From Figure it is evident that, over a wide temperature range, the temperature dependence of the thermal conductivity of many solids may be approximated by a linear expression of the form k = k_o + aT, where k_o is a positive constant and a is a coefficient that may be positive or negative. Obtain an expression for the heat flux across a plane wall whose inner and outer surfaces are maintained at T_o and T₁, respectively. Sketch the forms of the temperature distribution corresponding to a > 0, a = 0, and a < 0.

500 400 Silver Copper 300 Gold Aluminum Aluminum alloy 2024 Tungsten 200 100 Platinum- 50 Uron Stainless steel, AISI 304 20 10 Aluminum oxide- Pyroceram Fused quartz 500 Temperature (K) 1000 2000 4000 300 Thermat conductivity (W/m-KI 2.