Report 7Two flasks

Team Taiwan

Franklin Liou

2

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?

3

Overview• Introduction• Experiment– Experimental Setup– Experiment

• Results and Discussion• Conclusions & Summary

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Experiment Setup

•1300ml flask (200ml water)•Hot plate•Oil bath (for heating dry flask)

The heating apparatus and sensors•Pressure sensor•Thermocouple

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Experiment Setup

Transparent tube and long ruler

Water reservoir

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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

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Experiment Results: Dry Flask

• Height-Time curve is roughly a saturation curve

• Maximum height: 1.72m

0 200 400 600 800 1000 1200 1400 1600 18000

20406080

100120140160180200

dry, 2min dry, 5min

heigh

t (m

)

time (s)

•Temperature-Time curve is roughly an exponential decay•Max: 103oC, Min:31oC•Decay rate:0.0026

0 300 600 900 1200 1500

40

60

80

100 Dry, 2min Dry, 5min exp fit

Tem

pera

ure

(o C)

Time (s)

Dry Flask after heated at 100 oC for 2 minutes

Experiment Results: Dry Flask

• Pressure-Time curve is roughly an exponential decay• Maximum pressure: 103 kPa• Minimum pressure: 84 kPa

8

19P kPa

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Experiment Results: Wet Flask

0 500 1000 1500 2000 2500 3000 3500 400030

40

50

60

70

80

90

100

wet, 1min wet, 2min wet, 5min

Tem

pera

ture

(o C)time (s)

0 500 1000 1500 2000 2500 3000 35000

2

4

6

8

10

wet, 1min wet, 2min wet,5min

heigh

t (m

)

time (s)

• Height-Time curve is roughly a saturation curve

• Maximum height: 8.6m

•Temperature-Time curve is roughly an exponential decay•Max: 100oC, Min:31oC•Decay rate:0.0011

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Experiment Results: Wet Flask

• Pressure-Time curve is roughly an exponential decay

• Maximum pressure: 101 kPa• Minimum pressure: ~ 5 kPa

96P kPa

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Results and Discussion

dT T Hdt

tR H RT t T T T e

31.5 304.5oRT C K

71.5H RT T K We can obtain the decay rate , and hence the approximate T(t) function

0 300 600 900 1200 1500

40

60

80

100 Dry, 2min Dry, 5min exp fit

Tem

pera

ure

(o C)

Time (s)

Dry Flask after heated at 100 oC for 2 minutes

•Newton’s Law of Cooling:

Square of residual: 0.99974

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Dry flask• Ideal gas law: expansion of dry air~1900Pa

PV nRT 0 0 1V hA P h g n RT

•V0: initial volume•P0:initial pressure•N1: initial mole of gas

h h

•A cross section of tube•R: Ideal gas constant•T: temperature at a given time

0( ) th t h B C De

tR H RT t T T T e

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Dry Flask Results

0 300 600 900 1200 1500

0.5

1.0

1.5

2.0

2.5

Heated for 5 min

Hei

ght (

m)

Time (s)

Heated for 2 min

Ideal Gas Assumption

H=64.86-5.00*Sqrt(159.67+7.36*Exp(-0.0312t))

0( ) th t h B C De

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Wet flask

5132exp 20.386 ot

R H R

P h gT T T e

•Antoine equation:

•Assuming water vapor replaces all air

0( ) expexp( / )Dh t h B C

E F t G

•Water vapor can fill almost all volume -> condense -> large pressure difference~101300Pa

5132exp 20.386P kT

133.3 , ( , )k Pa T in K P in Pa

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Wet Flask Results

0 500 1000 1500 2000 2500 3000 35000

2

4

6

8

10

wet, 1min wet, 2min wet,5min

heigh

t (m

)

time (s)

0( ) expexp( / )Dh t h B C

E F t G

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Comparison of Wet and Dry Flask

0 500 1000 1500 2000 2500 3000 3500

0

2

4

6

8

10

wet, 1min wet, 2min wet, 5min dry, 2min dry, 5min

heigh

t (m

)

time (s)

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Results and Discussion

Time span of boiling at100oC/ maximum height

1min 2min 5min

Dry Flask 1.72m 1.69mTheoretical Dry Flask (Ideal gas law)

2.25m 2.25m

Wet Flask 8.65m 8.66m 8.42mTheoretical Wet Flask (Antoine equation)

9.12m 9.12m 9.12m

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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

0 500 1000 1500 2000 2500 3000 3500

0

2

4

6

8

10

wet, 1min wet, 2min wet, 5min dry, 2min dry, 5min

heigh

t (m

)

time (s)

• Maximum water height and water rising speed is independent of time of heating

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0 300 600 900 1200 1500

0.5

1.0

1.5

2.0

2.5

Heated for 5 min

H

eigh

t (m

)

Time (s)

Heated for 2 min

Ideal Gas Assumption