Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 63

Figure 18.26 shows (in cross section) a wall consisting of four layers, with thermal conductivities \(k_1 = 0.060 \text{ W/m}\cdot\text{K}\), \(k_3 = 0.040 \text{ W/m}\cdot\text{K}\), and \(k_4 = 0.12 \text{ W/m}\cdot\text{K}\) (\(k_2\) is not known). The layer thicknesses are \(L_1 = 1.5 \text{ cm}\), \(L_3 = 2.8 \text{ cm}\), and \(L_4 = 3.5 \text{ cm}\) (\(L_2\) is not known). The known temperatures are \(T_1 = 30^\circ\text{C}\), \(T_{12} = 25^\circ\text{C}\), and \(T_4 = -10^\circ\text{C}\). Energy transfer through the wall is steady. What is interface temperature \(T_{34}\)?