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Question

A body cools in 7 minutes from 60C to 40C. What will be its temperature after next 7 minutes, if the temperature of the surroundings is 10C?

A
20C
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B
24C
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C
28C
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D
35C
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Solution

The correct option is C 28C
Given that,
Temperature of surrounding, θo=10
θ1=60
θ2=40
Time taken to change from θ1 to θ2=7 min

According to Newton's law of cooling dθdt=K(θθ0)
t0dt=1Kθ2θ1dθ(θθ0)
t=1Kloge[θ1θθ2θ]
When temperature changes from 60 to 40
7=1Kloge[60104010] ...(i)
Let the the temperature after next 7 minutes is θ
7=1Kloge[4010θ10] ...(ii)
From equation (i) and (ii)
log5030=log30θ10
53=30(θ10)θ=28C
Hence, option, (c) correct

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