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Introductory Chemical Thermodynamics Equations - Final Exam | CHE 21100, Exams of Chemistry

Material Type: Exam; Class: Introductory Chemical Engineering Thermodynamics; Subject: CHE-Chemical Engineering; University: Purdue University - Main Campus; Term: Fall 2008;

Typology: Exams

2011/2012

Uploaded on 05/01/2012

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CHE211
CHEMICAL ENGINEERING THERMODYNAMICS
Final Exam Fall Semester 2008
Time Allowed: 120 minutes
Total Marks: 100 marks
Open Book Exam
Answer all questions
Formula sheet and Thermodynamic data supplied.
Any calculators allowed.
SHOW ALL WORKING ON THE EXAM PAPER.
STUDENT NAME: ______________________________
PUID: ______________________________
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Download Introductory Chemical Thermodynamics Equations - Final Exam | CHE 21100 and more Exams Chemistry in PDF only on Docsity!

CHE

CHEMICAL ENGINEERING THERMODYNAMICS

Final Exam Fall Semester 2008

Time Allowed: 120 minutes

Total Marks: 100 marks

Open Book Exam

Answer all questions

Formula sheet and Thermodynamic data supplied.

Any calculators allowed.

SHOW ALL WORKING ON THE EXAM PAPER.

STUDENT NAME: ______________________________

PUID: ______________________________

QUESTION 1

(a) During an isentropic, steady flow expansion, it is possible to prove that: dH VdP.

Derive an expression for work done per kg of fluid for an isentropic, steady flow

expansion from P 1 to P 2 for a fluid which obeys the following truncated Virial

Equation of State:

2

2 2

RT

C B P

RT

BP

Z

where B and C are the second and third virial coefficients. [Hint: start by writing

down the first law for a steady flow, isentropic expansion (turbine).] (10 marks)

(b) Outback Australia is sunny and hot for most of the year. A thermal solar power plant

claims to generate 5kW of electricity for every 50kW of solar energy captured by a

specially designed solar pond. The pond can be considered a constant temperature

heat reservoir at 60°C. Although the atmospheric temperature is very high, by taking

advantage of evaporative cooling, we can exchange heat in the condenser of our

power plant at 20°C. Evaluate this claim by comparing the efficiency of this power

plant to a Carnot cycle using the same temperature reservoirs. (10 marks)

(c) Steam at 5000 kPa and 500°C is expanded through a simple adiabatic throttling

valve. At the inlet conditions, the enthalpy and entropy of the steam are 3433.

kJ/kg and 6.9770 kJ/kg.K respectively.

a. What does the first law tell us about the enthalpy of the exit steam?

b. What does the second law tell us about the entropy of the exit steam?

State clearly any assumptions you make. (10 marks)

(d) We can write a fairly general expression for vapor-liquid equilibrium for a mixture

as follows, provided we assume the gas phase can be treated as an ideal solution:

RT

V P P

yP xP

sat i

l sat i i i i i i

  exp

A binary mixture of ethanol and water has an azeotrope at 0.89 mole fraction ethanol

at atmospheric pressure and a temperature of roughly 90°C. Simplify the above

expression as much as is reasonable for use in solving VLE problems for the

ethanol/water mixture at atmospheric pressure. State clearly the assumptions you

make to simplify the equation and justify each assumption qualitatively with one

sentence only. (10 marks)

[Hint: the math is trivial. The key is to clearly state and justify your assumptions.]

Total = 40 marks

WORKING FOR QUESTION 1 HERE

QUESTION 2

(a) I am exploring the idea of separating a binary mixture by multiple flash separation. The mixture

is throttled to a low pressure where it separates into a two phase mixture. The more volatile

component will concentrate in the vapor phase. A flash tank is used to separate the vapor from

the liquid. I repeat the process by recompressing the vapor phase and then flashing it into a

second tank and so forth.

Consider one flash separation stage only. I have a mixture of 80 mole% benzene and 20 mole%

Toluene. This mixture is flashed to a pressure of 1 Bar. The measured temperature in the flash

tank is 85°C. Under these conditions calculate the composition of the liquid and vapor phases

and the mole ratio of vapor to liquid.

The vapor pressures of the two component are given by:

Benzene: / 217. 572

ln 13. 7819 

kPa t C

P

sat

Toluene: / 217. 625

ln 13. 9320 

kPa t C

P

sat

You may assume that this mixture obeys Raoult’s Law. (14 marks)

(b) Unlike the benzene-toluene system, the benzene-cyclohexane binary system forms an

azeotrope at 0.525 mole fraction benzene at a temperature of 77.6°C and a total pressure of

1.013 Bar (atmospheric pressure). At this temperature, the vapor pressure of pure cyclohexane

is 0.980 Bar and that for benzene can be calculated from the expression given above.

Sketch the P-x-y diagram for the benzene-cyclohexane system making use of your knowledge of

the liquid and vapor compositions and total pressure at xbenzene =0.0, 0.525 and 1.0. Label the

regions that are liquid, vapor, and liquid-vapor mixture. (6 marks)

Total = 20 marks

WORKING FOR QUESTION 2 HERE

QUESTION 3

A large compressor is used to compress 1.5 kg/s of ethane from 25°C and 1 Bar until the

pressure is 39 Bar. To prevent the ethane becoming too hot, the compression is done in two

stages with an intercooler as shown in the figure below. The temperature of the ethane

leaving the compressor is controlled at 93°C. The power supplied to the compressor is 350kW.

(a) At the inlet, it is reasonable to assume that ethane is an ideal gas for a first order

calculation ie. Z > 0.95. Calculate the compressibility factor for ethane at the exit

conditions and show the ideal gas assumption is not appropriate at these conditions.

(6 marks)

(b) What is the heat duty for the intercooler in kW? (14 marks)

For ethane: Tc = 305.3K; Pc = 48.72Bar; ω = 0.100; Cp

ig =6.369R; MW=0.030 kg/mol

You may assume the ideal gas heat capacity of ethane does not vary with temperature over

this range. State clearly any other assumptions you make.

[Hint: Do the analysis for the combined compressor-intercooler as the system.]

Schematic of two stage compressor with intercooler for Q.3.

WORKING FOR QUESTION 3 HERE

QUESTION 4

Consider a simple, gas phase decomposition reaction:

A(g) →2B (g)

This reaction takes place at 1000K and 10 Bar. Initially there are 5 moles of A and no moles of

B present. The standard Gibbs energy and enthalpy of formation at 25°C A and B are:

H J mol

G J mol

H J mol

G J mol

f B

fB

fA

fA

0 ,

0 ,

0 ,

0 ,

(a) Calculate the value of the equilibrium constant K at 1000K assuming the temperature

effect can be predicted from the van’t Hoff equation. (5 marks)

(b) Calculate the final mole fraction of component A assuming (i) the system reaches

equilibrium, and (ii) the gas mixture behaves as an ideal gas. (10 marks)

(c) I want to increase the conversion of A in this reaction. Propose one way of doing this by

varying the reaction conditions. Explain why your suggestion will work in one or two

sentences. (5 marks)

[Hint: If you have trouble calculating K in part (a), assume a reasonable value for K in solving

parts (b) and (c).]

WORKING FOR QUESTION 4 HERE

Thermodynamic equations, constants and conversions

E E E U

E Q W

W PdV

PV NRT

P gz

k p

V

V

t

2

1

Ep mg( z 2 z 1 )

 

U U g z z ^ ^ q w

Q W

m U U mgz z

t t

2 1

2 2 1 2 1 2

2 1

2 (^21212)

u u

u u

     

     

2 1

2 2 1 2 1 2

2 1

2 2 1 2 1 2

u u

u u

q w H H gz z

Q W m H H gz z

sh

sh

U c T H c T T

H

c T

U

c

H U PV

v p p

p v

v        

2

1

2 1 T

dq S S

rev

nett

l fridge

H

L

H

nett carnot

W

Q

COP

T

T

Q

W

2

1

H 2 H 1 VdP

1

2

1

2

1

2

1

2 2 1 ln^ ln ln ln V

V

R

T

T

c P

P

R

T

T

S S cp   v 

V V

V V

x

V xV xV

g

g

 

2 1

2 2 2

  uu

m Ek

RT

PV

Z 

crit

R crit

R P

P

P

T

T

T  ; 

Constants and Conversions

 

ln

2

1

2

5

2

1 1

x

x dx x

K C

g ms

Atm Pa

bar Pa

Pa Nm

R Jmol K

x

x