A metal plate that has been heated cools from 180 F to 150 F in 20 minutes when surrounded by an air temperature of 60 F. Use Newton's Law of cooling to approximate its temperature at the end of one hour of cooling.

Thanks for your help.

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- Feb 11th 2009, 05:22 PMnystudent2729Newton's Law of Cooling
A metal plate that has been heated cools from 180 F to 150 F in 20 minutes when surrounded by an air temperature of 60 F. Use Newton's Law of cooling to approximate its temperature at the end of one hour of cooling.

Thanks for your help. - Feb 11th 2009, 05:36 PMskeeter
let $\displaystyle F$ = temperature of the plate at any time $\displaystyle t$ in minutes

$\displaystyle \frac{dF}{dt} = k(F - 60)$

separate variables and solve the differential equation using the conditions $\displaystyle F(0) = 180$ and $\displaystyle F(20) = 150$.