Hot coffee of temperature T[infinity] = 90°C is poured into a cup whose wall is initially at the temperature Ti= 10°C. The porcelain wall of the cup is 0.5 cm thick. The heat transfer coefficient between the coffee and the wetted surface is h= 700 W/m2-K. The external surface is effectively adiabatic. How much time elapses before the cup becomes too hot handle (assume an outside temperature of 50C is no longer comfortable to touch). Properties of porcelain: density = 2400 kg/m3, cp = 1.08 kJ/kg-K, k = 0.81 W/m-K alpha = 0.0034cm^2/s.