The calorie is a unit of energy defined as the amount of energy needed to raise 1 g of water by 1degree c. how many calories are required to bring a pot of water at 1degree c to a boil? the pot is full to the brim, with diameter 20 cm and depth 20 cm. the density of water is 1000 kg/m3. if we consider d for the pot to be 20 cm, approximately how much more energy is needed to heat a hot tub with d=2 m? how many calories is that? if energy costs 10 cents per kilowatt hour, how much does it cost to heat this hot tub? how does the price (in dollars) of heating the hot tub scale with the tub's characteristic dimension? what percentage of the cost of heating the tub would be saved by reducing the tub's characteristic dimension by 33%?