In this problem you will estimate the heat lost by a typical house, assuming that the temperature inside is Tin = 20°C and the temperature outside is Tout = 0°C. The walls and uppermost ceiling of a typical house are supported by 2 × 6-inch wooden beams (kwood insulation (kins = 0.04 W/(mK)) in between. The true depth of the beams is actually 5.625 inches, but we will take the thickness of the walls and ceiling to be Lwall interior and exterior covering. Assume that the house is a cube of length L = 9.0 m on a side. Assume that the roof has very high conductivity, so that the air in the attic is at the same temperature as the outside air. Ignore heat loss through the ground. The effective thermal conductivity of the wall (or ceiling) keff , is the area-weighted average of the thermal conductivities of the wooden beams and the fiberglass insulation that make up each of them. Allowing for the fact that the 2 x 6 beams 0.12 W/(mK)) with fiberglass 18 cm to allow for the are actually only 1.625 inches wide and are spaced 16 inches center to center, a calculation of this conductivity for the walls yields keff that 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 typical number of "heating degree days" observed in a winter along the northeastern US seaboard. (The cumulative number of heating degree days is given daily by the National Weather Service and is used by oil companies to determine when they should fill the tanks of their customers.) Given that a gallon (3.4 kg) of oil liberates Qg = 1.4 × 10° J when burned, how much oil will be needed to supply the heat lost by conduction from this house over a winter? Assume that the heating system is 75% efficient.

Question

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

In this problem you will estimate the heat lost by a
typical house, assuming that the temperature inside
is Tin = 20°C and the temperature outside is
Tout = 0°C. The walls and uppermost ceiling of a
typical house are supported by 2 × 6-inch wooden
beams (kwood
insulation (kins = 0.04 W/(mK)) in between.
The true depth of the beams is actually 5.625
inches, but we will take the thickness of the walls
and ceiling to be Lwall
interior and exterior covering. Assume that the
house is a cube of length L = 9.0 m on a side.
Assume that the roof has very high conductivity, so
that the air in the attic is at the same temperature
as the outside air. Ignore heat loss through the
ground. The effective thermal conductivity of the
wall (or ceiling) keff , is the area-weighted average
of the thermal conductivities of the wooden beams
and the fiberglass insulation that make up each of
them. Allowing for the fact that the 2 x 6 beams
0.12 W/(mK)) with fiberglass
18 cm to allow for the
are actually only 1.625 inches wide and are
spaced 16 inches center to center, a calculation of
this conductivity for the walls yields
keff
that the ceiling also has the same value of keff -
0.048 W/(mK). For simplicity, assume
Expand
Transcribed Image Text

In this problem you will estimate the heat lost by a typical house, assuming that the temperature inside is Tin = 20°C and the temperature outside is Tout = 0°C. The walls and uppermost ceiling of a typical house are supported by 2 × 6-inch wooden beams (kwood insulation (kins = 0.04 W/(mK)) in between. The true depth of the beams is actually 5.625 inches, but we will take the thickness of the walls and ceiling to be Lwall interior and exterior covering. Assume that the house is a cube of length L = 9.0 m on a side. Assume that the roof has very high conductivity, so that the air in the attic is at the same temperature as the outside air. Ignore heat loss through the ground. The effective thermal conductivity of the wall (or ceiling) keff , is the area-weighted average of the thermal conductivities of the wooden beams and the fiberglass insulation that make up each of them. Allowing for the fact that the 2 x 6 beams 0.12 W/(mK)) with fiberglass 18 cm to allow for the are actually only 1.625 inches wide and are spaced 16 inches center to center, a calculation of this conductivity for the walls yields keff that 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 typical
number of "heating degree days" observed in a winter along the northeastern US seaboard. (The cumulative number of
heating degree days is given daily by the National Weather Service and is used by oil companies to determine when they
should fill the tanks of their customers.) Given that a gallon (3.4 kg) of oil liberates Qg = 1.4 × 10° J when burned, how
much oil will be needed to supply the heat lost by conduction from this house over a winter? Assume that the heating
system is 75% efficient.
Expand
Transcribed Image Text

Let us assume that the winter consists of 150 days in which the outside temperature is 0°C. This will give the typical number of "heating degree days" observed in a winter along the northeastern US seaboard. (The cumulative number of heating degree days is given daily by the National Weather Service and is used by oil companies to determine when they should fill the tanks of their customers.) Given that a gallon (3.4 kg) of oil liberates Qg = 1.4 × 10° J when burned, how much oil will be needed to supply the heat lost by conduction from this house over a winter? Assume that the heating system is 75% efficient.

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