Question
Asked Dec 12, 2019
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When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round your answers to two decimal places.)

(a) What is the temperature of the drink after 30 minutes?
°C

(b) When will its temperature be 12°C?
min
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Expert Answer

Step 1

(a)

According to Newton’s law of cooling, says that the temperature follows differential equation.

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ат =k(T – 20) dt

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Step 2

Solve the differential equation with the given conditions and rewrite the equation.

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dT = kdt (T – 20) dT (7-20)kat In(T – 20) = kt +C T(t)=20+Ce* ..(1)

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Step 3

Apply the initial condition T(0)=5

Now...

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5= 20+ Ce*0) 5 = 20+C C =-15 T(t)= 20 – 15e* ..(2)

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