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ECE 102
Professor Sprague’s Coffee

Professor Sprague always enjoys a hot cup of coffee in the morning. Lately however, he has beenoverwhelmed with multiple school-related tasks that he forgets to drink his coffee before it gets toocold for his liking. He realized that certain morning tasks take priority before he can enjoy his coffeeuninterrupted, so he is summoning your modeling and empirical expertise to determine how long hecan devote to such tasks before his coffee becomes undrinkable.In order to predict the time the coffee temperature drops below his preferred110oF threshold, you will need to research which physical law applies to thissystem of coffee-and-cup. Based on this model you will construct a numerical
model using excel to compute the temperature as a function of time. To determine the model you will perform a simple experiment that will require a
Starbucks “Tall” coffee cup, a common household thermometer and a watch,
preferably a digital one that displays seconds. Ideally, you will also needStarbucks regular coffee, but that can be replaced by hot water. Measure andrecord the temperature of the hot water for different times and plot it usingexcel as a scatter plot. You should collect enough data points to accurately predict how long thecoffee will stay above 110oF be sure to include the initial temperature at t=0. How will you determinethe initial temperature of a tall cup of regular Starbucks coffee? One of these data points should becollected for a temperature value below 100oF. On the same graph plot the temperature youcalculated from the numerical model as a solid curve for the mathematical model that best matchesthe experimental data. Present this model as a legend on the upper right corner of the graph and in acaption placed below your plot describing what the figure shows.
 
Report Guidelines:
Your report should be a PDF file; submitted in Canvas with this problem statement as the cover sheet and should includethe following:a) Problem Definition. In one to two sentences describe the problem objectives.  [4 points]b) Data Collection. Present all data given and collected, describe how you collected it and how you verified itsaccuracy/validity. (A picture of your experimental setup would fit nicely here.) In this section you should also discuss anypossible errors associated with your experimental data and how you would/did attempt to minimize them. [4 points]c) Analysis method. Describe the model you used to predict the temperature as a function of time including the physicallaw and numerical method. Include any preliminary estimates of the solution and how/why they were/could be helpful.[4points]d) Solution. Your solution should include an Excel plot with caption showing the comparison of the measuredtemperature (as single points) and the numerical model (solid curve), Coefficient of Determination (R
2
) for your model, the
excel worksheet and the following text box (copy and paste) completed. [20 points]
e) Verification. Justify the validity of your results, e.g. does your response in the text box make sense? In this section you
should describe how you chose the timestep, t for the numerical model. Are there any possible effects to the accuracyof the solution if you changed the timestep? Also what happens at the extremes (time = 0 and time = ∞) with your model 
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