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Sonntag/Borgnakke
Study problems chapter 12
CHAPTER 12
STUDY PROBLEMS
MIXTURES
•
Mixtures of ideal gases
•
Moist air
•
The psychrometric chart
FUNDAMENTALS
of
Thermodynamics
Sixth Edition
SONNTAG
•
BORGNAKKE
•
VAN WYLEN
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Study problems chapter 12
12.1
Mixing in a rigid tank
A mixture of carbon dioxide and oxygen is made by having a rigid tank containing two
sections separated by a membrane. In A we have 1 kg CO
2
at 1000 K and in B we have 2
kg O
2
at 300 K both at 200 kPa. The membrane is broken and the mixture comes to a
uniform state without any external heat transfer. What is the final temperature and what
are the final partial pressures.
C.V. The whole tank.
Energy Eq.5.11:
U
2
 U
1
= 0 = m
CO
2
C
V0
(T
2
 T
A1
) + m
O
2
C
V0
(T
2
 T
B1
)
V
A
= m
CO
2
RT
A1
/P = 1
×
0.1889
×
1000/ 200 = 0.9445 m
3
V
B
= m
O
2
RT
B1
/P =
2
×
0.2598
×
300 / 200 = 0.7794 m
3
Continuity Eq.:
m
2
= m
CO
2
+ m
O
2
= 3 kg
Energy Eq.:
1
×
0.653 (T
2
 1000)
+ 2
× 0
.662 (T
2
 300) = 0
Solving, T
2
=
531.2 K
R
mix
=
Σ
c
i
R
i
=
1
3
×
0.1889 +
2
3
×
0.2598 = 0.2362 kJ/kg K
P
2
= m
2
RT
2
/(V
A
+V
B
) = 3
×
0.2362
×
531.2 / 1.5588 =
241.5 kPa
B
A
Comment:
We could also have used values of u from Table A.8 to write
U
2
= (mu)
CO
2
+ (mu)
O
2
= U
1
= 1
×
782.75 + 2
×
195.2 = 1173.15 kJ
But now it becomes trial and error to find the single T
2
.
Guess a T
2
and look in A.8
U
2 at 550 K
= 349.12 + 2
×
367.7 = 1084.5 kJ;
This is too low
U
2 at 600 K
= 392.72 + 2
×
404.46 = 1201.6 kJ
This a little too high
Interpolate to get:
T
2
= 550 + 50 (1173.15 – 1084.5)/(1201.6 – 1084.5) = 588 K
Notice here we got a T
2
that is 10% higher than before so we should have used a higher
average value for the heat capacity for CO
2
.
Sonntag/Borgnakke
Study problems chapter 12
12.2
Mixing in a flow setup
A mixture of carbon dioxide and oxygen is made by having a flow of 1 kmol/s CO
2
at
1000 K, 200 kPa mix with a flow of 2 kmol/s O
2
at 300 K, 200 kPa. The exit mixture has
a uniform state at 200 kPa total pressure and there is no external heat transfer and no
significant kinetic energy. What is the exit temperature and what are the partial pressures
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This note was uploaded on 10/20/2009 for the course MECHENG MEecheng 3 taught by Professor Borgnakke during the Fall '09 term at University of Michigan.
 Fall '09
 Borgnakke

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