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Thermodynamics Qualifying Exam

Study Material

The candidate is expected to have a thorough understanding of undergraduate engineeringthermodynamics topics. These topics are listed below for clarification. Not all instructors cover

exactly the same material during a course, thus it is important for the candidate to closely

examine the subject areas listed below. The textbooks listed below are a good source for thereview and study of a majority of the listed topics. One final note, the example problems made

available to the candidates are from past exams and do not cover all subject material. These

problems are not to be used as the only source of study material. The topics listed below should

be your guide for what you are responsible for knowing.

Suggested textbook: Fundamentals of Engineering Thermodynamics, 4

thEd., Michael Mortan and Howard

Shapiro, (John Wiley & Sons, pub.)

Thermodynamics: An Engineering Approach, 4th

Ed., Yunus Cengal and Michael Boles,

(McGraw Hill, pub.)

Fundamentals of Classical Thermodynamics, 4th Ed., Gordon Van Wylen, RichardSonntag, and Claus Borgnakke, (John Wiley & Sons, pub.)

Topic areas:

1. Properties of pure substances.

a. Identify states from properties

b. Using equations of state and general compressibility charts/tables

2. First Law

a. Application to closed and open systems b. Steady and unsteady formulations and use

3. Entropy and Second Lawa. Definition of entropy

b. Carnot efficiencyc. Application to closed and open systems

4. Irreversibility, Availability, and Energy

a. Application to closed and open systems

5. Power and refrigeration systems

a. Rankine cycle with modifications b. Vapor compression refrigeration

c. Air-standard cycles

d.

Calculation of efficiencies and COPs6. Thermodynamic relations

a. Maxwell relations

b. Behavior of real gases

c. Formulation for calculating changes in properties for real gasesd. Use of generalized correction charts/tables for entropy and enthalpy

7. Mixtures and Solutions

a. Ideal gases

b. Properties of mixtures

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8. Chemical reactions

a. Equation balancing / stoichiometry b. Enthalpy of formation

c. Heat of reaction

d. First law for a reacting system

9. Phase and chemical equilibriuma. Requirements for equilibrium

b. Phase equilibrium for a pure substance

c. Gibbs phase ruled. Chemical equilibrium for a mixture of reacting ideal gases

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

This portion of the qualifying exam is closed book. You may have a calculator.

Work 3 of the 4 problems. Be very clear which 3 you want graded (see below). It

is not acceptable to work all 4 problems and hope that the graders pick out the best

worked three.

I want problems #____, #____, and #____ graded.

Be sure to put your name on all papers handed in, including this cover sheet.

1. The differential of pressure obtained from a certain equation of state is given by one of the

following expressions.

dp = [2(v − b)/RT] dv + [(v − b)2 /RT2] dT

dp = [− RT/ (v − b)2] dv + [R/ (v − b)] dT

The other expression is incorrect. Determine the original equation of state from which the

correct differential of pressure was obtained.

2. Consider ideal combustion of one kmol of acetylene ( )2 2C H with 3 kmols of oxygen ( )2O

and 11.28 kmols of nitrogen ( )2 N . The initial temperature of the acetylene, oxygen, and

nitrogen is 25 C o . All reactants and products may be treated as ideal gases. Given that the

enthalpy of formation of acetylene is 226,731 f

h kJ kmol=o , and using the attached tables,

estimate the adiabatic flame temperature.

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

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Name ___________________________ Summer 2007

Qualifying Exam: Thermodynamics

CLOSED BOOK

3. A dam retains water of height h above the valley below. Using the First Law:

Q − W = m [g (z2 − z1)] + (m/2) [(V2)2 − (V1)

2]

a. if the water is allowed to flow through a pipe to the bottom of the dam, show that themaximum velocity of the water at the exit of the pipe is the classical value:

i. Vmax = (2 g h)1/2

b. Next, assume a hydro-turbine is placed at the pipe at the bottom of the dam to extract

useful power from the falling water. Using the First Law again, determine the velocity of

the water at the turbine exit that will allow the production of the maximum power in the

turbine. Express this optimum water velocity of the exit of the turbine, Vopt, in terms of Vmax, given above.

4. The Joule-Thomson or Joule-Kelvin coefficient is J

h

T

Pμ

∂⎛ ⎞= ⎜ ⎟

∂⎝ ⎠. This coefficient may be

negative, zero, or positive. Provide a physical explanation for each possible sign. Consider

non-reacting gaseous substances.

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Name ___________________________ Fall 2005

Qualifying Exam: Thermodynamics

CLOSED BOOK

This portion of the qualifying exam is closed book. You may have a calculator.

Work 3 of the 4 problems. Be very clear which 3 you want graded (see below). It

is not acceptable to work all 4 problems and hope that the graders pick out the best

worked three.

I want problems #____, #____, and #____ graded.

Be sure to put your name on all papers handed in, including this cover sheet.

1. Given that the Gibbs function is:

G = H − TS ( H = U + PV) ( dU = TdS − PdV) etc.

And since the Gibbs function is a “point function” and forms exact differentials, find a

simple expression for the change of entropy with respect to pressure for an isothermal

process with an ideal gas:

(∂S/ ∂P)T = ?

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Name ___________________________ Fall 2005

Qualifying Exam: Thermodynamics

CLOSED BOOK

2.

A stoichiometric mixture of oxygen (O2) and hydrogen (H2) are contained within a constantvolume container. The initial temperature and pressure are 273 K and 1 atm. At this

temperature there is negligible reaction between the oxygen and hydrogen. A spark initiates

the reaction, which goes very rapidly toward equilibrium. The measured temperature of the

products is 2000 K. Many products are possible but only the following will be considered: H,

H2, O, O2, OH, and H2O. The relevant equilibrium reactions are:

2 10

2 10

2 2 2 10

2 2 10

2 log 5.580

2 log 6.356

1log 3.540

21

log 3.7802

p

p

p

p

H H K

O O K

H O H O K

H O OH H K

= −

= −

+ = −

+ = −

The equilibrium constant is:

( ) ( )

( ) ( )for the reaction

E F

A B

E F

p A B E F

A B

p p K A B E F

p p

ν ν

ν ν ν ν ν ν = + +

where all partial pressures are measured in atmospheres. The mixture before and after the

reaction may be treated as an ideal gas. Determine the final partial pressures of the six

products considered.

Note: You cannot hope to finish this problem in the time allotted. Proceed as if you did have

enough time and you should be able to get to the point where you would need a computer to

actually solve the equations.

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Name ___________________________ Fall 2005

Qualifying Exam: Thermodynamics

CLOSED BOOK

3. A substance whose Joule-Thomson coefficient is positive is throttled. During this process:

(a) The temperature of the substance will increase

(b) The temperature of the substance will decrease

(c) The entropy of the substance will remain constant

(d) The entropy of the substance will decrease

(e) The enthalpy of the substance will decrease

Pick one correct answer and explain your logic or reasoning.

4. Consider ideal combustion of methane (CH4) and oxygen (O2).

a.

What are the products? Write out the balanced reaction equation.b. How would you find the adiabatic flame temperature for constant pressure

combustion?

c. How would you find the adiabatic flame temperature for constant volume

combustion?

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Qualifying Exam Spring 2003

Thermodynamics

This portion of the qualifying exam is closed book. You may have a calculator.

Work all three problems.

Be sure to put your name on all papers handed in, including this cover sheet.

Problem 1:

A gas has the following equation of state:

P PT v P

RT β−α−= 2

Find the following:a) The Joule-Thomson Coefficient

b) The Temperature at the inversion state in terms of α, β, and P.

Problem 2:

Rejected heat, Qi, from a Lenoir cycle is used to power a Diesel cycle in a new hybrid cycle

engine. The compression ratio, r, and cutoff ratio, r c, are assumed to be known. The efficiencyof a Lenoir cycle can be shown to be:

v p

k

L c/ck where)1r /()1r (k 1 =−−−=η

Find an expression for the Hybrid cycle efficiency ηh in terms of r, r c, and k.

Qin

Qi

Qout

V

D

LP

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Problem 3:

A tank of fixed volume V is filled with a saturated mixture with both liquid and vapor present.Gravity is present so the liquid is on the bottom and the vapor above. Other than this separation

of phases, gravity has no other effect (neglect pressure gradients). The tank is perfectly

insulated. A very slow leak is present. Set up the equations you would need to solve that wouldtell you the temperature and pressure in the tank as a function of mass in the tank. You may

assume that tables of properties are available. There is no way you can solve these equationshere, so indicate a method you would use to actually solve the equations. Be sure to state anyassumptions or simplifications you make. Please use standard nomenclature such as subscript ƒ

for the fluid phase and g for the vapor phase.

Would it make any difference if the leak were from a hole at the top versus the bottom?

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Qualifying Exam Spring 1999

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

Problem 1:

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Problem 2:

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Problem 3:

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Qualifying Exam Fall 1998

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

Problem 1:

Problem 2:

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Qualifying Exam Spring 1997

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work 3 of the 4 problems

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Qualifying Exam Spring 1996

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

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Qualifying Exam Spring 1995

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

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Qualifying Exam Spring 1994

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

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Qualifying Exam Spring 1993

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work 3 of the 4 problems

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Qualifying Exam Spring 1992

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

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Qualifying Exam Spring 1991

Thermodynamics

This portion of the qualifying exam is open book. You may have a calculator.

Work all problems

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Qualifying Exam Miscellaneous

Thermodynamics

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