#364 A cake is removed from an oven

A cake is removed from an oven - Math

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Free Chegg Question

A cake is removed from an oven at 210°F and left to cool at room temperature, which is 70° F. After 30 min the temperature of the cake is 140°F. When will it be 100°F?

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Free Chegg Answer

1. Step 1 of 2

   By ’s law of cooling, the time rate of change of the temperature of a body immersed in a medium of constant temperature A is proportional to the difference A – T.

   

    ---- (1) where k is the proportionality constant

   In the given case, t is in minutes.

    

   We have

   Equation (1) becomes

   

   By separate the variable we solve the differential equation and the solution is.

   

   Since,

   So we have C = 210 – 70 = 140.

    --- (2)

2. Step 2 of 2

   It is given that T = 140 when t = 30.

   From (2), we have

   

   

    

   Thus.

   Now, substitute T =100 in equation (2) and solve for t.

   

   The temperature will be 100⁰F after 66 min.