Exp Growth/Decay (1 Viewer)

[Jago]

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

Ans - 32.2min

I had no idea how to do this question. Help anyone?

 

[maths > english]

solution attached

 

[Jago]

ta.

p.s. nice handwriting

also, is this considered to be a hard growth/decay question? because i would never be able to reproduce that in an exam :/

 

[StGeorgeDragons]

where does the dT/dt, equation come from?

 

[KFunk]

Newton's law of cooling.

T = P + Ae^-kt

where T is the temperature of the object, P is the temperature of the surroundings and A is the difference (T - P)

Since T = P + Ae^-kt then dT/dt = -kAe^-kt [ where Ae^-kt = T - P]
hence dT/dt = -k(T - P)

In this case there's a +5 variant since the object is radiating heat while being heated.