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Two walls of thickness d1 and d2 and thermal conductivities K1 and K2 are in contact. In the steady state, if the temperatures at the outer surfaces are T1 and T2 the temperatures at the common wall is

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a
K1T1d2+K2T2d1K1d2+K2d1
b
K1T1+K2T2d1+d2
c
K1d1+K2d2T1+T2T1T2
d
K1T1d1+K2T2d2K1d1+K2d2

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detailed solution

Correct option is A

Let the temperature of common wall be T. ThenK1AT1−Ttd1=K1AT−T1td2K1T1−Td1=K2T−T2d2d2K1T1−T=d1K2T−T2K1T1d2−K1d2T=d1K2T−d1K2T2K1T1d2+K2T2d1=TK1d2+d1K2T=K1T1d2+K2T2d1K1d2+K2d1


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