A body cools from 60∘C to 50∘C in 10 minutes. If the room temperature is 25∘C and assuming that Newton's law of cooling holds good, the temperature of the body at the end of the next 10 minutes will be:
A
38.5∘C
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B
40∘C
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C
37.5∘C
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D
42.9∘C
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Solution
The correct option is D42.9∘C From Newton's law of cooling, we know that θ1−θ2t=k[θ1+θ22−θ0]
In first 10 minutes, from the data given in the question, we can say that 60−5010=k[60+502−25] ⇒k=130......(1)
Let θ be the temperature at the end of next 10 minutes. ⇒50−θ10=k[50+θ2−25]
Using (1) in the above equation, 50−θ10=θ60 ⇒7θ=300⇒θ≈42.9∘C
Thus, option (c) is the correct answer.