Physical experiments show that the rate of change of temperature T with
respect to time
,,tdTdt of a body is proportional to the difference
between the temperature of the body (T) and that of the surrounding
medium (T
0
).
This principle is known as Newton’s Law of Cooling and is expressed
through the following fi rst order and fi rst degree differential equation:
0
()(0)
dT
kT Tk
dt
=−−>
(2.95)
Separating the variables
0
()
dT
kdt
TT
=−
−
(2.96)
Integrating, we get
0
log()logTTktc−=−+
0
()
kt
TTce
−
⇒−=
(2.97)
If T
i
is the initial temperature of the body ...
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