Q.
A composite slab consists of two slabs A and B of different materials but of the same thickness placed in contact as shown in figure. The thermal conductivity of A and B are k1 and k2 respectively. A steady temperature difference of 12∘C is maintained across the composite slab. If k1=k22, the temperature difference across slab A will be:
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a
4∘C
b
8∘C
c
12∘C
d
16∘C
answer is B.
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Detailed Solution
Let temperature of junction be To∘CTemperature difference across slab A=T1−To∘CTemperature difference across slab B=To−T2∘CSince both slabs are connected in series, heat current through both will be equal k1AT1−T0l2=k2ATo−T2l2 As k1=k22⇒k22T1−To=To−T2k2⇒T1−To=2To−2T2⇒T1+2T2=3T0….(1) As T1−T2=12∘C⇒T2=T1−12…..(2) From (1) and (2), we get ⇒T1+2T1−12=3To⇒3T1−24=3T0⇒T1−T0=8∘C
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