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Q.

A body cools in 7 minutes from 60^oC to 40^oC. The temperature of the surrounding is 10^oC. The temperature of the body after the next 7 minutes will be:

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a

28^oC

b

34^oC

c

32^oC

d

30^oC

answer is A.

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Detailed Solution

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$\begin{array}{l} \frac{dθ}{dr} \propto (\frac{θ_{1} + θ_{2}}{2} - θ_{0}) \\ \Rightarrow \frac{20}{40 - θ} = \frac{50 - 10}{\frac{40 + θ}{2} - 10} \\ \Rightarrow 20 + θ = 160 - 4 θ \\ \Rightarrow 5 θ = 140 \\ \Rightarrow θ = 28^{\circ} C \end{array}$

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