Report

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