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An electrical coil is used to heat 20.0 kg of water in a closed well-insulated vessel. The water is initially at 25°C and 1 atm. The coil delivers a steady 2.50 kW of power to the vessel and its contents.

(a) Write a differential energy balance on the water, assuming that 97% of the energy delivered by the coil goes into heating the water. What happens to the other 3%?

(b) Integrate the equation of part (a) to derive an expression for the water temperature as a function of time.

(c) How long will it take for the water to reach the normal boiling point? Will it boil at this temperature? Why not?

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