# Math Help - newton's law of cooling problem..

1. ## newton's law of cooling problem..

Hi all,

having trouble trying to solve the following problem,

A duck is taken out from the fridge, where its temp is 4C, and placed in an oven where the temp is 180C. 40 min later, the thermometer shows the temp of the duck is 32C. if the duck is cooked till its temp reaches 60C, using newton's law of cooling (where now we are heating) to find the total time the chicken should be in the oven.

Thanks,

2. ## Re: newton's law of cooling problem..

Originally Posted by Oiler
Hi all,

having trouble trying to solve the following problem,

A duck is taken out from the fridge, where its temp is 4C, and placed in an oven where the temp is 180C. 40 min later, the thermometer shows the temp of the duck is 32C. if the duck is cooked till its temp reaches 60C, using newton's law of cooling (where now we are heating) to find the total time the chicken should be in the oven.

Thanks,
First do you know what Newton's law of cooling is? It states that the change in temperature is proportional to the difference in the temp of the enivorment and the object.

Let $T$ be the temp of the Duck then you get

$\frac{dT}{dt}=k(T-T_{0})$

So this gives the D.E

$\frac{dT}{dt}=k(T-180)$

With an intial condition $T(0)=4$ and to determine the proportionality constant we use $T(40)=32$