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°C and that of the outer surface is steady at ${12}^{\circ }C$, what is the temperature of the interface? The thermal conductivity of wood is 5 times that of cork.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

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

$\frac{k_{w}S(T_w-T)}{d_w}=\frac{k_{c}S(T-T_c)}{d_c}$

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

$\frac{T_w-T}{T-T_c}=\frac{d_w}{d_c}.\frac{k_c}{k_w}Or\frac{12-T}{T-0}=\frac{1.75}{2}\times \frac{1}{5}$

Which gives $T={10.2}^{\circ }C$