A cooking-pan containing 2 kg of water is heated by electric current flowing through some resistance, as shown in figure 1. The pan has a cylindrical shape, with a radius of 20 cm. The thickness of the aluminium section at the bottom is 10 mm. Assume there is no heat loss through the sides of the saucepan. The air temperature at the air/water interface is 25C, and water temperature in the pan is 100C.

a) Calculate the heat transfer rate via convection at the water-air surface. Take the coefficient of heat transfer via convection of air in this situation of 100 W/(m2 K).

(b) Calculate the heat transfer rate via conduction at the aluminium-resistance surface. Assume the resistance temperature is 150C. Take the thermal conductivity of aluminium to be 205 W/(m K).

(c) How much energy would it take to transform all water into steam? (d) How much time would it take to transform all water into steam? Constant to consider: Latent heat of water: 2260 J/g