How Does Newton's Law of Cooling Predict Time for Temperature Changes?

AI Thread Summary
Newton's Law of Cooling states that the rate of temperature change of an object is proportional to the difference between its temperature and the ambient temperature. In this scenario, a container of hot water cools from 80°C to 79°C in 15 seconds in a 20°C room. To estimate the time for the water to cool from 70°C to 69°C, the temperature difference decreases, leading to a longer cooling time. Similarly, the cooling time from 30°C to 29°C will also be longer due to the smaller temperature difference. Accurate calculations require applying the law properly to determine the time intervals for these temperature changes.
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Homework Statement


A container of hot water at 80°C cools to 79°C in 15 seconds when it is placed in a room that is at 20°C. Use Newton's law of cooling to estimate the time it will take for the container to cool from 70°C to 69°C.
And still later, from 30°C to 29°C.



Homework Equations


rate~change in temp.



The Attempt at a Solution


15*1.125=18.75 (incorrect)
 
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Look after Newton's law of cooling.

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