A slab consists of two parallel layers of copper and brass of same thickness and having thermal cond

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10-2.Transmission of Heat

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A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$ . If the free face of brass is at ${100^o}C$ and that of copper at $0^\circ C $, the temperature of interface is ........ $^oC$

A

$80$

B

$20$

C

$60$

D

$40$

(IIT-1981)

Solution

(a) Temperature of interface $\theta = \frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$

$(\because \,\frac{{{K_1}}}{{{K_2}}} = \frac{1}{4} \Rightarrow \,\,If\,\, K_1 = K \,\,then \,\,K_2 = 4K)$

==> $\theta = \frac{{K \times 0 + 4K \times 100}}{{5\,K}}$= $80°C$

Standard 11

Physics

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