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Question

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T2 and T1(T2>T1). The rate of heat transfer through the slab, in a steady state is (A(T2−T1)KX)f, with f equals to

41617_6b7030c7795d40ab984fe11875b03173.png

A
1
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B
1/2
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C
2/3
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D
1/3
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Solution

The correct option is D 1/3
The thermal resistance of both the blocks will be

xKA and 4x2KA=2xKA respectively. Since the two resistors are in series, (as same heat current will flow through both), equivalent thermal resistance will be

Req.=xKA+2xKA=3xKA

Thus, heat current will be

dQdt=T2T1Req.=13KA(T2T1)x

Hence, f=13

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