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In cold climates, including the northern United States, a house can be built with very large windows facing south to take advantage of solar heating. Sunlight shining in during the daytime is absorbed by the floor, interior walls, and objects in the room, raising their temperature to 38.0°C. If the house is well insulated, you may model it as losing energy by heat steadily at the rate 6 000 W on a day in April when the average exterior temperature is 4°C and when the conventional heating system is not used at all. During the period between 5:00 p.m. and 7:00 a.m., the temperature of the house drops and a sufficiently large "thermal mass" is required to keep it from dropping too far. The thermal mass can be a large quantity of stone (with specific heat 850 J/kg · °C) in the floor and the interior walls exposed to sunlight. What mass of stone is required if the temperature is not to drop below 18.0°C overnight?
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Chapter 20 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
- 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.)arrow_forwardTwo concrete spans that form a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P16.63a). If a temperature increase of T occurs, what is the height y to which the spans rise when they buckle (Fig. P16.63b)?arrow_forwardConsider 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 Jarrow_forward
- 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.arrow_forward(a) The inside of a hollow cylinder is maintained at a temperature Ta, and the outside is at a lower temperature, Tb (Fig. P19.45). The wall of the cylinder has a thermal conductivity k. Ignoring end effects, show that the rate of energy conduction from the inner surface to the outer surface in the radial direction is dQdt=2Lk[TaTbln(b/a)] Suggestions: The temperature gradient is dT/dr. A radial energy current passes through a concentric cylinder of area 2rL. (b) The passenger section of a jet airliner is in the shape of a cylindrical tube with a length of 35.0 m and an inner radius of 2.50 m. Its walls are lined with an insulating material 6.00 cm in thickness and having a thermal conductivity of 4.00 105 cal/s cm C. A heater must maintain the interior temperature at 25.0C while the outside temperature is 35.0C. What power must be supplied to the heater? Figure P19.45arrow_forwardThe average coefficient of linear expansion of copper is 17 106 (C)1. The Statue of Liberty is 93 in tall on a summer morning when the temperature is 25C. Assume the copper plates covering the statue are mounted edge to edge without expansion joints and do not buckle or bind on the framework supporting them as the day grows hot. What is the order of magnitude of the statues increase in height? (a) 0.1 mm (b) 1 mm (c) 1 cm (d) 10 cm (e) 1 marrow_forward
- At high noon, the Sun delivers 1 000 W to each square meter of a blacktop road. If the hot asphalt transfers energy only by radiation, what is its steady-state temperature?arrow_forwardWhy is a person able to remove a piece of dry aluminum foil from a hot oven with bare fingers, whereas a burn results if there is moisture on the foil?arrow_forwardThe 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.arrow_forward
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