EE 2001
Fall 2008
Problem Set 13
Solution
______________________________________________________________________
Thanksgiving dinner:
The turkey went into a 325
°
oven at 9 AM on Thanksgiving day.
Dinner was planned for
1 PM, but when dinner time came, the internal temperature of the turkey was only 170
°
.
(For safety, turkey should be cooked to an internal temperature of 190
°
.)
Estimate how much longer the turkey needs to cook.
Assume that the heat transfer to the turkey (and therefore the internal temperature of the
turkey) follows a first order model, and that the turkey started at 55
°
.
Solution
temp(t) = 325 – 270 exp(t/τ)
temp(t = 4) = 325 – 270 exp(4/ τ) = 170
exp(4/ τ) = 0.5741
τ = 4/ln(0.5741)
so τ = 7.208
temp(tf) = 190 = 325 – 270 exp(tf/7.208)
tf = 7.208 ln((190325)/270) = 5
So, the turkey should be done at 2 pm
 just 1 hour late.
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 Fall '08
 Staff
 Voltage divider, ia dt

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