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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 The Art of Experimenting - A Case Study John Zwart, Dept. of Physics and Astronomy, Dordt College, Sioux Center, IA zwart@dordt.edu

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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 = εσAT 4 relation?

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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.

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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.

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Theory and Analysis: The power law equation P = εσAT 4 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/m 2 K 4 ε = emissivity and 0 < ε < 1 In the experiment, P in = P electric + P absorbed = P out P elec = εσAT 4 – εσA(T room ) 4 is the expected relationship. Question: Hard to separate A and ε. Do we need to worry about this?

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Initial results: 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?

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Plotting measured power vs T 4 should yield a straight line with a negative intercept. [P elec = εσAT 4 – εσA(T room ) 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?

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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?

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Check the power by measuring bulb current and voltage as well as power into dimmer + bulb combination.

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Results : Power into bulb is determined by product of current and voltage. Use above curve to correct the original measured power data.

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Original plot

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Corrected Plot – Original Data and Corrected Data Now what is the problem? Am I measuring what I think I am? Solid boxes are ‘corrected’ data points. Open boxes are the initial results.

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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.home.howstuffworks.com/dimmer-switch2.htm 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.

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Other problems? -temperature dependent convection? -system not in equilibrium when measuring temperature? How can these problems be addressed?

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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.

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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?

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Are we done yet? What else can we check? Waiting 30 minutes to measure temperature after changing the power yields:

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More questions: What are we measuring temperature of? (T max = 105 0 C) Is assumption that P meter is proportional to P whatever OK? Is a factor of 3 in T 4 enough to convincingly show the relation of theory and data?

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A couple of checks: Mercury thermometer against glass of bulb yields temp close to that of the IR thermometer. Since P net = εσAT 4 – εσA(T room ) 4 |intercept/slope| should equal (T room ) 4 Values from least-squares fit yields T room = 25 0 C which is within uncertainty of the 22 0 C measured directly. But if we find εA by dividing the slope by σ we get 0.21 m 2 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?

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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.

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