ME4850 -- Thermodynamics of Materials -- A99

Course Information

Provisional Syllabus

Supplementary Problems

Just for fun...

COURSE INFORMATION

Instructor: Prof. Chrys Demetry. Office: Washburn 332. Tel: 831-5195. E-mail: cdemetry@wpi

Office hours: MTRF 3-4, or by appointment, or whenever you can find me. Wednesdays I'm usually at Norton Co.

Class Meetings: MTRF 9-9:50 AM, WB323

Required Text: David R. Gaskell, Introduction to the Thermodynamics of Materials, 3rd edition. Washington, D.C.: Taylor & Francis, 1995.

Other References:

Smithells Metals Reference Book, Butterworth-Heinemann, 1990.

JANAF Thermochemical Data, Army-Navy-Air Force Thermochemical Panel, The Dow Chemical Company, Midland, MI, 1962-63.

R.R. Hultgren, R.L. Orr, P.D. Anderson, and K.K. Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys, John Wiley, NY, 1963.

Course Goal: To learn to apply the underlying principles of thermodynamics to address problems in materials engineering, including material process design and materials selection. Specifically, thermodynamics will be applied to the understanding of gas mixtures and liquid and solid solutions, phase equilibria, and chemical reactions. For specific learning objectives that should be used as a study guide, see http://www.wpi.edu/~cdemetry/4850a99.html.

Recommended Background: Introductory materials science (ES2001), especially the interpretation of phase diagrams; differential and integral calculus. A previous thermodynamics course such as ES3001 is helpful but not essential.

Computer Usage: During this course you will need to use the following types of software: 1) a spreadsheet and graphing program such as Excel, with the ability to perform least-squares regression for fitting data with linear or polynomial functions; 2) TKSolver, MathCad, or equivalent, for solving simultaneous non-linear or non-quadratic equations.

Course Structure and Expectations: Class meetings will be a mixture of instructor-led review of new concepts and collaborative problem solving. Thus, this course will have much less traditional lecturing than you may be accustomed to. Why? First, my research as well as many others' has shown that a "learn by doing" classroom in which students are active participants in the educational process rather than passive spectators results in more student learning. Second, lectures are typically redundant in that the material presented is often identical with that in reading assignments. Thus, you will be expected to use the textbook rather than lectures as your primary source for "course content."

Individual and Group Efforts: The material in this course typically must be studied and learned withsignificant individual struggle and perseverance. At the same time, the power of collaboration and peer teaching in enhancing student learning is quite significant. Thus, the course is structured to promote both individual and group effort.

 

Evaluation and Grading:

Problem Assignments (25%)

Problems from the textbook and supplementary problems will be due twice a week (see syllabus). Solutions will be placed on reserve in Gordon Library that day. Each assignment will be graded on a scale of 1 to 20. Assignments must be completed in collaborative groups of 3 students each. Groups will be assigned based on your availability outside of class and on past coursework and experience. These groups will need to meet outside of class at least twice each week. Problems must be worked individually before the team convenes, but the team need only submit one set of solutions for grading. A student's name can be placed on the solutions only if s/he was present at the meeting at which the problems were discussed. The solutions must also include a record of the time the team met. The team is responsible for ensuring that each member has a good understanding of the material. As necessary, individual students will be called upon in class to explain their group's final solutions.

Class Participation/Preparation (5%)

Based on attendance and contributions to problem solving discussions. You have the responsibility to prepare for each class by carefully completing the assigned reading and by working example problems in the text.

Exams (70%)

Three exams are scheduled, and since all of the material in this course naturally builds from previous concepts, the exams will in some sense be cumulative. You will be allowed to prepare a 3"x5" notecard with equations to bring with you to the exam. (A few restrictions will apply.) Every effort will be made to give you "unlimited" time (within reason) on the exams by scheduling them to begin at 8:00 instead of 9:00, for example, if students' schedules allow. Your team will receive bonus points if all members earn a passing grade on the exam.

An optional, comprehensive "makeup" exam will be available on Friday, October 15 (the day after the last day of classes) for students who wish to demonstrate an improved understanding of the material and raise their final grade.

Final grades for the course will be determined as follows:

³ 88% = A

³ 78% = B

³ 68% = C

<68% = NR

I reserve the right to lower these cutoffs, but under no condition will I raise them. Please note that this is an absolute or criterion-based grading method; you will not be graded on a curve relative to the performance of your classmates. Thus, you are not in competition with your peers for high grades. Please take advantage of the absence of competition and help each other learn the course material. One learns most by teaching!

Course Policies:

  • Assignments are due at the start of class. Late assignments will receive only half credit unless prior arrangement has been made. No late work will be accepted for credit once solutions have been posted in the library.
  • If you have a long-standing personal commitment (religious observance, wedding, etc.) on one of the scheduled exam dates, you must notify me by the second week of class for alternative arrangements to be made. Short-notice changes will be made prior to exams only for those students with personal emergencies (illness, death in family, etc.) After-the-fact excuses are unacceptable, and absolutely no make-up arrangements will be made in these circumstances.
  • Academic integrity is a fundamental principle of learning and professionalism. Thus, it is an issue I take quite seriously. Examples (not an exhaustive list) of academically dishonest acts in the context of this course include removal of course material from the reserve notebook in Gordon Library, copying on exams, and submitting group work that you do not understand and cannot explain. I am responsible for being fair at all times, and for evaluating student performance solely on the basis of your academic work in the course. Any suspected cases of academic dishonesty will be confronted and reported to the Mechanical Engineering Department chairperson and to the Student Life Office for further action, as specified in Student Judicial Policies and Procedures.

Advice and Comments from Former Students:

  • "Work the assignments independently. Read and study the book over and over and over again."
  • "Try to keep up... Don't plan on a day without doing thermo for a few hours."
  • "Start all HW early because you'll need help with it."
  • "Keep up with the H.W. and try to do it early-- not the night before."
  • "Go to every single class and don't get left behind."
  • "I really thought that a thermo course would be kind of a waste of time. But this course really helps you to understand everything in Materials Science. I liked the fact that I feel I came away from ME4850 being able to tackle so many more problems, in and out of 4850. I learned a ton."

 

 

ME4850 — PROVISIONAL SYLLABUS — A99

Version 1.0

Class

Date

Topic

Reading Due

Assignment Due

1

R 8/26

Introduction

 

 

2

F 8/27

First Law

Ch. 1,2

#1

3

M 8/30

 

 

 

4

T 8/31

Second Law

Ch. 3

#2: 2.1, 2.4, 2.6, SP1, SP2*

5

R 9/2

 

 

 

6

F 9/3

Statistical Interpretation of Entropy, Auxiliary Functions, Maxwell Relations

Ch. 4, Ch. 5

#3: 3.3, 3.4, SP3-5

 

M 9/6

No Class - Labor Day

7

T 9/7

 

 

 

8

R 9/9

Heat Capacity, Temperature Dependence of Enthalpy, Third Postulate

Ch. 6

#4: 4.3, SP6-8

9

F 9/10

 

 

 

10

M 9/13

Review

 

#5: 6.6, 6.8, SP9-11

11

T 9/14

EXAM 1 (Ch. 2-6)

 

 

12

R 9/16

One Component Phase Equilibria

Ch. 7

 

13

F 9/17

 

 

 

14

M 9/20

Behavior of Gases

Ch. 8

#6: 7.1, 7.2, 7.5, 7.8, 7.9

15

T 9/21

 

 

 

16

R 9/23

Behavior of Solutions

 

Ch. 9

#7: 8.2, 8.3, 8.5, 8.6, 8.7

17

F 9/24

 

 

 

18

M 9/27

Review

 

#8: 9.2, 9.3, 9.4, 9.10, 9.11

19

T 9/28

EXAM 2 (Ch. 7-9)

 

 

20

R 9/30

Free Energy-Composition Diagrams

Ch. 10

 

21

F 10/1

 

 

 

22

M 10/4

Reactions Involving Gases

Ch. 11

#9: 10.1, 10.2, 10.3, 10.6, 10.7, SP13

23

T 10/5

 

 

 

24

R 10/7

Reactions of Gases with Condensed Phases

Ch. 12

#10: 11.1, 11.4, 11.7, 11.8, 11.10

25

F 10/8

 

 

 

26

M 10/11

Reaction Equilibria in Systems Containing Components in Condensed Solution

Ch. 13.1-13.2

 

27

T 10/12

Review

 

#11: 12.3, 12.4**, 12.5, 12.10, 13.22

28

R 10/14

EXAM 3 (Ch. 10-13)

 

 

 

F 10/15

Optional Comprehensive Makeup Exam

 

 

*SP= Supplementary Problem (handed out in class)

**For problem 12.4, solve two ways: using the Ellingham diagram in Ch. 12 and using the Gibbs free energy data in Table A-1 for the appropriate reactions.

The above schedule was planned such that the following process can be used to assist your learning:

Day n-1:

Read chapter in text assigned for the next day's class. In particular, study Gaskell's examples.

 

Day n:

In class: Chrys summarizes key concepts from reading and works additional example(s).

After class: Individuals work on assigned problems. Read chapter and Gaskell's examples again.

 

Day n+1

In class: Pairs or groups work additional problems with coaching from Chrys.

After class: Teams meet and prepare final solutions of assignment for next day. Read chapter in text assigned for the next day's class.

ME4850 Supplementary Problems — A99

SP1. Twenty liters of an aqueous aluminum nitrate solution ("metal salt" solution) are to be spray dried to form a powder precursor for aluminum oxide. An atomizer is used such that the solution is broken into droplets having a diameter of 30 m m at 20°C. Calculate the minimum work required for this atomization process, stating any assumptions. Water has a surface tension of 72.75 mN/m (mJ/m2) at 20°C.

SP2. Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25°C. The pressure is 20 atm. What will be the temperature of the helium entering the quench chamber when the pressure in the tank has fallen to 10 atm? State all assumptions.

SP3. A 75 kg load of steel parts at 800°C (assume a heat capacity equal to that of iron) is dumped into a tank containing 120 kg of quenching oil (specific heat= 2.081 kJ/kg K), the initial temperature of which is 75°C. The system is allowed to come to equilibrium so that the parts and oil are at the same temperature. a) Assuming that heat loss from the tank is negligible, what will the final temperature of the system be? b) How much heat is transferred and how much entropy is produced by the transfer?

SP4. A great deal of effort has been expended to find "high temperature superconductors"—materials that have a critical temperature Tc (below which the material has zero resistance) at temperatures higher than the boiling point of liquid nitrogen (77 K). Most conventional superconductors would have to be operated with liquid helium (boiling point 4.2K) as the cooling fluid. To estimate the savings possible in operating costs through the use of the high temperature superconductors, calculate the minimum work needed to compensate for a heat leak of 1 kJ into the superconductor for both high temperature superconductors and conventional superconductors. Assume that the ambient temperature is 300 K.

SP5. Under 1 atm pressure, helium boils at 4.216 K. The heat of vaporization is 84 J/mol. What size motor (in horsepower) is needed to run a refrigerator that must condense 2 mol of gaseous helium at 4.216 K to liquid at the same temperature in one minute? Assume that the ambient temperature is 300 K and that the coefficient of performance of the refrigerator is 40% of the maximum possible.

Hint for SP4-5 and SP9-10:

A limiting case that is quite useful when considering a materials processing operation is the steady state. Steady state is defined as one in which the system does not change with time. Every quantity or property of the system is time invariant. Material may enter and leave the system, but the system itself remains unchanged. This form of analysis is useful in the case of processing apparatus such as pumps, turbines, chemical reaction vessels, smelters, blast furnaces, etc. In these devices, once steady operations have been achieved, material enters and material leaves, but the system itself remains basically unchanged with time. In this case, a first law statement such as D U=0=q-w can be differentiated with respect to time such that power (), rates of heat removal (), and/or mass transfer rates () can be determined.

SP6. a) Derive an expression for the change of temperature of a solid material that is compressed adiabatically and reversibly in terms of physical quantities usually available, such as the ones listed below for iron.

b) The pressure on a block of iron is increased by 1000 atm adiabatically and reversibly. What is the temperature change? The initial temperature of the iron is 298 K.

Data (for Fe):

CP= 24 J/mol K

Compressibility= 6 x 10-7 atm-1

Linear coefficient of thermal expansion = 15 x 10-6 K-1

Density = 7.87 g/cm3

Molecular weight = 55.85 g/mol

Notes:

compressibility,

volumetric thermal expansion coefficient,

linear thermal expansion coefficient, a l=a V/3

 

SP7. A block of rubber weighing 100 g is to be compressed from a pressure of 1 atm to a pressure of 1001 atm.

a) What is the volume of the block of rubber?

b) The block of rubber is compressed isothermally at 298 K. What is its change of entropy? State any necessary assumptions.

c) How much heat must be added (or removed) from the rubber to maintain it at a constant temperature of 298 K? Specify whether heat is added or removed.

Data for rubber:

volumetric thermal expansion coefficient = 100 x 10-6 K-1

density = 1.0 g/cm3

SP8. Determine the work required to compress 20 cm3 of liquid mercury at a constant temperature of 0°C from a pressure of 1 bar to 1500 bars. The isothermal compressibility of mercury at this temperature is given by KT= 3.9x10-6 - 1.0x10-10P, where KT is in bar-1, and P is in bars. The density of mercury may be taken as 13.6 g/cm3.

SP9. An electric resistance furnace is used to melt pure aluminum at the rate of 100 kg/h. The furnace is fed with solid aluminum at room temperature. The liquid aluminum leaves the furnace at 760°C. What is the minimum electric power rating (kW) of the furnace? State assumptions.

SP10. Metals exhibit some interesting properties when they are rapidly solidified from the liquid state. An apparatus for the rapid solidification of copper is cooled by water. In the apparatus, liquid copper at its melting point (1356 K) is sprayed on a cooling surface, where it solidified and cools to 400 K. The copper is supplied to the apparatus at the rate of 1 kg/min. Cooling water is supplied at 20°C, and is not allowed to rise above 80°C. What is the minimum necessary flow rate of water in the apparatus, in cubic meters per minute?

SP11. Titanium dioxide (rutile) coatings are produced by reacting titanium tetrachloride (TiCl4) vapor with water vapor at 800 K. Is it necessary to supply heat to or remove heat from the reactor to keep the temperature constant?

SP12. A person with a body mass of 125 lb owns a pair of ice skates each of which has a knife edge 0.02 inches wide and 4 inches long. Calculate the minimum temperature of the ice on which the person can go skating. At 0°C and 1 atm pressure the densities of ice and liquid water are 0.917 g/cm3 and 0.998 g/cm3, respectively.
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Last modified: 26 August 1999