Report 7
Two flasks
Team Taiwan
Franklin Liou
Problem # 7
H
H
h?
?
Investigate and describe in which tube the water goes up
faster and in which the final height is greater. How does this
effect depend on the time of heating?
1
Overview
• Introduction
• Experiment
– Experimental Setup
– Experiment
• Results and Discussion
• Conclusions & Summary
2
Experiment Setup
The heating apparatus and sensors
•1300ml flask (200ml water) •Pressure sensor
•Thermocouple
•Hot plate
•Oil bath (for heating dry flask)
3
Experiment Setup
Transparent tube
and long ruler
Water reservoir
4
Experiment
• Initial conditions: 100 oC
• Conditions
– Flask with and without water
– Heating time after reaching 100 oC
(1min, 2min, 5min)
• Data
– Temperature-Time curve
– Pressure-Time curve
– Water height-Time curve
5
Experiment Results: Dry Flask
200
o
Dry Flask after heated at 100 C for 2 minutes
180
160
100
120
height (m)
Dry, 2min
Dry, 5min
exp fit
o
Temperaure ( C)
140
100
80
60
40
dry, 2min
dry, 5min
20
0
0
200
400
600
800 1000 1200 1400 1600 1800
time (s)
80
60
40
0
300
600 900
Time (s)
1200 1500
• Height-Time curve is roughly •Temperature-Time curve is
roughly an exponential
a saturation curve
decay
• Maximum height: 1.72m
•Max: 103oC, Min:31oC
•Decay rate:0.0026
6
Experiment Results: Dry Flask
• Pressure-Time curve is roughly an exponential decay
• Maximum pressure: 103 kPa

P

19
kP
a
• Minimum pressure: 84 kPa
7
Experiment Results: Wet Flask
10
100
8
Temperature ( C)
90
80
o
6
height (m)
wet, 1min
wet, 2min
wet, 5min
4
2
wet, 1min
wet, 2min
wet,5min
70
60
50
40
30
0
0
500
1000
1500
2000
time (s)
2500
3000
3500
0
500
1000
1500
2000
2500
3000
3500
4000
time (s)
• Height-Time curve is roughly •Temperature-Time curve is
roughly an exponential decay
a saturation curve
•Max: 100oC, Min:31oC
• Maximum height: 8.6m
•Decay rate:0.0011
8
Experiment Results: Wet Flask
• Pressure-Time curve is roughly an exponential
decay
• Maximum pressure: 101 kPa  P  96 kP a
• Minimum pressure: ~ 5 kPa
9
Results and Discussion
•Newton’s Law of Cooling:
dT
dt
   T  H
T  t   TR  TH  TR  e

 t
o
Dry Flask after heated at 100 C for 2 minutes
Dry, 2min
Dry, 5min
exp fit
o
Temperaure ( C)
100
80
60
T R  31.5 C  304.5 K
o
T H  T R  71.5 K
We can obtain the decay rate  , and
hence the approximate T(t) function
40
0
300
600 900
Time (s)
1200 1500
Square of residual: 0.99974
10
Dry flask
• Ideal gas law: expansion of dry air~1900Pa
PV  nRT
  V 0  hA   P0  h  g   n1 R T
T  t   TR  TH  TR  e
 t
h
h
h ( t )  h0  B C  D e
•V0: initial volume
•P0:initial pressure
•N1: initial mole of gas
 t

•A cross section of tube
•R: Ideal gas constant
•T: temperature at a given time
11
2.5
Dry Flask Results
Height (m)
2.0
Ideal Gas Assumption
Heated for 2 min
1.5
Heated for 5 min
1.0
0.5
h ( t )  h0  B C  D e
0
300
600 900
Time (s)
 t
1200 1500
H=64.86-5.00*Sqrt(159.67+7.36*Exp(-0.0312t))
12
Wet flask
•Water vapor can fill almost all volume -> condense ->
large pressure difference~101300Pa
•Antoine equation:
5132 

P  k exp  20.386 

T 

k  133.3 P a ,
( T in K , P in P a )
•Assuming water vapor replaces all air


5132
exp  20.386 
 Po  h  g
 t 
TR   TH  TR  e




D
h ( t )  h 0  B exp  C 

E  F exp(  t / G ) 

13
Wet Flask Results
10
8
height (m)
6
4
2
wet, 1min
wet, 2min
wet,5min
0
0
500
1000
1500
2000
2500
3000
3500
time (s)


D
h ( t )  h 0  B exp  C 

E  F exp(  t / G ) 

14
Comparison of Wet and Dry Flask
10
8
height (m)
6
wet, 1min
wet, 2min
wet, 5min
dry, 2min
dry, 5min
4
2
0
0
500
1000
1500
2000
2500
3000
3500
time (s)
15
Results and Discussion
Time span of boiling
at100oC/ maximum
height
1min
Dry Flask
Theoretical Dry Flask
(Ideal gas law)
2min
5min
1.72m
2.25m
1.69m
2.25m
Wet Flask
8.65m
8.66m
8.42m
Theoretical Wet Flask
(Antoine equation)
9.12m
9.12m
9.12m
16
Conclusions & Summary
• Two flaks : two mechanisms
– Dry flask: expansion of air~ 1.9 kPa
– Wet flask: condensation of vapor~ 101300 Pa
• Water rises faster in wet flask condition
• Maximum water height is greater in wet flask
10
8
6
height (m)
• Maximum water
height and water rising
speed is independent
of time of heating
wet, 1min
wet, 2min
wet, 5min
dry, 2min
dry, 5min
4
2
0
0
500
1000
1500
2000
time (s)
2500
3000 17
3500
2.5
Height (m)
2.0
Ideal Gas Assumption
Heated for 2 min
1.5
Heated for 5 min
1.0
0.5
0
300
600 900
Time (s)
1200 1500
18