A body initially at $$60$$°C cools to $$50$$°C in $$10$$ min. What will be its temperature at the end of next $$10$$ min. if the room temperature is $$25$$°C. Assume Newton's law of cooling

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Infinity Learn · Accepted Answer

According to Newton s law of cooling $$dTdt=$$−kT−$$T0where$$ T $$=$$ temperature of body and To $$=$$ temperature of surroundingsNow   ∫$$T1T2$$ dTT−$$T0=$$−k∫$$0t$$ dt      loge⁡T−$$T0T1T2=$$−k[t]$$0tor$$   loge⁡ $$T2$$−$$T0T1$$−$$T0=$$−ktor    loge⁡$$60$$−$$2550$$−$$25=$$−k×(10$$×$$60)       ...(1)Let$$ T' be the temperature at the end of $$10$$ min. In this case,     loge⁡$$50$$−$$25T$$′−$$25=$$−k×$$(10$$×$$60)             ...(2)Solving$$ eqs. $$(1) and (2), we get    T′$$=42$$⋅$$85$$∘C

A body initially at 60°C cools to 50°C in 10 min. What will be its temperature at the end of next 10 min. if the room temperature is 25°C. Assume Newton's law of cooling

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