Question

You cook a turkey until the internal temperature reaches 180°f. the turkey is placed on the table until the internal temperature reaches 100°f, and it can be carved. when the room temperature is 72°f, the cooling rate of the turkey is $r=0.067$ . how long do you have to wait until you can carve the turkey? use newton's law of cooling to solve the problem. round your answer to the nearest whole minute.

Answer 1

The newton's law of cooling is used to determine the waiting time

You will have to wait for 20 minutes to carve the turkey

How to determine the time?

By newton's law of cooling, we have:

$T = (T_o - T_R) e^{-rt} + T_R$

From the question, we have:

T = 100°f ---- The serving temperature

To = 180°f --- The initial temperature

TR = 72°f ----- the room temperature

r = 0.067 -- the cooling rate

So, we have:

$T = (T_o - T_R) e^{-rt} + T_R$

$100 = (180 - 72) e^{-0.067t} + 72$

Subtract 72 from both sides

$(180 - 72) e^{-0.067t} = 28$

Evaluate the difference

$108 e^{-0.067t} = 28$

Divide both sides by 108

$e^{-0.067t} = 0.25923$

Take the natural logarithm of both sides

$-0.067t = -1.3500$

Divide both sides by -0.067

$t = 20.149$

Approximate

$t = 20$

Hence, you will have to wait for 20 minutes to carve the turkey

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