• # question_answer A wall has two layers A and B made of different materials. The thickness of both the layers is the same. The thermal conductivity of A and B are ${{K}_{A}}$ and ${{K}_{B}}$ such that ${{K}_{A}}=3{{K}_{B}}$. The temperature across the wall is $20{}^\circ C$. In thermal equilibrium A) The temperature difference across $A=15{}^\circ C$ B) The temperature difference across $A=5{}^\circ C$ C) The temperature difference across A is $10{}^\circ C$ D) The rate of transfer of heat through A is more than that through B.

 In series rate of flow of heat is same $\Rightarrow$ $\frac{{{K}_{A}}A({{\theta }_{1}}-\theta )}{l}=\frac{{{K}_{B}}A(\theta -{{\theta }_{2}})}{l}$ $\Rightarrow$ $3{{K}_{B}}({{\theta }_{1}}-\theta )={{K}_{B}}(\theta -{{\theta }_{2}})$ $\Rightarrow$ $3({{\theta }_{1}}-\theta )=(\theta -{{\theta }_{2}})$ $\Rightarrow$ $3{{\theta }_{1}}-3\theta =\theta -{{\theta }_{2}}$ $\Rightarrow$ $4{{\theta }_{1}}-4\theta ={{\theta }_{1}}-{{\theta }_{2}}$ $\Rightarrow$ $4({{\theta }_{1}}-\theta )=({{\theta }_{1}}-{{\theta }_{2}})$ $\Rightarrow$ $4({{\theta }_{1}}-\theta )=20$ $\Rightarrow$ $({{\theta }_{1}}-\theta )=5{}^\circ C$