Question

Two sheets of thickness $d$ and $2d$ and same area are touching each other on their face. Temperature $T_A,T_B,T_C$ shown are in geometric progression with common ratio $r=2$. Then ratio of thermal conductivity of thicker sheet to thinner sheet is

Answer 1

Given that
$\frac{T_A}{T_B}=2,\frac{T_B}{T_C}=2\text{As heat transfered along both the sheets remains same}\Rightarrow \frac{K_{1}A(T_A-T_B)}{d}=\frac{K_{2}A(T_B-T_C)}{2d}\Rightarrow \frac{K_1(2T_B-T_B)}{d}=\frac{K_{2}A(T_B-\frac{T_B}{2})}{2d}\Rightarrow \frac{K_2}{K_1}=4$