# Thread: Cooling of a body.

1. ## Cooling of a body.

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

Thanks

2. Originally Posted by noobonastick

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

Thanks
the question seems vague. do we heat the body to 120 and then just leave it to cool? where is the body placed while it is cooling down?

3. sorry, thats the whole question, if it helps, the answer is 32.2 minutes

4. Originally Posted by noobonastick

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

Thanks
Start by solving the differential equation

$\displaystyle \frac{dT}{dt} = 5 - k (T - 20)$

subject to the following conditions:

1. T = 20 when t = 0.

2. $\displaystyle \lim_{t \rightarrow +\infty} T = 120$.

Note that k is a positve constant whose value needs to be found using the above conditions.

5. I think JHevon was interpreting the question as "Heat the body to 120 degrees then how long does it take to cool to 100 degrees?" I agree with mr fantastic.

"A reputation beyond repute"?? What does that mean?

Oh, well. I used to be "a name known to all". Didn't care for that at all. I mean, "Jack the Ripper" is a "name known to all"!