineering Units of course!In English Engineering Units of course! In the EEU system, the unit of force is the pound In the EEU system, the unit of force is the pound

force (lbforce (lbff or lbf) and the unit of mass is the or lbf) and the unit of mass is the pound mass (lbpound mass (lbmm or lbm). Length is in (ft), time in or lbm). Length is in (ft), time in (s), and temperature in (R). Both (s), and temperature in (R). Both forceforce and and massmass are primary. Absolutely brilliant!!! are primary. Absolutely brilliant!!!

A A force of one pound is the force that gives a force of one pound is the force that gives a one pound mass an acceleration equal to that of one pound mass an acceleration equal to that of the earth’s gravity gthe earth’s gravity g= 32.174 ft/s= 32.174 ft/s22. i.e. 1 lbf= 1 . i.e. 1 lbf= 1 lbm x 32.174 ft/slbm x 32.174 ft/s22

Newton’s Law then becomes:Newton’s Law then becomes:

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on Importance of Dimensions and UnitsImportance of Dimensions and Units

The constant gThe constant gcc = 32.174 (lbm ft)/(lbf s= 32.174 (lbm ft)/(lbf s22) is ) is required in any relationships derived from required in any relationships derived from Newton’s law.Newton’s law.

This constant of proportionality has both units This constant of proportionality has both units and a value that is not equal to unity.and a value that is not equal to unity.

Care must be taken when working in the EEU Care must be taken when working in the EEU system, to understand when a lbf or lbm are system, to understand when a lbf or lbm are specified. The course text adopts that (lb) is specified. The course text adopts that (lb) is (lbm). So be careful.(lbm). So be careful.

We will primarily use the SI system. We will primarily use the SI system. Occasionally, we will do an example in the EEU Occasionally, we will do an example in the EEU system.system.

Finally, note:Finally, note:

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on Importance of Dimensions and UnitsImportance of Dimensions and Units

British Gravitational UnitsBritish Gravitational Units In this system, force is defined in (lbf), length in In this system, force is defined in (lbf), length in

(ft), time in (s), and temperature in (R). The unit (ft), time in (s), and temperature in (R). The unit of mass the of mass the slug is secondary, such that:slug is secondary, such that:

The weight of one slug in earth’s gravity is then:The weight of one slug in earth’s gravity is then:

This leads to, using Newton’s Law from EEU, as:This leads to, using Newton’s Law from EEU, as:

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on ExampleExample

Let’s say a person who weighs 150 lbf in earth Let’s say a person who weighs 150 lbf in earth gravity is weighed on the moon where gravity is weighed on the moon where g=5.348ft/sg=5.348ft/s22. What is their new weight?. What is their new weight?

On earth we also say they have a mass of 150 On earth we also say they have a mass of 150 lbm! Thus:lbm! Thus:

In the BGU system, this person has a mass of In the BGU system, this person has a mass of 4.662 slug, such that:4.662 slug, such that:

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on Example (continued)Example (continued)

Now this same person has a mass of 68.04 kg in Now this same person has a mass of 68.04 kg in SI unitsSI units

On earth we would find this person weighs:On earth we would find this person weighs:

On the moon, this person now weighs:On the moon, this person now weighs:

In summary, SI is simpler. The BGU system is a In summary, SI is simpler. The BGU system is a little more practical than the EEU, as the pound little more practical than the EEU, as the pound is force and not mass as well. But you should see is force and not mass as well. But you should see the equality in BGU and EEU, since lbm/gthe equality in BGU and EEU, since lbm/gcc

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on Systems and Control VolumesSystems and Control Volumes

Thermodynamic Thermodynamic SystemSystem: Three-dimensional : Three-dimensional region of space which is bounded by an arbitrary region of space which is bounded by an arbitrary surface or a quantity of mass chosen for study..surface or a quantity of mass chosen for study..

Control SurfaceControl Surface: or : or BoundaryBoundary may be real or may be real or imaginary, may be at rest or in motion, and may imaginary, may be at rest or in motion, and may change its size or shape. It neither contains change its size or shape. It neither contains matter nor occupies a volume in space. matter nor occupies a volume in space. Thickness of a boundary is mathematically zero. Thickness of a boundary is mathematically zero. Depending of its properties it can be Depending of its properties it can be adiabatic adiabatic boundaryboundary: not allowing heat exchange; : not allowing heat exchange; rigid rigid boundaryboundary: not allowing exchange of work.: not allowing exchange of work.

A system can be very simple as a cylinder-A system can be very simple as a cylinder-piston, or as complex as portions of an oil piston, or as complex as portions of an oil refinery.refinery.

SurroundingSurrounding or or EnvironmentEnvironment: All physical space : All physical space which lies outside the boundary.which lies outside the boundary.

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on Systems and Control VolumesSystems and Control Volumes

A A Closed System Closed System or or Control-massControl-mass consists of a fixed consists of a fixed amount of mass, its analysis involves no mass amount of mass, its analysis involves no mass transfer across the boundaries (transfer across the boundaries (mass cannot enter or mass cannot enter or leaveleave). However, energy transfer, in the form of heat ). However, energy transfer, in the form of heat and work is allowed, as well as a change in chemical and work is allowed, as well as a change in chemical composition within the system. A special type of composition within the system. A special type of closed system that does not interact in any way with closed system that does not interact in any way with its surroundings is called a its surroundings is called a isolated systemisolated system. A . A common example is the piston-cylinder device.common example is the piston-cylinder device.

A A Control Volume Control Volume or or Open System Open System is a properly is a properly selected region in space where mass and energy may selected region in space where mass and energy may cross the boundary. It usually encloses a devices that cross the boundary. It usually encloses a devices that involves mass flow such as a compressor, turbine, involves mass flow such as a compressor, turbine, mixing chamber or nozzle.mixing chamber or nozzle.

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on Systems and Control VolumesSystems and Control Volumes

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CLOSEDCLOSEDSYSTEMSYSTEMm=constantm=constant

MASS -> NOMASS -> NO

ENERGY -> YESENERGY -> YES

System System BoundaryBoundary

ThermodynamicThermodynamicSurroundingSurrounding

MovingMovingBoundaryBoundary

FixedFixedBoundaryBoundary

CONTROLCONTROLVOLUMEVOLUME

ImaginaryImaginaryBoundaryBoundary

RealRealBoundaryBoundary

CONTROLCONTROLVOLUMEVOLUME

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on ExampleExample

Closed SystemClosed System

The air/fuel mixture in a The air/fuel mixture in a piston of an Internal piston of an Internal Combustion (IC) engine Combustion (IC) engine is considered the control is considered the control mass. The system mass. The system boundary or control boundary or control surface is placed around surface is placed around the gas mixture.the gas mixture.

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on ExampleExample

Open SystemOpen System

An IC engine can be analyzed as an open system. In An IC engine can be analyzed as an open system. In this case, air, fuel, and exhaust streams flow this case, air, fuel, and exhaust streams flow through the control volume. Heat (in the exhaust through the control volume. Heat (in the exhaust stream) and work also cross the control surface.stream) and work also cross the control surface.

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on Properties of a SystemProperties of a System

Any characteristic that describe a system is called a Any characteristic that describe a system is called a propertyproperty. A . A propertyproperty is a macroscopic characteristic of is a macroscopic characteristic of a system such as mass, volume, energy, pressure and a system such as mass, volume, energy, pressure and temperature. The properties can be:temperature. The properties can be:

directly measureddirectly measured defined by laws of thermodynamics, anddefined by laws of thermodynamics, and defined by mathematical combinations of other defined by mathematical combinations of other

properties.properties. The properties can be either The properties can be either intensiveintensive or or extensiveextensive. A . A

property is called property is called extensiveextensive if its value for an overall if its value for an overall system is the sum of its values for the parts into system is the sum of its values for the parts into which the system is divided (which the system is divided (mass, volume, energy, mass, volume, energy, etcetc). The ). The extensiveextensive properties depend on the size or properties depend on the size or extent of the system and can change with time. extent of the system and can change with time.

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on Properties of a SystemProperties of a System

IntensiveIntensive properties are not additive in the sense properties are not additive in the sense previously considered. They are those that are previously considered. They are those that are independent of the size or extent of a system, and independent of the size or extent of a system, and may vary from place to place within the system at may vary from place to place within the system at any time (any time (temperature, pressure and densitytemperature, pressure and density)). When . When an extensive property is divided by mass, the an extensive property is divided by mass, the resultant is called resultant is called specific propertyspecific property. It becomes an . It becomes an intensive propertyintensive property..

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P

T

V

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P

T

V

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ExtensiveExtensivepropertiesproperties

IntensiveIntensivepropertiesproperties

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on Properties of a SystemProperties of a System

Consider a block of material of mass (m), volume Consider a block of material of mass (m), volume (V) and uniform temperature (T). If we cut it up (V) and uniform temperature (T). If we cut it up into pieces, the total mass of the system and into pieces, the total mass of the system and total volume are the sum of the pieces, but the total volume are the sum of the pieces, but the temperature is not the sum of the temperatures temperature is not the sum of the temperatures of the pieces, nor is the density the sum of the of the pieces, nor is the density the sum of the densities, i.e.densities, i.e.

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on Properties of a SystemProperties of a System

ContinuumContinuum: Matter is made up of atoms that are : Matter is made up of atoms that are widely spaced in the gas phase. Yet it is very widely spaced in the gas phase. Yet it is very convenient to disregard the atomic nature of a convenient to disregard the atomic nature of a substance and view it substance and view it as a continuous, as a continuous, homogeneous matter with no holeshomogeneous matter with no holes, that is, a , that is, a continuum. The continuum idealization allows us continuum. The continuum idealization allows us to treat properties as point functions and to to treat properties as point functions and to assume the properties vary continually in space assume the properties vary continually in space with no jump discontinuities. with no jump discontinuities. The continuum The continuum idealization is implicit in many statements idealization is implicit in many statements we we make, such as “the density of water in a glass is make, such as “the density of water in a glass is the same at any point.”the same at any point.”

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on Density and Specific GravityDensity and Specific Gravity

DensityDensity is defined as mass per unit volume. is defined as mass per unit volume.

The density of a quantity of matter is defined as:The density of a quantity of matter is defined as:

V’ is the smallest volume containing enough V’ is the smallest volume containing enough particles such that statistical averages are particles such that statistical averages are significant. It is also the smallest volume that we significant. It is also the smallest volume that we can consider the region a “point” and still can consider the region a “point” and still maintain the continuum hypothesis.maintain the continuum hypothesis.

Density can vary from point to point within the Density can vary from point to point within the system.system.

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on Density and Specific GravityDensity and Specific Gravity

The reciprocal of density is the The reciprocal of density is the specific volume specific volume v, v, which is defined as volume per unit mass. That which is defined as volume per unit mass. That is,is,

Sometimes the density of a substance is given Sometimes the density of a substance is given relative to the density of a well-known relative to the density of a well-known substance. Then it is called substance. Then it is called specific gravityspecific gravity, or , or relative densityrelative density, and is defined as , and is defined as the ratio of the the ratio of the density of a substance to the density of some density of a substance to the density of some standard substance at a specified temperaturestandard substance at a specified temperature (usually water at 4°C, (usually water at 4°C, for which for which ρρHH22OO =1000 =1000 kg/mkg/m33). That is,). That is,

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on Density and Specific GravityDensity and Specific Gravity

The weight of a unit volume of a substance is The weight of a unit volume of a substance is called called specific weight specific weight and is expressed asand is expressed as

Where g is the gravity accelerationWhere g is the gravity acceleration

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on State, Equilibrium, Processes and CycleState, Equilibrium, Processes and Cycle

StateState is defined as the description of the condition of is defined as the description of the condition of a system at a given instant. The properties are a system at a given instant. The properties are defined only when a system is in defined only when a system is in equilibriumequilibrium (this (this imply a state of balance). Any transformation of a imply a state of balance). Any transformation of a system from one equilibrium state to another is system from one equilibrium state to another is called a called a processprocess. The . The pathpath of a process is the series of of a process is the series of states through which the system passes. A process is states through which the system passes. A process is described by its initial and final states, the followed described by its initial and final states, the followed path and the interaction with its surrounding.path and the interaction with its surrounding.

When a system is infinitesimally close to equilibrium When a system is infinitesimally close to equilibrium at all times during a process, the process is calledat all times during a process, the process is called quasistatic.quasistatic.

CycleCycle is a sequence of processes that begin and is a sequence of processes that begin and end at the same state.end at the same state.

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on State, Equilibrium, Processes and CycleState, Equilibrium, Processes and Cycle

Gas is compressed from Gas is compressed from state 2 to state 1 or state 2 to state 1 or expanded from state 1 to expanded from state 1 to state 2. The process occurs state 2. The process occurs from 1 to 2 or 2 to 1.from 1 to 2 or 2 to 1.

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on State, Equilibrium, Processes and CycleState, Equilibrium, Processes and Cycle

A simple cycle for power A simple cycle for power generation. Water flows generation. Water flows through the pump, is through the pump, is heated in a boiler, steam heated in a boiler, steam expands through a expands through a turbine, and then the turbine, and then the condensed water flows condensed water flows through the 1 pump through the 1 pump again.again.

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on State, Equilibrium, Processes and CycleState, Equilibrium, Processes and Cycle

The Steady-Flow ProcessThe Steady-Flow Process: The terms : The terms steadysteady and and uniformuniform are used frequently in engineering are used frequently in engineering. The . The term term steadysteady implies no change with time. The implies no change with time. The opposite of steady is opposite of steady is unsteadyunsteady, or , or transienttransient. The . The term term uniformuniform, however, implies no change with , however, implies no change with location over location over a specified region.a specified region.

A large number of engineering devices operate A large number of engineering devices operate for for long periods long periods of time under the same of time under the same conditions, and they are classified as conditions, and they are classified as steady-flow steady-flow devicesdevices. . Processes involving such devices can be Processes involving such devices can be represented reasonably well by a somewhat represented reasonably well by a somewhat idealized process, called the idealized process, called the steady-flow processsteady-flow process, , which can be defined as a which can be defined as a process during which process during which a fluid flows through a control volume steadily.a fluid flows through a control volume steadily.

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on Temperature and Zeroth Law of ThermodynamicsTemperature and Zeroth Law of Thermodynamics

What is temperature?What is temperature? A definition of temperature in terms of concepts A definition of temperature in terms of concepts

that are independently defined or accepted is that are independently defined or accepted is difficult to give, despite the fact that we are difficult to give, despite the fact that we are aware of it through our senses.aware of it through our senses.

Temperature is a perception that is associated Temperature is a perception that is associated with the notions of “hotness” and “coldness”with the notions of “hotness” and “coldness”

It is easier to obtain an objective understanding It is easier to obtain an objective understanding through the equality of temperature, by using through the equality of temperature, by using the fact that when the temperature of an object the fact that when the temperature of an object changes other properties also changechanges other properties also change

Temperature is an intensive property.Temperature is an intensive property.

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on Temperature and Zeroth Law of ThermodynamicsTemperature and Zeroth Law of Thermodynamics

If we had two blocks of copper each at a If we had two blocks of copper each at a different different temperature temperature and each in contact with a mercury and each in contact with a mercury thermometer, which are suddenly thermometer, which are suddenly brought into brought into contact,contact, several things will happen:several things will happen:As the warm block cools, its electrical resistance As the warm block cools, its electrical resistance and volume, measurably decrease, and the mercury and volume, measurably decrease, and the mercury level dropslevel dropsAs the cooler block warms, its electrical resistance As the cooler block warms, its electrical resistance and volume, measurably increase, and the mercury and volume, measurably increase, and the mercury level increaseslevel increasesEventually the two blocks come into thermal Eventually the two blocks come into thermal equilibrium and the changes in properties cease equilibrium and the changes in properties cease and the two thermometers read the same leveland the two thermometers read the same level

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on Temperature and Zeroth Law of ThermodynamicsTemperature and Zeroth Law of Thermodynamics

Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics States that when two bodies have equality of States that when two bodies have equality of

temperature with a third body, they in turn have temperature with a third body, they in turn have equality of temperature with each other.equality of temperature with each other.

Why is it the Why is it the Zeroth Law?Zeroth Law? While this principle seems obvious, it is not While this principle seems obvious, it is not

derivable from other laws, and because it derivable from other laws, and because it precedes the First and Second laws of precedes the First and Second laws of thermodynamics in the logical presentation of thermodynamics in the logical presentation of fundamentals, it has come to be known as the fundamentals, it has come to be known as the Zeroth Law!Zeroth Law!

This is the This is the basis for measurement of basis for measurement of temperature.temperature.

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on Temperature and Zeroth Law of ThermodynamicsTemperature and Zeroth Law of Thermodynamics

Temperature ScalesTemperature Scales 4 - Temperature Scales4 - Temperature Scales Celsius Scale (Celsius Scale (ooC)C)

Ice point HIce point H220 = 00 = 0ooCC

Boiling point HBoiling point H220 = 1000 = 100ooCC

Fahrenheit Scale (Fahrenheit Scale (ooF)F)

Ice point HIce point H220 = 32 0 = 32 ooFF

Body temperature = 98.6Body temperature = 98.6ooFF

Boiling point HBoiling point H220 = 2120 = 212ooFF

Kelvin (K) - AbsoluteKelvin (K) - Absolute

T(K) = T(T(K) = T(ooC) + 273.15C) + 273.15 Rankine (R) - AbsoluteRankine (R) - Absolute

T(R) = T(T(R) = T(ooF) + 459.67F) + 459.67

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on PressurePressure

What is pressure?What is pressure? PressurePressure is the normal or compressive force per is the normal or compressive force per

unit area exerted by a fluid at a point.unit area exerted by a fluid at a point. Consider a small infinitesimal area A in medium Consider a small infinitesimal area A in medium

of fluid at rest. At some point on this surface, a of fluid at rest. At some point on this surface, a normal force is exerted by the fluid on the top normal force is exerted by the fluid on the top and bottom of this area. The pressure is defined and bottom of this area. The pressure is defined in the limit as this area becomes smaller, until it in the limit as this area becomes smaller, until it is the smallest area that can be considered is the smallest area that can be considered measureable:measureable:

Pressure is an intensive property.Pressure is an intensive property.

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on PressurePressure

For a For a fluid at restfluid at rest, pressure is the same in all , pressure is the same in all directions directions at this point. But can vary from point at this point. But can vary from point to point, e.g. hydrostatic pressure.to point, e.g. hydrostatic pressure.

For a For a fluid in motion fluid in motion additional forces arise due additional forces arise due to shearing action and we refer to the normal to shearing action and we refer to the normal force as a normal stress. The state of stresses in force as a normal stress. The state of stresses in a fluid in motion is dealt with further in a fluid in motion is dealt with further in Fluid Fluid Mechanics.Mechanics.

In the context of In the context of thermodynamicsthermodynamics, we think of , we think of pressure as pressure as absolute, with respect to pressure of absolute, with respect to pressure of a complete a complete vacuum (space) which is zero.vacuum (space) which is zero.

In In Fluid Mechanics Fluid Mechanics we often use gage pressure we often use gage pressure and vacuum pressure.and vacuum pressure.

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on PressurePressure

Absolute PressureAbsolute PressureForce per unit area exerted Force per unit area exerted by a fluidby a fluid

Gage PressureGage PressurePressure abovePressure above

atmosphericatmospheric

PPgaggag=P=Pabsabs - P - Patmatm

Vacuum PressureVacuum PressurePressure below atmosphericPressure below atmospheric

PPvacvac=P=Patmatm - P - Pabsabs

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on PressurePressure

Common Pressure Units are:Common Pressure Units are:

Pa (Pascal), mmHg (mm of Mercury), atm Pa (Pascal), mmHg (mm of Mercury), atm (atmosphere), psi (lbf per square inch)(atmosphere), psi (lbf per square inch)

1 Pa = 1 N/m1 Pa = 1 N/m22 (S.I. Unit)(S.I. Unit) 1 kPa =101 kPa =1033 PaPa 1 bar = 101 bar = 1055 Pa (note the bar is not an SI unit)Pa (note the bar is not an SI unit) 1 MPa = 101 MPa = 1066 PaPa

1 atm = 760 mmHg = 101,325 Pa = 14.696 psi1 atm = 760 mmHg = 101,325 Pa = 14.696 psi

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on Variation of Pressure with DepthVariation of Pressure with Depth

The pressure of a fluid at rest increases with The pressure of a fluid at rest increases with depth (as a result of added weight).depth (as a result of added weight).

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on Variation of Pressure with DepthVariation of Pressure with Depth

To obtain a relation for the To obtain a relation for the variation of pressure with variation of pressure with depth, consider a rectangular depth, consider a rectangular fluid element of height fluid element of height ΔΔz, z, length length ΔΔx, and unit depth x, and unit depth (into the page) in equilibrium. (into the page) in equilibrium. Assuming the density of the Assuming the density of the fluid ρ to be constant, a force fluid ρ to be constant, a force balance in the vertical z-balance in the vertical z-direction givesdirection gives

Where W=mg= ρgWhere W=mg= ρgΔΔxxΔΔz is the z is the weight of the fluid element weight of the fluid element

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on Variation of Pressure with DepthVariation of Pressure with Depth

If we take point 1 to be at the If we take point 1 to be at the free surface of a liquid open to free surface of a liquid open to the atmosphere, where the the atmosphere, where the pressure is the atmospheric pressure is the atmospheric pressure Ppressure Patmatm, then the pressure , then the pressure at a depth at a depth hh from the free from the free surface becomessurface becomes

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on Variation of Pressure with DepthVariation of Pressure with Depth

A consequence of the pressure A consequence of the pressure in a fluid remaining constant in in a fluid remaining constant in the horizontal direction is that the horizontal direction is that the pressure applied to a the pressure applied to a confined fluid increases the confined fluid increases the pressure throughout by the pressure throughout by the same amountsame amount. This is called . This is called Pascal’s lawPascal’s law, after Blaise Pascal , after Blaise Pascal (1623–1662).(1623–1662).

The area ratio The area ratio AA22//AA11 is called the is called the ideal mechanical advantage ideal mechanical advantage of of the hydraulic lift.the hydraulic lift.

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on The manometerThe manometer

The elevation change of The elevation change of ΔΔz in a fluid at rest corresponds to z in a fluid at rest corresponds to ΔΔP/P/ρρg, which suggests that a fluid column can be used to g, which suggests that a fluid column can be used to measure pressure differences. A device based on this measure pressure differences. A device based on this principle is called a principle is called a manometermanometer, and it is commonly used to , and it is commonly used to measure small and moderate pressure differences. A measure small and moderate pressure differences. A manometer mainly consists of a glass or plastic U-tube manometer mainly consists of a glass or plastic U-tube containing one or more fluids such as mercury, water, containing one or more fluids such as mercury, water, alcohol, or oil.alcohol, or oil.

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on The manometerThe manometer

Many engineering problems and some manometers involve Many engineering problems and some manometers involve multiple immiscible fluids of different densities stacked on multiple immiscible fluids of different densities stacked on top of each other. Such systems can be analyzed easily by top of each other. Such systems can be analyzed easily by remembering that:remembering that:

1.1. The pressure change across a fluid column of height h The pressure change across a fluid column of height h is is ΔΔP=P=ρρghgh

2.2. Pressure increases downward in a given fluid and Pressure increases downward in a given fluid and decreases upward (i.e., Pdecreases upward (i.e., Pbottombottom>P>Ptoptop), and ), and

3.3. Two points at the same elevation in a continuous fluid Two points at the same elevation in a continuous fluid at rest are at the same pressure.at rest are at the same pressure.

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on The manometerThe manometer

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Due Date:

Omar E. Meza Castillo Ph.D.

Homework1 Homework1 Web Page Web Page

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