Engineering Problem Solving as Model Building

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Engineering Problem Solving as Model Building Part 1. How professors think about problem solving. Part 2. Mech2 and Brain-Full Crisis Part 1 How experts think about problem solving

2 When we solve a problem using theory, we are (whether we realize it or not) constructing a model of the problem. Why model? A physical model boat is different from the real boat, but by pushing or pulling on the model, we can get information about the real boat (your foam boats taught you about stability and drag). A theoretical model is similar in that once it is constructed, we can use it to answer many questions. Construction of the model means selecting a consistent set of sub-models, assumptions and conservation principles.

3 Possible model structure for many thermodynamics problems Problem Statement (specify known, unknown desired quantities, and possibly some assumptions to fill gaps) Control mass or control volume drawing, boundaries usually chosen where things are known or desired Mass, Energy Conservation Entropy Balance State Change, E 2 -E 1 =, S 2 - S 1 = Process: Rev., Irrev., adiabatic, PV n =constant.. Other Physics Mechanics, heat transfer theory,. State diagram (P-V, T-S ) (optional but usually VERY helpful) Property Model Ideal gas, incompressible liquid, real gas, 2-phase Thermodynamic Relations H=U+PV, du=tds-pdv, Cp=.(puts variables in more convenient forms)

4 This is not a set of directions! Arrows show that boxes are connected and consistent, not steps in problem solving. Together, modules (the boxes) make a complete model. From the model we get mathematical relations between the variables. The solution order depends on what we seek. A simple example Steel Mass M A mass M of steel is heated from T 1 to T 2, there is heat transfer to the steel, and work W by the steel. Variants of the problem: 1. M, T 1, T 2 given, find, W 2., M, T 1 given, find T 2 3., T 1, T 2 given, find M 4. M, T 1, T 2 given find S 2 -S 1

5 Control mass there is no flow, and it is sensible to take the same system (the steel) for all problem variants W Steel Mass M Mass conservation is trivial (M=constant) Energy conservation is E 2 -E 1 =-W Entropy Balance is ds=δ/t +ds gen Assumptions Steel Mass M No information on elevation change or velocity, so neglect them. No information on the steel, so based on past problems, we might assume that it behaves like an incompressible and constant volume solid, with property information in textbook. Keep open to the possibility that later these assumptions are inconsistent with the other parts of the problem model, and therefore inappropriate.

6 Property Model Steel Mass M Simple compressible substance (only boundary work is possible, and it is zero in this case) v=constant even if T, P change so (C p =C v =C) u=u(t) s=s(t) Because these properties are independent of pressure, we may not need to worry about lack of information on P Process Information Steel Mass M Constant volume, so W=0 No information to suggest is zero, so it must be retained in 1 st Law May or may not be reversible, so unclear if we can relate to entropy

7 Other Physics Steel Mass M In some problems, we might need to relate applied forces to pressures in the system, solving equations of statics or dynamics. In some problems, heat transfer might be related to temperatures thought heat transfer theory. In this particular example, we need not worry about any such constraints because our system is a static, incompressible lump. Thermodynamic Relations Steel Mass M Text provides C (kj/kg/k), and the problem statement may involve temperature. The first law involves energy, so we need to relate, u, C, T: C=du/dT (for our case with the solid) du=tds-pdv or ds= du/t=cdt/t

8 The complete model Steel Mass M U 2 -U 1 =-W but W=0 and U related to T MC(T 2 -T 1 )= for problems #1, 2, 3, use trivial algebra. for problem #4, we also need to integrate ds=cdt/t State diagrams It has NOT been necessary to assume reversibility in this problem, so we DON T know for sure the path from 1 2. Steel Mass M The diagrams reinforce important parts of the model related to our property model and the path. T 2 T T T 1 v S

9 Problem A mass M of steel is heated from T1 to T2, there is heat transfer to the steel, and work W by the steel. M, T1, T2 given, find, W Control mass drawing Steel W Mass M Mass, Energy Conservation E 2 -E 1 =-W Entropy Balance ds δ/t State Change, E 2 -E 1 =U 2 -U 1 =MC(T 2 - T 1 ) S 2 -S 1 =MC ln (T 2 /T 1 ) Process: Constant V so W=0 Other Physics Seems KE, PE not relevant State diagram (P-V, T-S ) (optional but usually VERY helpful) Property Model V const; u(t), s(t) Thermodynamic Relations du=tds-pdv, du=cdt (const. V) Experts vs Novices Experts tend to have a good framework or structure for their models, and are practiced in the art of assembling the model building blocks. Novices tend to focus on the final model, because it provides a fast way to compute answers.

10 Part 2. Why Mech 2 Brings you to the Point of Crisis Should you construct or memorize models? Construction Requires skills in math and very firm foundations Only memorize the building blocks Essential for new problems Not the fastest way to solve old problems Memorization Does not depend on foundations. Many, many models to memorize. Useless for new problems. Fastest way to solve old problems

11 Thermo Lectures 1-3 PVT Properties 3 Model Building Blocks 3 Complete Models Ideal gas Ideal gas Incompressible liquids and solids Incompressible liquids and solids Steam Tables Steam Tables Thermo Lectures 1-9 PVT, Energy and First Law 3 Major Model Components, Perhaps 9 Sub-models 3x2x4=24 Complete Models Ideal gas liquids and solids Steam Tables For example, just using First Law in Integrated form, 12 models: Const V Const V Const V E 2 -E 1 =-W Const V Const V Const V or rate form Cylinder Cylinder Cylinder Const V Cylinder Cylinder Cylinder Cylinder Insulated vs isothermal

12 Add springs 1 more variation in model building blocks Each piston problem could now be with or without springs (insulated or not) Now 3x2x6=36 complete models Add possibility of piston kinetic energy 1 more variation in model building blocks Piston problems now insulated (or not), with spring (or not), with KE (or not) = 8 piston variants Total complete models =3x2x(2+8)=60

13 Add all the rest Control volume analysis 2 nd Law Machinery with many parts.. Steady vs transient problems Textbook has over 1000 problems! Fluids + Thermo + Math? In the first few years of mech 2, we set exam problems combining all 3 subjects. How many complete models to memorize? How do think students liked this?

14 Things to remember Over the weeks # complete models Your brain capacity # model building blocks time Things to remember Over the weeks Best test scores by memorizing examples # complete models Need to construct models Your brain capacity # model building blocks time

15 Things to remember Over the weeks Brain Full Crisis # complete models Your brain capacity Mech 2 First Year UBC # model building blocks High-school time Have you reached Brain-Full Crisis (BFC)?

16 We ve given you mixed messages Stressed importance of derivations, understanding Assigned model building MATLAB and physical labs Given quiz problems not exactly like past examples Given time-limited computational tests Assigned relatively few marks to complex, longer model building assignments The time to start practicing model construction is today. In studying for the finals Review and list the basic building blocks. Focus on how building blocks have been glued together in past problems. DO NOT spend time on new examples, except to test your model building. Remember that this is a long-term investment.

17 Discussion What sort of exercises would promote ability to construct models rather than just use them? What sort of testing would discourage memorization of problem solutions (this could influence how the final exams are set). Do you already have experience with constructing models from scratch, but in another part of your life? From the discussion after the lecture Should consider unlimited-time exams to remove the incentive to memorize whole problems (this will take some work, but should be possible for some, if not all, exams). Exam marking schemes should clearly indicate (where appropriate) that most of the marks come from problem setup (ok we will check final exams for this) Vista problem sets might be set up to emphasize construction of models from building blocks (not sure how to do this, but it is worth considering)

18 Extra slides not covered in class (but probably worth a quick read) Another example: A diesel pump with friction might be thought of as an ideal, frictionless pump in series with a flow resistance (a throttling process). At the inlet to the pump (1), the mass flow is 0.2 kg/s, the temperature T 1 =25 C, and the pressure is P 1 =120 kpa. At the outlet (3), P 3 =50,000 kpa and T 3 =25.6 C All parts of the pump, piping and flow resistance are well insulated. The fluid is diesel with density ρ=820 kg/m 3 and heat capacity 2.0 kj/kg/k. Find the shaft work from the pump. Indicate your choice of control volumes carefully and explain any further assumptions needed. TRY THIS: TAKE THIS PROBLEM AND COMPLETE THE MODEL TEMPLATE ON THE NEXT PAGE. Ideal pump Flow resistance Shaft work

19 Problem Control volume Ideal pump 1 Shaft work Flow resistance 2 3 Mass, Energy Conservation Other Physics Entropy Balance State Change Process: State diagram Property Model Thermodynamic Relations Alternative connections between ideas Course concept road map showing the order topics covered (based how theory is developed) Components of the problem solving process given in text (and earlier notes) Thinking of problem solving as construction of a model rather than applying a problem template.

20 Mech222 Notes Text/Notes Cengel &Boles Equilibrium state, PVT exist Conservation of Energy de=δ-δw Property Models (Ch. 3) Ideal gas, tables Given a few properties, calculate others (Ch. 3) 1 st Law control mass problems Ch. 4 RTT CV analysis Zeroth Law Existence of E de=δ-δw ds univ max at equilibrium U T S V equality of temperature 1 st Law CV problems Ch.5 T res. E W δ ds T Simple heat engine/pump Problems Ch. 6 η=1-t L /T H T res. E W η=1-t L /T H 1 st +2 nd Law problems Ch. 7 δ 0 T δ ds T The road map Explains how ideas depend on previous material. Compares approaches of text vs. notes Is unrelated to how we normally solve problems.

21 Problem Solving Method (CB 1-12) 1. Physical layout of the problem? Make a sketch!. 2. What control mass do you choose? Show on sketch! 3. Initial state? 4. Final state? 5. Process: is any property fixed or otherwise specified? 6. What thermodynamic properties are convenient? Use these for a state diagram 7. What model do you use for the material of interest? 8. What laws are needed (mass, 1 st Law, 2 nd Law )? 9. Solution method needed? Do you need to iterate.? Textbook problem solving steps comforting step-by-step process Identifies some of the key concept blocks : process, states, property models. We don t always solve problems in exactly the order stated, even if we do hit all of the concept blocks.

The First Law of Thermodynamics: Closed Systems. Heat Transfer

The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

Dynamic Process Modeling. Process Dynamics and Control

Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits

(b) 1. Look up c p for air in Table A.6. c p = 1004 J/kg K 2. Use equation (1) and given and looked up values to find s 2 s 1.

Problem 1 Given: Air cooled where: T 1 = 858K, P 1 = P = 4.5 MPa gage, T = 15 o C = 88K Find: (a) Show process on a T-s diagram (b) Calculate change in specific entropy if air is an ideal gas (c) Evaluate

Sheet 5:Chapter 5 5 1C Name four physical quantities that are conserved and two quantities that are not conserved during a process.

Thermo 1 (MEP 261) Thermodynamics An Engineering Approach Yunus A. Cengel & Michael A. Boles 7 th Edition, McGraw-Hill Companies, ISBN-978-0-07-352932-5, 2008 Sheet 5:Chapter 5 5 1C Name four physical

Chapter 6 Energy Equation for a Control Volume

Chapter 6 Energy Equation for a Control Volume Conservation of Mass and the Control Volume Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries,

Mass and Energy Analysis of Control Volumes

MAE 320-Chapter 5 Mass and Energy Analysis of Control Volumes Objectives Develop the conservation of mass principle. Apply the conservation of mass principle to various systems including steady- and unsteady-flow

Lesson 5 Review of fundamental principles Thermodynamics : Part II

Lesson 5 Review of fundamental principles Thermodynamics : Part II Version ME, IIT Kharagpur .The specific objectives are to:. State principles of evaluating thermodynamic properties of pure substances

APPLIED THERMODYNAMICS TUTORIAL 1 REVISION OF ISENTROPIC EFFICIENCY ADVANCED STEAM CYCLES

APPLIED THERMODYNAMICS TUTORIAL 1 REVISION OF ISENTROPIC EFFICIENCY ADVANCED STEAM CYCLES INTRODUCTION This tutorial is designed for students wishing to extend their knowledge of thermodynamics to a more

THERMODYNAMICS NOTES - BOOK 2 OF 2

THERMODYNAMICS & FLUIDS (Thermodynamics level 1\Thermo & Fluids Module -Thermo Book 2-Contents-December 07.doc) UFMEQU-20-1 THERMODYNAMICS NOTES - BOOK 2 OF 2 Students must read through these notes and

SOLUTION MANUAL SI UNIT PROBLEMS CHAPTER 9 SONNTAG BORGNAKKE VAN WYLEN. FUNDAMENTALS of. Thermodynamics. Sixth Edition

SOLUTION MANUAL SI UNIT PROBLEMS CHAPTER 9 SONNTAG BORGNAKKE VAN WYLEN FUNDAMENTALS of Thermodynamics Sixth Edition CONTENT SUBSECTION PROB NO. Correspondence table Concept-Study Guide Problems -20 Steady

CO 2 41.2 MPa (abs) 20 C

comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle

The First Law of Thermodynamics

The First Law of Thermodynamics (FL) The First Law of Thermodynamics Explain and manipulate the first law Write the integral and differential forms of the first law Describe the physical meaning of each

Diesel Cycle Analysis

Engineering Software P.O. Box 1180, Germantown, MD 20875 Phone: (301) 540-3605 FAX: (301) 540-3605 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Diesel Cycle Analysis Diesel Cycle

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Thermodynamics study and application of thermal energy temperature quantity

ME 201 Thermodynamics

ME 0 Thermodynamics Second Law Practice Problems. Ideally, which fluid can do more work: air at 600 psia and 600 F or steam at 600 psia and 600 F The maximum work a substance can do is given by its availablity.

Basic Concepts of Thermodynamics

Basic Concepts of Thermodynamics Every science has its own unique vocabulary associated with it. recise definition of basic concepts forms a sound foundation for development of a science and prevents possible

20 m neon m propane 20

Problems with solutions:. A -m 3 tank is filled with a gas at room temperature 0 C and pressure 00 Kpa. How much mass is there if the gas is a) Air b) Neon, or c) Propane? Given: T73K; P00KPa; M air 9;

Compressor Efficiency Definitions

Compressor Efficiency Definitions K. Ueno, PhD, and R. E. Bye, VAIREX Corporation K. S. Hunter, PhD, University of Colorado May 12th, 2003 Many standard efficiency definitions exist that qualify the mass

Chapter 10 Temperature and Heat

Chapter 10 Temperature and Heat What are temperature and heat? Are they the same? What causes heat? What Is Temperature? How do we measure temperature? What are we actually measuring? Temperature and Its

Chapter 7 Energy and Energy Balances

CBE14, Levicky Chapter 7 Energy and Energy Balances The concept of energy conservation as expressed by an energy balance equation is central to chemical engineering calculations. Similar to mass balances

Chapter 6: Using Entropy

Chapter 6: Using Entropy Photo courtesy of U.S. Military Academy photo archives. Combining the 1 st and the nd Laws of Thermodynamics ENGINEERING CONTEXT Up to this point, our study of the second law has

The Second Law of Thermodynamics

The Second aw of Thermodynamics The second law of thermodynamics asserts that processes occur in a certain direction and that the energy has quality as well as quantity. The first law places no restriction

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

ES-7A Thermodynamics HW 1: 2-30, 32, 52, 75, 121, 125; 3-18, 24, 29, 88 Spring 2003 Page 1 of 6

Spring 2003 Page 1 of 6 2-30 Steam Tables Given: Property table for H 2 O Find: Complete the table. T ( C) P (kpa) h (kj/kg) x phase description a) 120.23 200 2046.03 0.7 saturated mixture b) 140 361.3

Lecture 36 (Walker 18.8,18.5-6,)

Lecture 36 (Walker 18.8,18.5-6,) Entropy 2 nd Law of Thermodynamics Dec. 11, 2009 Help Session: Today, 3:10-4:00, TH230 Review Session: Monday, 3:10-4:00, TH230 Solutions to practice Lecture 36 final on

Esystem = 0 = Ein Eout

AGENDA: I. Introduction to Thermodynamics II. First Law Efficiency III. Second Law Efficiency IV. Property Diagrams and Power Cycles V. Additional Material, Terms, and Variables VI. Practice Problems I.

Problem Set 1 3.20 MIT Professor Gerbrand Ceder Fall 2003

LEVEL 1 PROBLEMS Problem Set 1 3.0 MIT Professor Gerbrand Ceder Fall 003 Problem 1.1 The internal energy per kg for a certain gas is given by U = 0. 17 T + C where U is in kj/kg, T is in Kelvin, and C

Fundamentals of THERMAL-FLUID SCIENCES

Fundamentals of THERMAL-FLUID SCIENCES THIRD EDITION YUNUS A. CENGEL ROBERT H. TURNER Department of Mechanical JOHN M. CIMBALA Me Graw Hill Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 Web Site:

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Brayton Cycle (Gas Turbine) for Propulsion Application

THE SECOND LAW OF THERMODYNAMICS

1 THE SECOND LAW OF THERMODYNAMICS The FIRST LAW is a statement of the fact that ENERGY (a useful concept) is conserved. It says nothing about the WAY, or even WHETHER one form of energy can be converted

ESO201A: Thermodynamics

ESO201A: Thermodynamics Instructor: Sameer Khandekar First Semester: 2015 2016 Lecture #1: Course File Introduction to Thermodynamics, Importance, Definitions Continuum, System: closed, open and isolated,

The First Law of Thermodynamics

Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat Pumps The Carnot

Entropy and The Second Law of Thermodynamics

The Second Law of Thermodynamics (SL) Entropy and The Second Law of Thermodynamics Explain and manipulate the second law State and illustrate by example the second law of thermodynamics Write both the

THERMODYNAMIC PROPERTIES AND CALCULATION. Academic Resource Center

THERMODYNAMIC PROPERTIES AND CALCULATION Academic Resource Center THERMODYNAMIC PROPERTIES A quantity which is either an attribute of an entire system or is a function of position which is continuous and

Entropy. Objectives. MAE 320 - Chapter 7. Definition of Entropy. Definition of Entropy. Definition of Entropy. Definition of Entropy + Δ

MAE 320 - Chapter 7 Entropy Objectives Defe a new property called entropy to quantify the second-law effects. Establish the crease of entropy prciple. Calculate the entropy changes that take place durg

Second Law of Thermodynamics Alternative Statements

Second Law of Thermodynamics Alternative Statements There is no simple statement that captures all aspects of the second law. Several alternative formulations of the second law are found in the technical

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

WEEKLY SCHEDULE. GROUPS (mark X) SPECIAL ROOM FOR SESSION (Computer class room, audio-visual class room)

SESSION WEEK COURSE: THERMAL ENGINEERING DEGREE: Aerospace Engineering YEAR: 2nd TERM: 2nd The course has 29 sessions distributed in 14 weeks. The laboratory sessions are included in these sessions. The

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Ideal Gas Laws, Different Processes Let us continue

Exergy: the quality of energy N. Woudstra

Exergy: the quality of energy N. Woudstra Introduction Characteristic for our society is a massive consumption of goods and energy. Continuation of this way of life in the long term is only possible if

Statistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004

Statistical Mechanics, Kinetic Theory Ideal Gas 8.01t Nov 22, 2004 Statistical Mechanics and Thermodynamics Thermodynamics Old & Fundamental Understanding of Heat (I.e. Steam) Engines Part of Physics Einstein

Supplementary Notes on Entropy and the Second Law of Thermodynamics

ME 4- hermodynamics I Supplementary Notes on Entropy and the Second aw of hermodynamics Reversible Process A reversible process is one which, having taken place, can be reversed without leaving a change

Lesson. 11 Vapour Compression Refrigeration Systems: Performance Aspects And Cycle Modifications. Version 1 ME, IIT Kharagpur 1

Lesson Vapour Compression Refrigeration Systems: Performance Aspects And Cycle Modifications Version ME, IIT Kharagpur The objectives of this lecture are to discuss. Performance aspects of SSS cycle and

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS

Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright

Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long

= Q H Q C Q H Q C Q H Q C. ω = Q C W =

I.D The Second Law The historical development of thermodynamics follows the industrial olution in the 19 th century, and the advent of heat engines. It is interesting to see how such practical considerations

QUESTIONS THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS. Thermodynamic Properties

QUESTIONS THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS Thermodynamic Properties 1. If an object has a weight of 10 lbf on the moon, what would the same object weigh on Jupiter? ft ft -ft g

AC 2011-2088: ON THE WORK BY ELECTRICITY IN THE FIRST AND SECOND LAWS OF THERMODYNAMICS

AC 2011-2088: ON THE WORK BY ELECTRICITY IN THE FIRST AND SECOND LAWS OF THERMODYNAMICS Hyun W. Kim, Youngstown State University Hyun W. Kim, Ph.D., P.E. Hyun W. Kim is a professor of mechanical engineering

Textbook: Introduction to Fluid Mechanics by Philip J. Pritchard. John Wiley & Sons, 8th Edition, ISBN-13 9780470547557, -10 0470547553

Semester: Spring 2016 Course: MEC 393, Advanced Fluid Mechanics Instructor: Professor Juldeh Sesay, 226 Heavy Engineering Bldg., (631)632-8493 Email: Juldeh.sessay@stonybrook.edu Office hours: Mondays

Differential Balance Equations (DBE)

Differential Balance Equations (DBE) Differential Balance Equations Differential balances, although more complex to solve, can yield a tremendous wealth of information about ChE processes. General balance

The Second Law of Thermodynamics

Objectives MAE 320 - Chapter 6 The Second Law of Thermodynamics The content and the pictures are from the text book: Çengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw-Hill,

INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

Refrigeration and Air Conditioning Prof. M. Ramgopal Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Refrigeration and Air Conditioning Prof. M. Ramgopal Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No. # 18 Worked Out Examples - I Welcome back in this lecture.

a) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L

hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 Web Site:

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Carnot Cycle Analysis Carnot Cycle Analysis by Engineering

Entropy and the Second Law of Thermodynamics. The Adiabatic Expansion of Gases

Lecture 7 Entropy and the Second Law of Thermodynamics 15/08/07 The Adiabatic Expansion of Gases In an adiabatic process no heat is transferred, Q=0 = C P / C V is assumed to be constant during this process

Learning Module 4 - Thermal Fluid Analysis Note: LM4 is still in progress. This version contains only 3 tutorials.

Learning Module 4 - Thermal Fluid Analysis Note: LM4 is still in progress. This version contains only 3 tutorials. Attachment C1. SolidWorks-Specific FEM Tutorial 1... 2 Attachment C2. SolidWorks-Specific

Heat as Energy Transfer. Heat is energy transferred from one object to another because of a difference in temperature

Unit of heat: calorie (cal) Heat as Energy Transfer Heat is energy transferred from one object to another because of a difference in temperature 1 cal is the amount of heat necessary to raise the temperature

Technical Thermodynamics

Technical Thermodynamics Chapter 2: Basic ideas and some definitions Prof. Dr.-Ing. habil. Egon Hassel University of Rostock, Germany Faculty of Mechanical Engineering and Ship Building Institute of Technical

Laws of Thermodynamics

Laws of Thermodynamics Thermodynamics Thermodynamics is the study of the effects of work, heat, and energy on a system Thermodynamics is only concerned with macroscopic (large-scale) changes and observations

The Equipartition Theorem

The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics

An analysis of a thermal power plant working on a Rankine cycle: A theoretical investigation

An analysis of a thermal power plant working on a Rankine cycle: A theoretical investigation R K Kapooria Department of Mechanical Engineering, BRCM College of Engineering & Technology, Bahal (Haryana)

ENERGY TRANSFER SYSTEMS AND THEIR DYNAMIC ANALYSIS

ENERGY TRANSFER SYSTEMS AND THEIR DYNAMIC ANALYSIS Many mechanical energy systems are devoted to transfer of energy between two points: the source or prime mover (input) and the load (output). For chemical

Physics 200A FINALS Shankar 180mins December 13, 2005 Formulas and figures at the end. Do problems in 4 books as indicated

1 Physics 200A FINALS Shankar 180mins December 13, 2005 Formulas and figures at the end. Do problems in 4 books as indicated I. Book I A camper is trying to boil water. The 55 g aluminum pan has specific

Chapter 6 The first law and reversibility

Chapter 6 The first law and reversibility 6.1 The first law for processes in closed systems We have discussed the properties of equilibrium states and the relationship between the thermodynamic parameters

OUTCOME 2 INTERNAL COMBUSTION ENGINE PERFORMANCE. TUTORIAL No. 5 PERFORMANCE CHARACTERISTICS

UNIT 61: ENGINEERING THERMODYNAMICS Unit code: D/601/1410 QCF level: 5 Credit value: 15 OUTCOME 2 INTERNAL COMBUSTION ENGINE PERFORMANCE TUTORIAL No. 5 PERFORMANCE CHARACTERISTICS 2 Be able to evaluate

ENTROPY AND THE SECOND LAW OF THERMODYNAMICS

Chapter 20: ENTROPY AND THE SECOND LAW OF THERMODYNAMICS 1. In a reversible process the system: A. is always close to equilibrium states B. is close to equilibrium states only at the beginning and end

An introduction to thermodynamics applied to Organic Rankine Cycles

An introduction to thermodynamics applied to Organic Rankine Cycles By : Sylvain Quoilin PhD Student at the University of Liège November 2008 1 Definition of a few thermodynamic variables 1.1 Main thermodynamics

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension forces. 2 Objectives Have a working knowledge of the basic

Practice Problems on Conservation of Energy. heat loss of 50,000 kj/hr. house maintained at 22 C

COE_10 A passive solar house that is losing heat to the outdoors at an average rate of 50,000 kj/hr is maintained at 22 C at all times during a winter night for 10 hr. The house is to be heated by 50 glass

Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator

Lecture. Real eat Engines and refrigerators (Ch. ) Stirling heat engine Internal combustion engine (Otto cycle) Diesel engine Steam engine (Rankine cycle) Kitchen Refrigerator Carnot Cycle - is not very

Compressible Fluids. Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004

94 c 2004 Faith A. Morrison, all rights reserved. Compressible Fluids Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004 Chemical engineering

Answer, Key Homework 6 David McIntyre 1

Answer, Key Homework 6 David McIntyre 1 This print-out should have 0 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

1.4 Review. 1.5 Thermodynamic Properties. CEE 3310 Thermodynamic Properties, Aug. 26,

CEE 3310 Thermodynamic Properties, Aug. 26, 2011 11 1.4 Review A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container

= T T V V T = V. By using the relation given in the problem, we can write this as: ( P + T ( P/ T)V ) = T

hermodynamics: Examples for chapter 3. 1. Show that C / = 0 for a an ideal gas, b a van der Waals gas and c a gas following P = nr. Assume that the following result nb holds: U = P P Hint: In b and c,

APPLIED THERMODYNAMICS. TUTORIAL No.3 GAS TURBINE POWER CYCLES. Revise gas expansions in turbines. Study the Joule cycle with friction.

APPLIED HERMODYNAMICS UORIAL No. GAS URBINE POWER CYCLES In this tutorial you will do the following. Revise gas expansions in turbines. Revise the Joule cycle. Study the Joule cycle with friction. Extend

Esystem = 0 = Ein Eout

AGENDA: I. Introduction to Thermodynamics II. First Law Efficiency III. Second Law Efficiency IV. Property Diagrams and Power Cycles V. Additional Material, Terms, and Variables VI. Practice Problems I.

Macroscopic Balances for Nonisothermal Systems

Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

where V is the velocity of the system relative to the environment.

Exergy Exergy is the theoretical limit for the wor potential that can be obtaed from a source or a system at a given state when teractg with a reference (environment) at a constant condition. A system

Module 3. First law of thermodynamics

Module 3 First law of thermodynamics First Law of Thermodynamics Statement: When a closed system executes a complete cycle the sum of heat 1 B interactions is equal to the sum of work interactions. Y A

The final numerical answer given is correct but the math shown does not give that answer.

Note added to Homework set 7: The solution to Problem 16 has an error in it. The specific heat of water is listed as c 1 J/g K but should be c 4.186 J/g K The final numerical answer given is correct but

Entropy Changes & Processes

Entropy Changes & Processes Chapter 4 of Atkins: he Second Law: he Concepts Section 4.3, 7th edition; 3.3, 8th edition Entropy of Phase ransition at the ransition emperature Expansion of the Perfect Gas

UNIT 2 REFRIGERATION CYCLE

UNIT 2 REFRIGERATION CYCLE Refrigeration Cycle Structure 2. Introduction Objectives 2.2 Vapour Compression Cycle 2.2. Simple Vapour Compression Refrigeration Cycle 2.2.2 Theoretical Vapour Compression

REFRIGERATION (& HEAT PUMPS)

REFRIGERATION (& HEAT PUMPS) Refrigeration is the 'artificial' extraction of heat from a substance in order to lower its temperature to below that of its surroundings Primarily, heat is extracted from

THE CLAUSIUS INEQUALITY

Part IV Entropy In Part III, we introduced the second law of thermodynamics and applied it to cycles and cyclic devices. In this part, we apply the second law to processes. he first law of thermodynamics

LECTURE 28 to 29 ACCUMULATORS FREQUENTLY ASKED QUESTIONS

LECTURE 28 to 29 ACCUMULATORS FREQUENTLY ASKED QUESTIONS 1. Define an accumulator and explain its function A hydraulic accumulator is a device that stores the potential energy of an incompressible fluid

Lesson 42c: PV Diagrams

Lesson 42c: V Diagrams From the last section, you were probably wondering what happens when we do something like add heat to a sealed cylinder. This sounds like a pretty dangerous idea if you think back

PSS 17.1: The Bermuda Triangle

Assignment 6 Consider 6.0 g of helium at 40_C in the form of a cube 40 cm. on each side. Suppose 2000 J of energy are transferred to this gas. (i) Determine the final pressure if the process is at constant

Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

A Survey of Thermodynamics

A Survey of Thermodynamics Objective In this lab various topics relating to the study of thermodynamics will be explored. First, the flow of heat will be examined. Here an ice cube will be placed in a

VAPOUR-COMPRESSION REFRIGERATION SYSTEM

VAPOUR-COMPRESSION REFRIGERATION SYSTEM This case study demonstrates the modeling of a vapour compression refrigeration system using R22 as refrigerant. Both a steady-state and a transient simulation will

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

FLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1

COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT

Experiment 8 ~ Rotational and Translational Energies

Experiment 8 ~ Rotational and Translational Energies Purpose: The objective of this experiment is to examine the conversion of gravitational potential energy to different types of energy: translational,

Mohan Chandrasekharan #1

International Journal of Students Research in Technology & Management Exergy Analysis of Vapor Compression Refrigeration System Using R12 and R134a as Refrigerants Mohan Chandrasekharan #1 # Department

THERMODYNAMICS TUTORIAL 5 HEAT PUMPS AND REFRIGERATION. On completion of this tutorial you should be able to do the following.

THERMODYNAMICS TUTORIAL 5 HEAT PUMPS AND REFRIGERATION On completion of this tutorial you should be able to do the following. Discuss the merits of different refrigerants. Use thermodynamic tables for

Reservoir Fluids PETE 310

Reservoir Fluids PETE 31 Lab 2: Determination of the Vapor Pressure of Propane Learning Objectives When you complete this laboratory, you should be able to: Use closed-cell and sight-glass methods for