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Question

A bucket full of hot water cools from 75C to 70C in time T1, from 70C to 65C in time T2 and from 65C to 60C in time T3. Then:

A
T1=T2=T3
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B
T1>T2>T3
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C
T1<T2<T3
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D
T1>T2<T3
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Solution

The correct option is C T1<T2<T3
From Newton's law of cooling, we know that,
θ1θ2T(θ1+θ22θ0)
where T is the time taken for cooling.
From the data given in the question, we find θ1+θ22 in every case.
(θ1+θ22)1>(θ1+θ22)2>(θ1+θ22)3
[i.e 72.5C>67.5C>62.5C]
and θ1θ2=5C is the same in all cases,
we can say that, T1<T2<T3.
Hence, option (c) is the correct answer.

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