When heating water for cooking food, it is common to use an electric or natural-gas cooktop. A metal pot with radius r = 0.11 m is filled with water to a depth of h = 0.18 m and heated on such a cooktop. The water is initially at a temperature of T = 25°C. Enter an expression for the amount of heat required to raise the temperature of the water to its boiling point of Tv = 100°C, in terms of r, h, T, Tv, the density of water, ρ = 1.00 × 103 kg/m3, and the specific heat of water, c = 4.186 × 103 J/(kg⋅°C). Calculate the amount of heat, in joules, required to raise the temperature of the water to its boiling point. According to the U.S. Energy Information Administration, the average cost of electricity in the U.S. is about $0.10 per kilowatt-hour, or $0.028 per megajoule of electrical energy. Assuming all the electrical energy goes into heating the water on the cooktop, how much does it cost, in dollars, to heat the pot of water with electricity? Ignore the heat required to raise the temperature of the pot.

When heating water for cooking food, it is common to use an electric or natural-gas cooktop. A metal pot with radius r = 0.11 m is filled with water to a depth of h = 0.18 m and heated on such a cooktop. The water is initially at a temperature of T = 25°C. Enter an expression for the amount of heat required to raise the temperature of the water to its boiling point of Tv = 100°C, in terms of r, h, T, Tv, the density of water, ρ = 1.00 × 103 kg/m3, and the specific heat of water, c = 4.186 × 103 J/(kg⋅°C). Calculate the amount of heat, in joules, required to raise the temperature of the water to its boiling point. According to the U.S. Energy Information Administration, the average cost of electricity in the U.S. is about $0.10 per kilowatt-hour, or $0.028 per megajoule of electrical energy. Assuming all the electrical energy goes into heating the water on the cooktop, how much does it cost, in dollars, to heat the pot of water with electricity? Ignore the heat required to raise the temperature of the pot.