Your Thanksgiving turkey has been in the refrigerator for several days and has a

Question

Your Thanksgiving turkey has been in the refrigerator for several days and has a uniform temperature of 40 degree 7. After preheating your oven to 325 degree F, you place the turkey in the oven. Twenty minutes later, a meat thermometer gives the temperature of the turkey to be 60 degree F. Set up die ODE and give the two additional conditions that model this scenario. Determine the exact length of tune that the turkey should be in the oven to reach a temperature of 185 degree F. Give an appropriate approximation of this tune.

Explanation / Answer

a) ODE according to newton's law of cooling is

dT/dt = -k(T-Ta)

Ta = ambiance temp = 325 F , at t= 0 , T = 40 F and condition 2: at t = 20 , T = 60 F

solving ODE , we have

T(t) = Ta +(To-Ta) *e^(-kt)

60 = 325 +(40-325)*e^(-k*20) , solving for K , we get

k = 0.003638

b) 185 = 325 + (40-325)*e^(-0.003638*t) ,

solving for t , we get t = 195.395 minutes

c) approximation is t = 195 minutes

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