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Material Type: Exam; Class: Introductory Chemical Engineering Thermodynamics; Subject: CHE-Chemical Engineering; University: Purdue University - Main Campus; Term: Fall 2008;
Typology: Exams
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(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
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:
yP xP
sat i
l sat i i i i i i
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
(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
sat
Toluene: / 217. 625
ln 13. 9320
kPa t C
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
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.
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).]
Thermodynamic equations, constants and conversions
W PdV
P gz
k p
V
V
t
2
1
Ep mg( z 2 z 1 )
U U g z z ^ ^ 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
c T
c
v p p
p v
v
2
1
2 1 T
dq S S
rev
nett
l fridge
H
L
H
nett carnot
2
1
H 2 H 1 VdP
1
2
1
2
1
2
1
2 2 1 ln^ ln ln ln V
c P
S S cp v
x
V xV xV
g
g
2 1
2 2 2
u u
m Ek
crit
R crit
R P
ln
2
1
2
5
2
1 1
x
x dx x
g ms
Atm Pa
bar Pa
Pa Nm
R Jmol K
x
x