Problem 86 Hard Difficulty

During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 $\mathrm{kWh}$ of heat provided by a natural gas furnace with 89$\%$ efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house).
(a) Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was $56^{\circ} \mathrm{F} ;$ at this temperature and a pressure of $1 \mathrm{atm},$ natural gas has a density of 0.681 $\mathrm{g} / \mathrm{L} .$
(b) How many gallons of LPG (liquefied petroled petrold be required to replace the natural gas used? Assume the LPG is liquid propane $\left[\mathrm{C}_{3} \mathrm{H}_{8} : \text { density }, 0.5318 \mathrm{g} / \mathrm{mL} ; \text { enthalpy of combustion, } 2219 \mathrm{kJ} / \mathrm{mol} \text { for the formation of }\right.$ $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) ]$ and the furnace used to burn the LPG has the same efficiency as the gas furnace.
(c) What mass of carbon dioxide is produced by combustion of the methane used to heat the house?
(d) What mass of water is produced by combustion of the methane used to heat the house?
(e) What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains 23$\%$ oxygen by mass. The average density of air during the month was 1.22 $\mathrm{g} / \mathrm{L}$ .
(f) How many kilowat--hours $\left(1 \mathrm{kWh}=3.6 \times 10^{6} \mathrm{J}\right)$ of electricity would be required to heat necessary to heat the house? Note electricity is 100$\%$ efficient in producing heat inside a house.
(g) Although electricity is 100$\%$ efficient in producing heat inside a house, production and distribution of electricity is not 100$\%$ efficient. The efficiency of production and distribution of electricity produced in a coal-fired power plant is about 40$\%$ . A certain type of coal provides 2.26 $\mathrm{kWh}$ per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation
and distribution is 40$\% ?$

Answer

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Video Transcript

caution number 86. The last question off the chapter on the longest. We'll start with the basics. The definition off standard Intel pecan can compassion is the Intel API change for one more off substance that bones or combines with the oxygen under standard state condition. That is one more pressure and 2 98 Calvin and preacher for but a assuming that the natural gas is pure meeting meeting. Therefore, the heat provided is 3500 kilowatt with 89% fullness. Efficiency deter mining the amount off heat provided by meeting in Tokyo. Jules, we can calculate it has 1.26 into 10 days to pass seven kilo Jules. But as the efficiency off gas furnace is the percent off heat produced by the commotion that is transferred into the house, therefore it is decreased to 1.42 into 10 days to par seven. Colonials, therefore, calculating the number off moles off meeting required to produce this amount off heat, we can refer to the table for standard heat compassion provided into the textbook that is negative off 890.8 killa jewels, so the number off meeting required would be 15,940 moves. Okay, that's quite tight. After calculating the number of moves off meeting, the total mass off meeting can be calculated substituting in the values off. Okay, we can calculate the number off moles that is mass by motor miles, So the total mass off meeting turns out to be 255700 Graham. That's a lot. No substituting in the value off density off meeting on the mask off meeting being calculate the volume off meeting in leaders that turns out to be 375 500 leaders. We can convert the above volume off, meeting in leaders in tow, cubic feet using this correlation. So the volume in cubic feet turns out to be 13,260 cubic feet for part B, as the heat produced by compassion off gas that is transferred into the house is already calculated, which is one point for doing to tend to surpass seven, Kill a Jew. Assuming that the LPD is liquid propane, we can again refer to the table, and we can have the heat off condition that turns out to be 2219. Killer trooper move As the last time we can calculate the number off Moulds were stoned. That Toby 6399 moods substituting in the values off Moeller Mass. On number off moves off propane into the given equation, which is represented Over here, we can calculate the total mass of propane required. That turns out to be 28,200 grounds using the density mass relation, which is represented by the equation. Over here, we can calculate the total volume that turns out to be 53.7 leaders. We can't own that leader in tow. The gallons. It's through this correlation. It turns out to be 100 and 41.2 gallons, considering the falling reaction off meeting, which leads to Formacion off to mood off water and one more off carbon dioxide, According to the reaction, same amount of carbon dioxide is produced by compassion off meeting. So the total mass off carbon dioxide produced can be calculated as follows, substituting in the value for mama's off carbon excite number off moles off carbon or excite in tow. This formula here, the total mass of carbon dioxide produces 701.52 kilograms. Next considering the falling reaction meeting plus oxygen leads to carbon dioxide plus water. So according to the given reaction, the amount of water is twice the amount off meeting. Therefore, number off mold off water will be twice off. Meeting. That comes out to be 3 1880 molds substituting in the values off water into the given relation, we can find the total mass off what are produced. That is 574.32 kilograms. That's a lot of water, considering the falling reaction off compassion off meeting, as the number off mold off meeting require is already calculated in part A, which is 15,940 mole, we can calculate the number of moons off oxygen required, which turns out to be twice off molds off. Meeting that is 31,880 substituting in the value off mass off oxygen on number off molds off oxygen in tow. This relation, we can have the total mass off photo that is 102 0160 grams now as only 23% off areas oxygen. Therefore, the overall overall mass off oxygen is as follows, which is 443 5478 point to six grams substituting in the density off. Groping on Mars off propane we can finally, we can find the volume off Oxygen or Marshall Faulk season which stones out do we? 3635637.92 leader. This volume off here is required to provide oxygen for the combustion off meeting to eating our house. Oh, last. But if, as the electricity is 100% efficient in producing heat inside those, therefore the amount off heat required would be same as 3500. Killer ward the body As the efficiency off production on distribution off electricity produce in coal fire plant is approximately 40% their fire. We can use the unitary method to find 8750 kilowatt off energy is transferred, the moss off cooled required. It can be calculated as represented over here, which turns out to be £3872. This mask off cool isn't pounds, but the mass off cool required is in kilogram. So there's a correlation between pound and kilogram, which is represented by this using the common unitary method, we can convert pounds into kilogram. That turns out to be 1756.34 kilograms. This amount off cool is required to produce the electrical energy necessary to heat the house if the efficiency off production and distribution is about what he poisoned.

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