Two walls of thickness $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. Find the temperature of the common interface.

  • A
    $\frac{k_1 T_1 d_2 + k_2 T_2 d_1}{k_1 d_2 + k_2 d_1}$
  • B
    $\frac{k_1 T_1 + k_2 T_2}{d_1 + d_2}$
  • C
    $\left[ \frac{k_1 d_1 + k_2 d_2}{T_1 + T_2} \right] T_1 T_2$
  • D
    $\frac{k_1 d_1 T_1 + k_2 d_2 T_2}{k_1 d_1 + k_2 d_2}$

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