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Chapter 3
Properties of Pure Substances
Review Problems
3107
A smoking lounge that can accommodate 15 smokers is considered. The required minimum flow
rate of air that needs to be supplied to the lounge and the diameter of the duct are to be determined.
Assumptions
Infiltration of air into the smoking lounge is negligible.
Properties
The minimum fresh air requirements for a smoking lounge is given to be 30 L/s per person.
Analysis
The required minimum flow rate of air that needs
to be supplied to the lounge is determined directly from
30 L/s person
15 smokers
Smoking Lounge
&&
(
VV
air
air per person
No. of persons)
= (30 L /s person)(15 persons) = 450 L /s =
=
⋅
0.45 m / s
3
The volume flow rate of fresh air can be expressed as
&
(/
VA
D
==
π
2
4
)
Solving for the diameter
D
and substituting,
m
0.268
V
=
=
=
m/s)
(8
)
/s
m
45
.
0
(
4
4
3
ππ
V
D
&
Therefore, the diameter of the fresh air duct should be at least 26.8 cm
if the velocity of air is not to exceed 8 m/s.
3108
The minimum fresh air requirements of a residential building is specified to be 0.35 air changes per
hour. The size of the fan that needs to be installed and the diameter of the duct are to be determined.
√
Analysis
The volume of the building and the required minimum volume flow rate of fresh air are
L/min
3150
=
=
=
=
×
=
=
=
L/h
189,000
h
/
m
189
)
/h
35
.
0
)(
m
540
(
ACH
m
540
)
m
m)(200
7
.
2
(
3
3
room
3
2
room
V
V
V
&
The volume flow rate of fresh air can be expressed as
&
D
2
4
)
Solving for the diameter
D
and substituting,
m
0.106
V
=
=
=
m/s)
(6
)
/s
m
3600
/
189
(
4
4
3
V
D
&
Therefore, the diameter of the fresh air duct should be at least 10.6 cm
if the velocity of air is not to exceed 6 m/s.
House
200 m
2
0.35 ACH
335
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Properties of Pure Substances
3109
The pressure in an automobile tire increases during a trip while its volume remains constant. The
percent increase in the absolute temperature of the air in the tire is to be determined.
Assumptions
1
The volume of the tire remains constant.
2
Air is an ideal gas.
Properties
The local atmospheric pressure is 90 kPa.
TIRE
200 kPa
0.022 m
3
Analysis
The absolute pressures in the tire before and after the trip are
PP
P
P
1
2
200
90
290
220
90
310
=+
=
+
=
=
+
=
gage,1
atm
gage,2
atm
kPa
kPa
Noting that air is an ideal gas and the volume is constant, the ratio of
absolute temperatures after and before the trip are
PV
T
T
T
T
P
P
11
1
22
2
2
1
2
1
=→
=
=
310 kPa
290 kPa
=1.069
Therefore, the absolute temperature of air in the tire will increase by
6.9%
during this trip.
336
Chapter 3
Properties of Pure Substances
3110
A hot air balloon with 3 people in its cage is hanging still in the air. The average temperature of the
air in the balloon for two environment temperatures is to be determined.
Assumptions
Air is an ideal gas.
Properties
The gas constant of air is
R
= 0.287 kPa.m
3
/kg.K.
Analysis
The buoyancy force acting on the balloon is
N
44,700
m/s
kg
1
N
1
)
m
)(4189
m/s
)(9.8
kg/m
(1.089
kg/m
1.089
K)
K)(288
/kg
m
kPa
(0.287
kPa
90
m
4189
/3
m)
(10
4
3
/
4
2
3
2
3
balloon
air
cool
3
3
air
cool
3
3
3
balloon
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
=
=
=
⋅
⋅
=
=
=
=
=
gV
F
RT
P
r
V
B
ρ
ππ
Hot air balloon
D
= 20 m
The vertical force balance on the balloon gives
m
cage
= 80 kg
P
atm
= 90 kPa
T
= 15
°
C
g
m
m
m
W
W
W
F
B
)
(
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This note was uploaded on 04/14/2008 for the course ME 320 taught by Professor Dr.kinne during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Dr.Kinne

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