In 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 x 6-inch woodenbeams (kwood = 0.12 W/(mK)) with fiberglassinsulation (kins = 0.04 W/(mK)) in between.The true depth of the beams is actually 5.625%3D%3D%3Dinches, but we will take the thickness of the wallsand ceiling to be Lwall = 18 cm to allow for theinterior 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 beamsare actually only 1.625 inches wide and arespaced 16 inches center to center, a calculation ofthis conductivity for the walls yieldskeff = 0.048 W/(mK). For simplicity, assumethat the ceiling also has the same value of keff - 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 numberof heating degree days is given daily by the National Weather Service and is used by oil companies to determinewhen they should fill the tanks of their customers.) Given that a gallon (3.4 kg) of oil liberates Qg = 1.4 x 10° Jwhen 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.Give your answer numerically in gallons to two significant figures.• View Available Hint(s)?Gallons consumed =gallons per winter

The inside temperature of the house Tin = 20oC The outside temperature of the house Tout = 0oC…

las tion (kins = 0.04 W/(mK)) in between. ue depth of the beams is actually 5.625 , but we will take the thickness of the walls eiling to be Lwall = 18 cm to allow for the r and exterior covering. Assume that the is a cube of length L = 9.0 m on a side. he that the roof has very high conductivity, so e air in the attic is at the same temperature outside air. Ignore heat loss through the d. The effective thermal conductivity of the or ceiling) keff , is the area-weighted average thermal conductivities of the wooden beams wood glass o fiborglacs inculation that mako up nch of

las tion (kins = 0.04 W/(mK)) in between. ue depth of the beams is actually 5.625 , but we will take the thickness of the walls eiling to be Lwall = 18 cm to allow for the r and exterior covering. Assume that the is a cube of length L = 9.0 m on a side. he that the roof has very high conductivity, so e air in the attic is at the same temperature outside air. Ignore heat loss through the d. The effective thermal conductivity of the or ceiling) keff , is the area-weighted average thermal conductivities of the wooden beams wood glass o fiborglacs inculation that mako up nch of

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter17: Energy In Thermal Processes: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 69P: An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a...

See similar textbooks

Similar questions

The thermal conductivities of human tissues vary greatly. Fat and skin have conductivities of about 0.20 W/m K and 0.020 W/m K, respectively, while other tissues inside the body have conductivities of about 0.50 W/m K. Assume that between the core region of the body and the skin sin face lies a skin layer of 1.0 mm, fat layer of 0.50 cm, and 3.2 cm of other tissues. (a) Find the R-factor for each of these layers, and the equivalent R-factor for all layers taken together, retaining two digits. (b) Find the rate of energy loss when the core temperature is 37C and the exterior temperature is 0C. Assume that both a protective layer of clothing and an insulating layer of unmoving air a absent, and a body area of 2.0 m2.
One easy way to reduce heating (and cooling) costs is to add extra insulation in the attic of a house. Suppose a single-story cubical house already had 15 cm of fiberglass insulation in the attic and in all the exterior surfaces. If you added an extra 8.0 cm of fiberglass to the attic, by what percentage would the heating cost of the house drop? Take the house to have dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heat loss through windows and doors, and assume that the interior is uniformly at one temperature and the exterior is uniformly at another.
The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is 35.0 . What will its height be on a day when the temperature falls to -10.0 ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.
To help prevent frost damage, 4.00 kg of water at 0 is sprayed onto a fruit tree. (a) How much heat transfer occurs as the water freezes? (b) How much would the temperature of the 200-kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be 3.35k J/kg. , and assume that no phase change occurs in the tree.
Consider the latent heat of fusion and the latent heat of vaporization for H2O, 3.33 105 J/kg and 2.256 106 J/kg, respectively. How much heat is needed to a. melt 2.00 kg of ice and b. vaporize 2.00 kg of water? Assume the temperatures of the ice and steam are at the melting point and vaporization point, respectively. (a). UsingEq21.9, Q = mLF = (2.00 kg) (3.33l05 J/kg) = 6.66105 J (b).UsingEq21.10. Q = mLV = (2.00kg) (2.256106 J/kg) = 14.51106 J
An aluminum rod 0.500 m in length and with a cross sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 3(H) K. (a) If one-halt of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool, (b) If the circular surface of the upper end of the rod is maintained at 300 K. what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 YV/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)
Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of 10.0 m2 and a thermal conductivity that of glass wool with the rate of heat conduction through a 0.750-cm-thick window that has an area of 2.00 m2, assuming the same temperature difference across each.
An astronaut performing an extra-vehicular activity (space walk) shaded from the Sun is wearing a spacesuit that can be approximated as perfectly white ( e=0 ) except for a 5 cm × 8 cm patch in the form of the astronaut's national flag. The patch has emissivity 0.300. The spacesuit under the patch is 0.500 cm thick, with a thermal conductivity k 0.0600 W/m , and its inner surface is at a temperature of 20.0 . What is the temperature of the patch, and what is the rate of heat loss through it? Assume the patch is so thin that its outer surface is at the same temperature as the outer surface of the spacesuit under it. Also assume the temperature of outer space is 0 K. You will get an equation that is very hand to solve in closed form, so can solve it numerically with a graphing calculator, with software, or even by trial and error with a calculator.
Suppose you stand with one foot on ceramic flooring and one foot on a wool carpet, making contact over an area of 80.0 cm2 with each foot. Both the ceramic and the carpet are 2.00 cm thick and ale 10.0 on their bottom sides. At what rate must heat transfer occur from each foot to keep the top of the ceramic and carpet at 33.0 ?
An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 300 K. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at 300 K, what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 W/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)
Estimate the rate at which heat can be conducted from theinterior of the body to the surface. As a model, assume thatthe thickness of tissue is 4.0 cm, that the skin is at 34°Cand the interior at 37°C, and that the surface area is 1.5m2Compare this to the measured value of about 230 W thatmust be dissipated by a person working lightly. This clearlyshows the necessity of convective cooling by the blood
A furnace is shaped like a long equilateral-triangularduct where the width of each side is 2 m. Heat is supplied fromthe base surface, whose emissivity is «1 = 0.8, at a rate of800 W/m2 while the side surfaces, whose emissivities are 0.5,are maintained at 500 K. Neglecting the end effects, determinethe temperature of the base surface. Can you treat this geometryas a two-surface enclosure?