Newton's Law Of Cooling question from old New Senior Mathematics 3UNIT (1 Viewer)

McRafi9

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Ex25(e) page 129 Q4. old New Senior Mathematics 3UNIT

A body, initially at room temperature 20°C, is heated so that its temperature would rise by 5°C/min if no cooling took place. Cooling does occur in accordance with Newton's Law of Cooling and the maximum temperature the body could attain is 120°C. How long would it take to reach a temperature of 100°C?

Please explain like I am not smart. I can do the basic Law of Cooling questions, but I have no idea how to even approach this one.
 
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Mahan1

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Ex25(e) page 129 Q4. old New Senior Mathematics 3UNIT

A body, initially at room temperature 20°C, is heated so that its temperature would rise by 5°C/min if no cooling took place. Cooling does occur in accordance with Newton's Law of Cooling and the maximum temperature the body could attain is 120°C. How long would it take to reach a temperature of 100°C?

Please explain like I am not smart. I can do the basic Law of Cooling questions, but I have no idea how to even approach this one.
Well


Using the Newton's law:



We want to find the time it takes for for the body temp reaches 100, so assume for some t, T(t) =100:



 

McRafi9

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Well


Using the Newton's law:



We want to find the time it takes for for the body temp reaches 100, so assume for some t, T(t) =100:




Answers say 32.2 min. ln(5)/5 = 0.322 (3d.p.). Why do we need to multiply by 100?
 

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