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A cake recipe says to bake the cake until the center is 180 degrees, then let the cake cool to 120 degrees. Given a room temperature of 70 degrees,how long does it take the cake to cool to the desired temperature?

Time (min) Temp (F)
0 180
5 126
10 94
15 80
20 73
 Mar 10, 2019
 #1
avatar+19707 
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Are you studying Newton's Law of Cooling?    I THINK this is how to solve this Q:

 

T(t) = Ta + (Ti-Ta)e^-kt       Ti = initial temp    Ta = Temp ambient

 

T(t) = 126   =  70 + (180-70) e^-k5     results in k = .1350257

 

           120 = 70+ (180-70)e^-(.1350257t)         t = 5.84 minutes   =   5 minutes 50 seconds        

 Mar 11, 2019

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