80 gallon water heater that operates on natural gas. theefficiency of the heater

Question

80 gallon water heater that operates on natural gas. theefficiency of the heater is 60%. heat energy put into water/ energy content of the gas consumed=0.6 the temp of the water entering the tank is 50 degrees F,and the final temp achieved is 120 degrees F Calculate the quantity of natural gas consumed to bring all 80gallons to the holding temp.Express in cu./ft of natural gas. 80 gallon water heater that operates on natural gas. theefficiency of the heater is 60%. heat energy put into water/ energy content of the gas consumed=0.6 the temp of the water entering the tank is 50 degrees F,and the final temp achieved is 120 degrees F Calculate the quantity of natural gas consumed to bring all 80gallons to the holding temp.Express in cu./ft of natural gas.

Explanation / Answer

I feel a piece of data is missing in the problem i.e. the heatgiven out by natural gas per cubic feet. . The change in temperature of water = 120 - 50 F = 70 F Converting this into degrees celsius: 9 * C = (F-32) * 5 Substituting the value of F, we get C = 21.1 C . 80 gallons of water is heated. Volume = 80 gallons = 302.8 L Since mass of water = 1 kg for 1 L, mass of water = 302.8 kg . So heat absorbed by water = mass * specific heat *temperature difference                                          = 302.8 * 10^3 g * 4.18 J per gram.C * 21.1C                                          = 2.67 * 10^7 J                                          =2.67 * 10^4 kJ . Given that Heat put into water = 0.6 * energy content of gasconsumed So energy content of gas consumed = 4.45 * 10^4 kJ . Use the heat given out by the natural gas per cubic feet to findout the quantity of natural gas consumed.

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