A body which is initially at $$800C$$ cools to $$640C$$ in $$5$$ min and to $$520C$$ in $$10$$ min. The temperature of the surrounding should be

Question

A body which is initially at $$800C$$ cools to $$640C$$ in $$5$$ min and to $$520C$$ in $$10$$ min.  The temperature of the surrounding should be

Infinity Learn · Accepted Answer

Using Newton's law of cooling∆θ∆t $$=$$ K[θ$$av-$$θ$$0$$]$$($$θ$$1-$$θ$$2t)$$ $$=$$ K[θ$$1+$$θ$$22-$$θo]In the $$1st$$ case, $$80-645$$ $$=$$ K[$$80+642-$$θo]Or $$3.2$$ $$=$$ K[$$72-$$θ$$0$$]$$-------(i)In$$ the $$2nd$$ case, $$64-525$$ $$=$$ K[$$64-522-$$θ$$0$$]or $$2.4$$ $$=$$ $$K(58-$$θ$$0)$$ $$------(ii)From$$ (i) by (ii), we get $$3.22.4$$ $$=$$ $$72-$$θ$$058-$$θ$$0Or$$ $$185.6-3.2$$θ$$0$$ $$=$$ $$172.8$$ $$-2.4$$θ$$0$$ or θ$$0$$ $$=$$ $$160C$$

A body which is initially at $80^{0} C cools to 64^{0} C in 5 \min and to 52^{0} C in 10 \min .$ The temperature of the surrounding should be

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A body which is initially at 800C cools to 640C in 5 min and to 520C in 10 min. The temperature of the surrounding should be

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A body which is initially at $80^{0} C cools to 64^{0} C in 5 \min and to 52^{0} C in 10 \min .$ The temperature of the surrounding should be