### pptx - IYPT Archive

```Report 7
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
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
• Pressure-Time curve is roughly an exponential decay
• Maximum pressure: 103 kPa

P

19
kP
a
• Minimum pressure: 84 kPa
7
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
• 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
• 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
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
•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
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
(Ideal gas law)
2min
5min
1.72m
2.25m
1.69m
2.25m
8.65m
8.66m
8.42m
(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
```