ERIC Number: EJ1411113
Record Type: Journal
Publication Date: 2024
Pages: 12
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: EISSN-1464-5211
Cooling the Perfect Cup with Laplace
International Journal of Mathematical Education in Science and Technology, v55 n2 p212-223 2024
After waiting in a long line for your favourite cup of coffee, you finally sit down with your mug and find that the coffee is still scalding hot! How long do you need to wait before you can enjoy it? Once it cools enough, how much time do you have to enjoy it? Are there ways to speed up the process? These questions motivate the presented modelling scenario about tracking the temperature of a cup of coffee as it cools. Students are put in the role of an inquisitive coffee enthusiast who does their due diligence in preventing burns and carefully experimenting on their coffee so that they, and others to come, can enjoy that perfect cup. They identify their assumptions and interventions before developing model differential equations for each case, which force discontinuities on the derivative and even on the solution itself. Being familiar with basic Laplace transforms and learning key properties of the unit step and unit impulse functions, they solve these differential equations and compare the interval of time when the coffee will be at its peak level of enjoyment. This paper includes an implementation guide, grading rubric, example solutions, and example assessment questions.
Descriptors: Heat, Thermodynamics, Science Experiments, Food, Time, Decision Making, Mathematical Concepts, Mathematical Logic, Creativity, Fractions, Student Projects
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A