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KEAM 2018 Physics and Chemistry Paper
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© examsnet.com
Question : 39
Total: 120
A uniform copper rod of 50 cm length is insulated on the sides, and has its ends exposed to ice and steam respectively. If there is a layer of water 1 mm thick at each end, the temperature gradient (in °C
m
−
1
) in the bar is (Assume that the thermal conductivity of copper is 400
Wm
−
1
K
−
1
)
60
40
50
55
65
Validate
Solution:
Given,
K
c
=
400
W
M
−
1
K
−
1
K
w
=
0.4
W
M
−
1
K
−
1
θ
1
=
100
∘
C
,
θ
2
=
0
∘
C
In steady state, flow of heat will be same throughout the whole system
K
w
A
(
100
−
θ
)
10
−
3
=
K
c
A
(
θ
−
θ
)
(
50
/
100
)
or
(
100
−
θ
)
=
K
c
K
w
×
10
−
3
×
(
θ
−
θ
)
0.5
=
400
0.4
×
10
−
3
×
(
θ
−
θ
)
0.5
(
100
−
θ
)
=
2
(
θ
−
θ
)
⇒
(
100
−
θ
)
=
2
(
θ
−
100
+
θ
)
(
∵
100
−
θ
=
θ
′
given
)
or
(
100
−
θ
)
=
4
θ
−
200
⇒
5
θ
=
300
⇒
θ
=
60
∘
C
∴
θ
′
=
100
−
θ
=
100
−
60
=
40
∘
C
Hence, temperature gradient along the bar
=
θ
−
θ
′
0.5
=
60
−
40
0.5
=
40
∘
c
m
© examsnet.com
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