Transcript Case Study - Dordt College Homepages

The Art of Experimenting - A Case Study
John Zwart, Dept. of Physics and Astronomy, Dordt College, Sioux Center, IA
[email protected]
Experimental work includes making judgment calls, such as using
preliminary results to change the design of an experiment, determining
whether equipment is measuring what you think it is measuring, evaluating
whether data support a particular conclusion, and communicating results in
a convincing manner.
For most introductory labs, these judgment calls are made for you ‘behind
the scenes.’ However being able to make them is an important part of the
‘art of experimenting.’ This case study is intended to help you in
developing this understanding via questions and discussion. Please note
that some of the experiment variations presented are not necessarily the
best possible options
Introduction to the case study:
• Stumbled on cheap power meter ($32) and IR
thermometer ($22) in a surplus catalog (Sciplus.com)
• Could they by used in an experiment, relating the power
used by a light bulb to its temperature?
• Show the P = εσAT4 relation?
Initial questions:
• How can light bulb power be varied in a
controlled manner?
• What kind of light bulb should be used?
• How should the equipment be arranged?
The next slide shows one possible set up.
Set-up:
Power meter to dimmer switch to 200W clear incandescent light bulb.
Played with IR thermometer locations – horizontal 25 cm offset seemed best.
Not shown – aluminum foil shroud on thermometer to keep electronics from
overheating.
Theory and Analysis:
The power law equation P = εσAT4 describes both the
radiation away of power as well as absorption from
surroundings. In the equation:
P = power
T = temperature in Kelvin
A = surface area of the object
σ = Stefan-Boltzmann constant = 5.67 x 10-8 W/m2K4
ε = emissivity and 0 < ε < 1
In the experiment, Pin = Pelectric + Pabsorbed = Pout
Pelec = εσAT4 – εσA(Troom)4 is the expected relationship.
Question: Hard to separate A and ε. Do we need to worry
about this?
Initial results:
Power used versus temperature for a bulb filament
200
Power (W)
150
yi
 125 10 10  zi 4 ( 122)
100
50
0
 50
280
304
328
352
376
zi
T (K)
Curve represents a fit to the data of the form expected from theory.
Questions: Is it convincing that theory fits the data?
Or that it doesn’t?
Can we display the data and fit differently to clarify this?
400
Plotting measured power vs T4 should yield a straight line
with a negative intercept.
[Pelec = εσAT4 – εσA(Troom)4 ]
Good enough?
What about the curvature? Is there a valid reason for dropping data?
Are there experimental design and/or implementation problems?
What might they be?
Some Possible Problems:
-non-linear power consumption by dimmer switch
-temperature dependent convection
-system not in equilibrium when measuring temperature
How can these problems be tested?
Check the power by measuring bulb current and voltage as
well as power into dimmer + bulb combination.
Results:
Power into bulb is determined by product of current and
voltage.
Use above curve to correct the original measured power data.
Original plot
Corrected Plot – Original Data and Corrected Data
Solid boxes are ‘corrected’ data points. Open boxes are the initial results.
Now what is the problem? Am I measuring what I think I am?
Checked into operation of dimmer switches – they work by
clipping part of the 60 Hz sine wave
See: home.howstuffworks.com/dimmer-switch2.htm for a discussion.
The DMMs used to get I, V data expected 60 Hz sinusoids, so displayed values
when clipping occurs are erroneous – need to use true rms meters.
True rms meters show dimmer used negligible power.
Back to original plot.
Other problems?
-temperature dependent convection?
-system not in equilibrium when measuring
temperature?
How can these problems be addressed?
Experiment modifications
Use 150W flood lamp to limit
convection
Check time to get to equilibrium by
measuring Temp vs time.
Note: foil shroud shown on IR
thermometer here has been used
throughout all variations of the
experiment.
With dimmer set to provide maximum power to the bulb, measure
temperature as a function of time. Results below.
How long should we wait between data points?
Waiting 30 minutes to measure temperature after changing the power yields:
Are we done yet? What else can we check?
More questions:
What are we measuring temperature of? (Tmax = 105 0C)
Is assumption that Pmeter is proportional to Pwhatever OK?
Is a factor of 3 in T4 enough to convincingly show the
relation of theory and data?
A couple of checks:
Mercury thermometer against glass of bulb yields temp
close to that of the IR thermometer.
Since Pnet = εσAT4 – εσA(Troom)4
|intercept/slope| should equal (Troom)4
Values from least-squares fit yields Troom = 25 0C which is
within uncertainty of the 22 0C measured directly.
But if we find εA by dividing the slope by σ we get 0.21 m2
and 0 < ε < 1, so what does this (larger than a light bulb)
area mean? Is it an ‘effective area’ viewed by the IR
thermometer? What does that mean?
When is the experiment over????
Thanks to colleagues:
Doug De Boer for dimmer switch and true rms discussions.
Carl Fictorie for photo editing and Powerpoint advice.