A can of coke is taken from a refrigerator set at 40 degrees F and lef ton the k

Question

A can of coke is taken from a refrigerator set at 40 degrees F and lef ton the kitchen table. When you come home from work at 5pm, you grab the can and see that it is still full and begin wondering how long it has been there. You immediately find that the temperature is 52 degrees F then one hour later you find its temperature has increased to 56 degrees F. The temperature in the room is controlled 65 degrees F. use Newtons law of cooling to set up a differential equation for the temperature of this can at any time t. sole this differential equation and estimate the time the can was taken from the refrigerator.

Explanation / Answer

dT/dt = -4,

dT/dt = -k(T-Tm), so
dT/(T-Tm) = -kdt
set T-Tm to u,dT= du, so
?du/u = - k?dt
ln u - ln u0 = -kt
ln (T-Tm) - ln(T0-Tm) = -kt
ln(56-65) - ln(52-65) = -k(1)
k = 0.3677

Now ln [(56-40)/(65-40)] = -0.3677 t
t = 1.21 hours

the time the can was taken from the refrigerator = 5-1.21 = 3:39 pm

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