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A body in air at 25℃ cools from 100℃ to 75℃ in 1 minute. What is the temperature of the body at the end of 3 minutes? (Take log(1.5)=0.4)

A body in air at 25℃ cools from 100℃ to 75℃ in 1 minute. What is the temperature of the body at the end of 3 minutes? (Take log(1.5)=0.4) Correct Answer 47.5℃

By Newton’s law of cooling w.k.t T = t2 + (t1-t2) e-kt, given t1=100℃, t2=25℃ when t=1 –> T(1) = 25 + 75 e-k = 75℃ –> 50/75 = 2/3 = e-k –> 3/2=ek taking log k=log(1.5)=0.4. to find T when t=3 minute using the value of k we get T = 25 + 75e-0.4*3 = 47.5℃……e-1.2=0.3.

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