DUE at 12am [within an hour]

ECE 102

Professor Sprague’s Coffee Professor Sprague always enjoys a hot cup of coffee in the morning. Lately however, he has been overwhelmed with multiple school-related tasks that he forgets to drink his coffee before it gets too cold for his liking. He realized that certain morning tasks take priority before he can enjoy his coffee uninterrupted, so he is summoning your modeling and empirical expertise to determine how long he can devote to such tasks before his coffee becomes undrinkable.

In order to predict the time the coffee temperature drops below his preferred 110

o F threshold, you will need to research which physical law applies to this

system 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 need Starbucks regular coffee, but that can be replaced by hot water. Measure and record the temperature of the hot water for different times and plot it using

excel as a scatter plot. You should collect enough data points to accurately predict how long the coffee will stay above 110

o F be sure to include the initial temperature at t=0. How will you determine

the initial temperature of a tall cup of regular Starbucks coffee? One of these data points should be collected for a temperature value below 100

o F. On the same graph plot the temperature you

calculated from the numerical model as a solid curve for the mathematical model that best matches the experimental data. Present this model as a legend on the upper right corner of the graph and in a caption 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 include the 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 its accuracy/validity. (A picture of your experimental setup would fit nicely here.) In this section you should also discuss any possible 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 physical law and numerical method. Include any preliminary estimates of the solution and how/why they were/could be helpful.[4 points] d) Solution. Your solution should include an Excel plot with caption showing the comparison of the measured temperature (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 accuracy of the solution if you changed the timestep? Also what happens at the extremes (time = 0 and time = ∞) with your model [8 points]

Professor Sprague’s coffee, originally at an initial temperature of ______ o F, will remain

above 110 o F for about ______minutes in a room of ambient temperature of _______

o F.

The system follows the mathematical model _________________ for a domain of

__________ and a range of __________.