Need Help Newton's Law Of Cooling Fitzpatrick qu (1 Viewer)

[norez]

Hi guys. I have no idea how to do this. How do you take into account the conflicting forces? Here it is:

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 to Newton's Law Of Cooling, and the maximum temperature the body could attain is 120*C. How long would it take for the body to reach a temperature of 100*C?

Answer: 32.2 minutes.

(From New senior mathematics, J Fitzpatrick ex 25e qu 4)

Any help would be greatly appreciated

Thanks

 

[funnytomato]

dT/dt = -k (T-20) +5

 

[funnytomato]

dt/dT = 1/(-kT+20k+5)
t = ln( c*(-kT+20k+5) ) / (-k)

but at t=0, T=20 , we get c=1/5
t = ln( (-kT+20k+5)/5 ) / (-k) *

and the other condition is "the maximum temperature the body could attain is 120"
which mean T=120 at t=infinity
from * , we get T = (5e^(-kt) - 20k - 5 )/ (-k)
which means 5e^(-kt) approaches 0 as t approaches infinity
then (20k+5) / k =120, k= 1/20

then substitute k= 1/20, T=100 into *
you'd get t = -20ln(0.2) = 32.188...= 32.2 minutes

 

[Drongoski]

Brilliant funnytomato!

 

[Drongoski]

Brilliant funnytomato!

 

[norez]

Brilliant funnytomato!

Agreed! Thanks so much!

 

[funnytomato]

Brilliant funnytomato!

lol, this happened to me as well

it showed nothing after I replied , so I replied again and I ended up replying twice