## Question

An ice-box is made of wood 1.75 cm thick, lined inside with cork 2 cm thick. If the temperature of the inner surface of the cork is steady at 0^{o}C and that of the outer surface is steady at 12^{o}C, what is the temperature of the surface? The thermal conductivity of wood is 5 times that of cork.

### Solution

10.2^{o}C

Let *T *be the temperature of the interface in the steady state. Since the rate of flow of heat through wood and cork must be the same in the steady state, we have

Where *S* is the area of the interface. Thus we have

Or

Which gives *T = *10.2^{o}C

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