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AIEEE 2005 Physics Solved Paper
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© examsnet.com
Question : 28
Total: 74
The figure shows a system of two concentric spheres of radii
r
1
and
r
2
are kept at temperatures
T
1
and
T
2
, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
In
(
r
2
r
1
)
(
r
2
−
r
1
)
(
r
1
r
2
)
(
r
2
−
r
1
)
r
1
r
2
(
r
2
−
r
1
)
Validate
Solution:
Consider a shell of thickness
(
d
r
)
and of radius
(
r
)
and the temperature of inner and outer surfaces of this shell be
T
,
(
T
−
d
T
)
H
=
K
A
[
(
T
−
d
T
)
−
T
]
d
r
=
−
K
A
d
T
d
r
H
=
−
4
π
K
r
2
d
T
d
r
as
A
=
4
π
r
2
)
Then,
(
H
)
r
2
∫
r
1
1
r
2
d
r
=
−
4
π
K
T
2
∫
T
1
d
T
H
[
1
r
1
−
1
r
2
]
=
−
4
π
K
[
T
2
−
T
1
]
or
H
=
−
4
π
→
K
r
1
r
2
(
T
2
−
T
1
)
(
r
2
−
r
1
)
© examsnet.com
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