A long wire of diameter D = 1 mm is submerged in an oil bath of temperature T_∞ = 25°C. The wire has an electrical resistance per unit length of R = 0.01Ω/m. If a current of I = 100 A flows through the wire and the convection coefficient is h = 500 W/m² ∙ K, what is the steady-state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°C of the steady-state value? The properties of the wire are p = 8000 kg/m³, c = 500 J/kg ∙ K, and k = 20 W/m ∙ K.