Consider a 1.5-m-high and 0.6-m-wide plate whose thickness is 0.15 m. One side of the plate is maintained at a constant temperature of 500 K while the other side is maintained at 350 K. The thermal conductivity of the plate can be assumed to vary linearly in that temperature range as k(T) = k₀(1 + βT) where k₀ = 18 W/m · K and b = 8.7 × 10^-4 K^-1. Disregarding the edge effects and assuming steady one dimensional heat transfer, determine the rate of heat conduction through the plate.