Bus bars proposed for use in a power transmission station have a rectangular cross section of height H = 600 mm and width W = 200 mm. The electrical resistivity, ρ_c<μΩ ∙ m), of the bar material is a function of temperature, ρ_c = ρ_c,o [1 + α(T - T_o)], where ρ_c,o = 0.0828 μΩ ∙ m, T_o = 25°C, and α = 0.0040 K^-1' . The emissivity of the bar's painted surface is 0.8, and the temperature of the surroundings is 30°C. The convection coefficient between the bar and the ambient air at 30°C is l0W/m² ∙ K.

(a) Assuming the bar has a uniform temperature T, calculate the steady-state temperature when a current of 60,000 A passes through the bar.

(b) Compute and plot the steady-state temperature of the bar as a function of the convection coefficient for 10 ≤ h ≤ 100 W/m² ∙ K. What minimum convection coefficient is required to maintain a safe operating temperature below 120°C? Will increasing the emissivity significantly affect this result?