A body cools from a temperature $$3T$$ to $$2T$$ in $$10$$ minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next $$10$$ minutes will be

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Infinity Learn · Accepted Answer

According to Newton's law of cooling, $$dTdt=KT-Ts$$ For two cases, $$dT1dt=KT1-Ts$$ and $$dT2dt=KT2-Ts$$ Here, $$Ts=T$$,$$T1=3T+2T2=2.5T$$ and $$dT1dt=3T-2T10=T10T2=2T+T$$'$$2$$ and $$dT2dt=2T-T$$'$$10$$ So,   $$T10=K(2.5T-T)$$………….(1)2T-T$$'$$10=K2T+T$$'$$2-T$$………$$(2)From$$ eq $$(1) & $$(2)T2T-T$$'$$=(2.5T-T)2T+T$$'$$2-T2T+T$$'$$2-T=2T-T$$'×$$32T$$'$$=32T-T$$' or, $$4T$$'$$=6T$$∴T'$$=32T$$

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

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