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dav/pid-7929239-dt-content-rid-23585314 1/courses/EGD126 1913TP1 Part A (Based off week 4/5 Workshop content) It has been proposed that the ideal temperature for producing a coffee is 90°C. However, this is too hot to enjoy the beverage. After completing the week 5 workshop content, it is up to you to mathematically model how a coffee cup's temperature varies over time. 1. Consider a hot cup of coffee. The temperature in the coffee cup will decrease at a rate proportional to the difference in the current tem- perature and the ambient temperature. Based on this statement, show how we can model our coffee cup with the ODE dT dt where T is the temperature of the coffee cup, T is the ambient tem- 2. Solve the ODE for T(t) given the cup of coffee is initially 90°C and th 3. The coffee cup takes 10 minutes (t = 1/6) to drop to 48 degrees. Using 4. Using MATLAB, plot the temperature of the coffee cup against time. perature and k is a constant. ambient temperature is a constant 25°C. Leave k as unknown. this information, calculate the cooling coefficient k. Comment on whether the plot is correctly modeling the temperature of the coffee cup and provide reasoning as to why (Hint: there are three observations you should be able to comment on!). 5. You buy another 90C coffee and use the same cup (ie. same k value). but are outside where the ambient temperature can be approximated as: nt Tc(t) = 7 sin (12) + 25 Solve for Tt

Answer 1

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