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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
2-74 Diff erential Equations
2.2 APPLICATIONS OF ORDINARY DIFFERENTIAL
EQUATIONS
Newton’s Law of Cooling
Physical experiments show that the rate of change of temperature T with
respect to time
,,tdT dt 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 T k
dt
=− >
(2.95)
Separating the variables
0
()
dT
kdt
TT
=−
(2.96)
Integrating, we get
0
log( ) logTT kt c−=−+
0
()
kt
TT ce
⇒− =
(2.97)
If T
i
is the initial temperature of the body ...
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Publisher Resources

ISBN: 9781299487406Publisher Website