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PhysicsQ&A LibraryIn this problem you will estimate the heat lost by atypical house, assuming that the temperature insideis Tin = 20°C and the temperature outside isTout = 0°C. The walls and uppermost ceiling of atypical house are supported by 2 × 6-inch woodenbeams (kwoodinsulation (kins = 0.04 W/(mK)) in between.The true depth of the beams is actually 5.625inches, but we will take the thickness of the wallsand ceiling to be Lwallinterior and exterior covering. Assume that thehouse is a cube of length L = 9.0 m on a side.Assume that the roof has very high conductivity, sothat the air in the attic is at the same temperatureas the outside air. Ignore heat loss through theground. The effective thermal conductivity of thewall (or ceiling) keff , is the area-weighted averageof the thermal conductivities of the wooden beamsand the fiberglass insulation that make up each ofthem. Allowing for the fact that the 2 x 6 beams0.12 W/(mK)) with fiberglass18 cm to allow for theare actually only 1.625 inches wide and arespaced 16 inches center to center, a calculation ofthis conductivity for the walls yieldskeffthat the ceiling also has the same value of keff -0.048 W/(mK). For simplicity, assume Let us assume that the winter consists of 150 days in which the outside temperature is 0°C. This will give the typicalnumber of "heating degree days" observed in a winter along the northeastern US seaboard. (The cumulative number ofheating degree days is given daily by the National Weather Service and is used by oil companies to determine when theyshould fill the tanks of their customers.) Given that a gallon (3.4 kg) of oil liberates Qg = 1.4 × 10° J when burned, howmuch oil will be needed to supply the heat lost by conduction from this house over a winter? Assume that the heatingsystem is 75% efficient.Question

Asked Jan 27, 2020

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What are the gallons consumed in units of gallons per winter?

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