The general form for Newton's Law of Cooling is...
if my memory serves my correctly.
Hi, I have tried this many times and just can't seem to figure it out.
A body, initially at room temperature 20C, is heated so that its temperature would rise by 5C/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 120C. How long would it take to reach a temperature of 100C?
using dt/dt = -k(T - P) where T is the current temp and P is the temp of the surrounding medium.
any help wouuld be appreciated, thanks
the answer provided is 32.2 mins
The rate of change of temperature is the sum of the heating component andOriginally Posted by jacs
the cooling component.
So in this case:
The on the RHS is the contribution to the rate of change of
temp from the heating, the rest is the contribution to the rate of change of
temp due to the cooling (the is the temp of the surrounding
medium).
At a temp of the rate of change of temp is zero, so:
.
Hence:
,
which is a DE of variables separable type, so:
.
Hence:
,
so:
again:
Putting into this will allow you to find the corresponding
.
RonL