Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 60

Figure 18.23 shows the cross section of a wall made of three layers. The layer thicknesses are \(L_1, L_2 = 0.700L_1\), and \(L_3 = 0.350L_1\). The thermal conductivities are \(k_1, k_2 = 0.900k_1\), and \(k_3 = 0.800k_1\). The temperatures at the left side and right side of the wall are \(T_H = 30.0^\circ\text{C}\) and \(T_C = -15.0^\circ\text{C}\), respectively. Thermal conduction is steady. (a) What is the temperature difference \(\Delta T_2\) across layer 2 (between the left and right sides of the layer)? If \(k_2\) were, instead, equal to \(1.1k_1\), (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) what would be the value of \(\Delta T_2\)?