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Question

A body cools from 60C to 50C in 10 minutes. If the room temperature is 25C 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
38.5C
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B
40C
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C
37.5C
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D
42.9C
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Solution

The correct option is D 42.9C
From Newton's law of cooling, we know that
θ1θ2t=k[θ1+θ22θ0]
In first 10 minutes, from the data given in the question, we can say that
605010=k[60+50225]
k=130 ......(1)
Let θ be the temperature at the end of next 10 minutes.
50θ10=k[50+θ225]
Using (1) in the above equation,
50θ10=θ60
7θ=300θ42.9C
Thus, option (c) is the correct answer.

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