Question

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, Too is the ambient tem- perature and k is a constant 2. Solve the ODE for T(t) given the cup of coffee is initially 90°C and the 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 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: Tt Sin 3 12 Solve for T(t)

Answer 1

d T dt ns . ct ② T… = 2ỢC , T=go.at t=0 un (23) = ーらナ In 65 冶 2 3 2 3 CS Scanned with CamScanner