2018 BFY III Abstract Detail Page
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||W06: Transient Heat Conduction in a Rod: Priceless Skills for $25
||The bottom of a rod, which may be a simple nail, is dipped in ice water. Temperature sensors superglued to the rod are wired to an Arduino. A Python script is used to plot temperatures in real time and then fit the data with a complicated theoretical equation (a truncated infinite series in which each term requires the numerical solution of a different transcendental equation; details are in Brody and Brown, AJP vol. 85, pp. 582-586). The temperature drops almost immediately in the lower positions and is well fit by the first term in the series (exponential decay from initial temperature to final steady-state temperature). Higher up the rod, however, the temperature remains constant for some time after the bottom of the rod enters the ice water, and the fit may require more than just the first term in the series.
Students learn broadly applicable experimental skills (wiring sensors to an Arduino and averaging rapidly repeated measurements in Arduino), computational skills (real-time data plotting, curve fitting, and numerical solutions in Python), and theoretical skills (Fourier series to solve a partial differential equation derived from thermodynamic analysis of an infinitesimal volume element).
All the necessary software is free. Besides standard equipment (nails, superglue, breadboard, wires, support rod, clamps, computer), this experiment requires only a ~$20 Arduino Uno, a $2 USB cable, and a $2 temperature sensor. For a more deluxe version, add a $3 steel rod and a couple more $2 temperature sensors. For a simpler version that online students can perform at home, forego the support rod and clamps, and tape the breadboard to the wall.
According to the instructor's interests, the students' background, and the time available, this experiment can be a long-term project or a quick lab. For a long-term project, students can be guided to develop the theoretical equations, Arduino sketches, and Python scripts. For a quick lab, students can be given all the necessary tools.
For more information, please see http://www.physics.emory.edu/faculty/brody/transient_heat.html, where the second paragraph explains how to install the Arduino and Python software. Please install the software on your laptop if you'll have it at the workshop. (A limited number of computers will be available if you don't bring your own.)
N201 Math&Science Center
400 Dowman Dr
Atlanta, GA 30322