A body is allowed to cool in still air. Its temperature falls from $70^{o} C$ to $64^{o} C$ in 5 minutes and then from $64^{o} C$ to $60^{o}$ in another 5 minutes. Assuming Newton's Law of cooling is valid, find the temperature of air.

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$52^{o} C$

$48^{o} C$

$56^{o} C$

$42^{o} C$

answer is D.

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Detailed Solution

$\frac{70 - 64}{5} = C (\frac{70 + 64}{2} - θ_{0})$

and $\frac{64 - 60}{5} = C (\frac{64 + 60}{2} - θ_{0})$

$∴ \frac{6}{4} = \frac{67 - θ_{0}}{62 - θ_{0}} \Rightarrow θ_{0} = 52^{o} C$

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