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  4. A body cools from 60° C to 40° C in 6 minutes. If, temperature of surroundings is 10° C. Then, after the next 6 minutes, its temperature will be ° C.

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Q. A body cools from $60^{\circ} C$ to $40^{\circ} C$ in $6$ minutes. If, temperature of surroundings is $10^{\circ} C$. Then, after the next $6$ minutes, its temperature will be ___${ }^{\circ} C$.

JEE MainJEE Main 2023Thermal Properties of Matter

Solution:

By average form of Newton's law of cooling
$ \frac{20}{6}=k(50-10) .....$(i)
$ \frac{40- T }{6}= K \left(\frac{40+ T }{2}-10\right)....$(ii)
From equation (i) and (ii)
$\frac{20}{40- T }=\frac{40}{10+ T / 2} $
$10+\frac{ T }{2}=80-2 T$
$ \frac{5 T }{2}=70 \Rightarrow T =28^{\circ} C$