A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable, the temperature of the body at the end of next 10 minutes will be
A
43T
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B
T
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C
74T
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D
32T
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Solution
The correct option is D32T By using Newton's law of cooling, T1−T2t=k(Tavg−Ts)
Case 1: In 10 minutes it cools from 3T to 2T 3T−2T10=k((3T+2T2)−T) T10=k3T2 k=115
Case 2: In next 10 minutes it cools from 2T to some temperature T′ 2T−T′10=k((2T+T′2)−T) 2T−T′10=115T′2 6T−3T′=T′ T′=3T2