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Question
Two plates of same area are placed in contact. Their thickness as well as thermal conductivities are in the ratio 2 : 3. The outer surface of one plate is maintained at 10∘C and that of other at 0∘C. What is the temp.of the common surface?
Two plates of same area are placed in contact. Their thickness as well as thermal conductivities are in the ratio 2 : 3. The outer surface of one plate is maintained at 10∘C and that of other at 0∘C. What is the temp.of the common surface?
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Solution
The correct option is C 5∘C
Let A be the area of the both the plates.
Given ,
k1k2 = 23 -------(i)
where
k1 and k2 are the thermal conductivities of plate 1 and 2
respectively.
And
l1l2 = 23 ------- (ii)
where l1 and l2 are the thermal conductivities of plate 1 and
2 respectively.
Let the temperature of the common surface be T
Equating the rate of heat transfers through both the plates
k1A(10−T)L1 = k2A(T−0)L2
Using (i) and (ii)
We have ,
10−T=T−0
Hence , T=50C
Let A be the area of the both the plates.
Given ,
k1k2 = 23 -------(i)
where k1 and k2 are the thermal conductivities of plate 1 and 2 respectively.
And
l1l2 = 23 ------- (ii)
where l1 and l2 are the thermal conductivities of plate 1 and 2 respectively.
Let the temperature of the common surface be T
Equating the rate of heat transfers through both the plates
k1A(10−T)L1 = k2A(T−0)L2
Using (i) and (ii)
We have ,
10−T=T−0
Hence , T=50C
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