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All Textbook Solutions for College Physics

The density of lead is greater than iron, and both metals are denser than water. Is the buoyant force on a solid lead object (a) greater than, (b) equal to, or (c) less than the buoyant force acting on a solid iron object of the same dimensions?You observe two helium balloons floating next to each other at the ends of strings secured to a table. The facing surfaces of the balloons are separated by 1-2 cm. You blow through the opening between the balloons. What happens to the balloons? (a) They move toward each other. (b) They move away from each other. (c) They are unaffected.Physics Review A soap bubble hovers motionlessly in the air. If the soap bubbles mass, including the air inside it, is 2.00 104 kg determine the magnitude of the upward force acting on it. (See Section 4.5.)Physics Review A team of huskies performs 7 440 J of work on a loaded sled of mass 124 kg, drawing it from rest up a 4.60-m high snow-covered rise while the sled loses 1 520 J due to friction, (a) What is the net work done on the sled by the huskies and friction? (b) What is the change in the sleds potential energy? (c) What is the speed of the sled at the top of the rise? (See Section 5.5.)3WUE 4WUE Humans can bite with a force of approximately 800 N. If a human tooth has the Youngs modulus of bone, a cross-sectional area of 1.0 cm2, and is 2.0 cm long, determine the change in the tooths length during an 8.0 102 N bite. (See Section 9.3.)A hydraulic jack has an input piston of area 0.050 m2 and an output piston of area 0.70 m2. How much force on the input piston is required to lift a car weighing 1.2 104 N?7WUE 8WUE 9WUE A horizontal pipe narrows from a radius of 0.250 m to 0.100 m. If the speed of the water in the pipe is 1.00 m/s in the larger radius pipe, what is the speed in the smaller pipe?A large water tank is 3.00 m high and filled lo the brim, the top of the tank open to the air. A small pipe with a faucet is attached to the side of the tank, 0.800 m above the ground. If the valve is opened, at what speed will water come out of the pipe?1CQ The density of air is 1.3 kg/m3 at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of uniform density up to some height, after which the density rapidly falls to zero. (In reality, the density of the atmosphere decreases as we go up.) (This question is courtesy or Edward F. Redish. For more questions of this type, see http://www.physics.umd.edu/perg/.)Why do baseball home run hitters like to play in Denver, but curveball pitchers do not?Figure CQ9.4 shows aerial views from directly above two dams. Both dams are equally long (the vertical dimension in the diagram) and equally deep (into the page in the diagram). The (dam on the left holds hack a very large lake, while the dam on the right holds back a narrow river. Which dam has to be built more strongly? Figure CQ9.4 5CQ 6CQ Suppose a damaged ship just barely floats in the ocean after a hole in its hull has been sealed. It is pulled by a tugboat toward shore and into a river, heading toward a dry dock for repair. As the boat is pulled up the river, it sinks. Why?During inhalation, the pressure in the lungs is slightly less than external pressure and the muscles controlling exhalation are relaxed. Under water, the body equalizes internal and external pressures. Discuss the condition of the muscles if a person under water is breathing through a snorkel. Would a snorkel work in deep water?The water supply for a city is often provided from reservoirs built on high ground. Water flows from the reservoir, through pipes, and into your home when you turn the tap on your faucet. Why is the water flow more rapid out of a faucet on the first floor of a building than in an apartment on a higher floor?An ice cube is placed in a glass of water. What happens to the level of the water as the ice melts?Place two cans of soft drinks, one regular and one diet, in a container of water. You will find that the diet drink floats while the regular one sinks. Use Archimedes principle to devise an explanation. Broad Hint: The artificial sweetener used in diet drinks is less dense I than sugar.Will an ice cube float higher in water or in an alcoholic beverage?13CQ 14CQ A person in a boat floating in a small pond throws an anchor overboard. What happens to the level of the pond? (a) It rises. (b) It falls. (c) It remains the same.One of the predicted problems due to global warming is that ice in the polar ice caps will melt and raise sea levels everywhere in the world. Is that more of a worry for ice (a) at the North Pole, where most of the ice floats on water; (b) at the South Pole, where most of the ice sits on land; (c) both at the North and South Poles equally; or (d) at neither pole?1P 3P Calculate the mass of a solid gold rectangular bar that, has dimensions of 4.50 cm x 11.0 cm 26.0 cm.5P 6P Suppose a distant world with surface gravity of 7.44 m/s2 has an atmospheric pressure of 8.04 104 Pa at the surface. (a) What force is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of a methane ocean? (b) What is the weight of a 10.0-m deep cylindrical column of methane with radius 2.00 m? (c) Calculate the pressure at a depth of 10.0 m in the methane ocean. Note: The density of liquid methane is 415 kg/m3.Evaluate Young's modulus for the material whose stress-strain curve is shown in Figure 9.8. Figure 9.8 Stress-versus-strain curve for an clastic solid.The Deformation of Solids 65. A 200.-kg load is hung on a wire of length 4.00 m, cross-section area 0.200 104 m2, and Youngs modulus 8.00 1010 N/m2. What is its increase in length?Comic-book superheroes are sometimes able to punch holes through steel walls, (a) If the ultimate shear strength of steel is taken to be 2.50 108 Pa, what force is required to punch through a steel plate 2.00 cm thick? Assume the superheros fist has cross-sectional area of 1.00 102 cm2 and is approximately circular, (b) Qualitatively, what would happen to the superhero on delivery of the punch? What physical law applies?A plank 2.00 cm thick and 15.0 cm wide is firmly attached to the railing of a ship by clamps so that the rest of the board extends 2.00 m horizontally over the sea below. A man of mass 80.0 kg is forced to stand on the very end. If the end of the board drops by 5.00 cm because of the mans weight, find the shear modulus of the wood.Assume that if the shear stress in steel exceeds about 4.00 108 N/m2, the steel ruptures. Determine the shearing force necessary to (a) shear a steel bolt 1.00 cm in diameter and (b) punch a 1.00-cm-diameter hole in a steel plate 0.500 cm thick.For safety in climbing, a mountaineer uses a nylon rope that is 50. m long and 1.0 cm in diameter . When supporting a 90.-kg climber, the rope clongates 1.6 m. Find its Youngs modulus.A stainless-steel orthodontic: wire is applied to a tooth, as in Figure P9.72. The wire has an unstretched length of 3.1 cm and a radius of 0.11 mm. If the wire is stretched 0.10 mm, find the magnitude and direction of the force on the tooth. Disregard the width of the tooth and assume Youngs modulus for stainless steel is 18 1010 Pa. Figure P9.72 Bone has a Youngs modulus of 18 109 Pa. Under compression, it can will island a stress or about 160 106 Pa before breaking. Assume that a femur (thigh bone) is 0.50 m long, and calculate the amount of compression this bone can withstand before breaking.A high-speed lifting mechanism supports an 800.-kg object with a steel cable that is 25.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. (b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 3.0 m/s2? (c) What is the greatest mass that can be accelerated upward at 3.0 m/s2 if the stress in the fable is not to exceed the elastic limit of the cable, which is 2.2 108 Pa?17P The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately 2.4 cm2. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of 80 km/h in 5.0 ms. If the arm has an effective mass of 3.0 kg and bone material can withstand a maximum compressional stress of 16 107 Pa, is the arm likely to withstand the crash?19P 20P (a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 27.5 m. Assume the density of the water is 1.00 103 kg/m3 and the air above is at a pressure of 101.3 kPa. (b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 35.0 cm?Mercury is poured into a U-tube as shown in Figure P9.10a. The left arm of the cube has cross-sectional area A1 of 10.0 cm2, and the right arm has a cross-sectional area A2 of 5.00 cm2. One hundred grams of water are then poured into the right arm as shown in Figure P9.10b. (a) Determine the length of the water column in the right arm of the U-tube. (b) Given that the density of mercury is 13.6 g/cm3, what distance h does the mercury rise in the left arm? Figure P9.10 A collapsible plastic bag (Fig. F9.11) contains a glucose solution. If the average gauge pressure in the vein is 1.33 103 Pa, what must be the minimum height h of the bag to infuse glucose into the vein? Assume the specific gravity of the solution is 1.02. 12. A hydraulic jack, has an input piston of area 0.050 m2 and an output piston of area 0.70 m2. How much force on the input piston is required to lift a car weighing 1.2 104 N?24P A container is filled to a depth of 20.0 cm with water. On top of the water floats a 30.0-cm-thick layer of oil with specific gravity 0.700. What is the absolute pressure at the bottom of the container?Blaise Pascal duplicated Torricellis barometer using a red Bordeaux wine, of density 984 kg/m3 as the working liquid (Fig. P9.14). (a) What was the height h of the wine column for normal atmospheric, pressure? (b) Would you expert the vacuum above the column to be as good as for mercury?Figure P9.27 shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is 1.8 cm2 and that of the piston in the brake cylinder is 6.4 cm2. The coefficient of friction between shoe and wheel drum is 0.50. If the wheel has a radius of 34 cm, determine the frictional torque about the axle when a force of 44 N is exerted on the brake pedal. Figure P9.27 Piston in Figure P9.16 has a diameter of 0.25 in.; piston has a diameter of 1.5 in. In the absence of friction, determine the force F necessary to support the 500-lb weight. Figure P9.16 Buoyant Forces and Archimedes Principle A table-tennis ball has a diameter of 3.80 cm and average density of 0.084 0 g/cm3. What force is required to hold it completely submerged under water?The average human has a density of 945 kg/m3 after in haling and 1 020 kg/m3 after exhaling. (a) Without making any swimming movements, what percentage of the human body would be above the surface in the Dead Sea (a body of water with a density of about 1 230 kg/m3) in each of these cases? (b) Given that bone and muscle are denser than fat, what physical characteristics differentiate sinkers (those who tend to sink in water) from floaters (those who readily float)?A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. What is the weight of the truck?A 62.0-kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m 2.00 m 0.090 0 m. The bottom 0.024 m of the raft is submerged. (a) Draw a force diagram of the system consisting of the survivor and raft. (b) Write Newtons second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Set a = 0.) (c) Calculate the numeric value for the buoyancy, B. (Seawater has density 1 025 kg/m3.) (d) Using the value of B and the weight w of the survivor, calculate the weight w, of the Styrofoam. (e) What is the density of the Styrofoam? (f) What is the maximum buoyant, force, corresponding to the raft being submerged up to its top surface? (g) What total mass of survivors can the raft support?A wooden block of volume 5.24 104 m3 floats in water, and a small steel object of mass m is placed on top of the block. When m = 0.310 kg, the system is in equilibrium, and the top of the wooden block is at the level of the water, (a) What is the density of the wood? (b) What happens to the block when the steel object is replaced by a second steel object with a mass less than 0.310 kg? What happens to the block when the steel object is replaced by yet another steel object with a mass greater than 0.310 kg?A large balloon of mass 226 kg is filled with helium gas until its volume is 325 m3. Assume the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3 (a) Draw a forcediagram for the balloon. (b) Calculate the buoyant force acting on the balloon. (c) Find the net force on the balloon and determine whether the balloon will rise or fall after it is released (d) What maximum additional mass can the balloon support in equilibrium? (e) What happens to the balloon if the mass of the load is less than the value calculated in part (d)? (f) What limits the height to which the balloon can rise?A spherical weather balloon is filled with hydrogen until its radius is 3.00 m. Its total mass including the instruments it carries is 15.0 kg. (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?A man of mass m = 70.0 kg and having a density of = 1 050 kg/m3 (while holding his breath) is completely submerged in water, (a) Write Newtons second law for this situation in terms of the mans mass m, the density of water , his volume V, and g. Neglect any viscous drag of the water, (b) Substitute m = V into Newtons second law and solve for the acceleration a, canceling common factors, (c) Calculate the numeric value of the mans acceleration, (d) How long does it take the man to sink 8.00 m to the bottom of the lake?On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of 3.35 km (11 000 ft) powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about 0.50 m and an estimated mass of 0.30 kg. (a) Estimate the total buoyant force on the 600 balloons. (b) Estimate the net upward force on all 600 balloons, (c) Ashpole parachuted to Earth after the balloons began to burst at the high altitude and the system lost buoyancy. Why did the balloons burst?The gravitational force exerted on a solid object is 5.00 N as measured when the object is suspended from a spring scale as in Figure P9.26a. When the suspended object is submerged in water, the scale reads 3.50 N (Fig. P9.26b). Find the density of the object. Figure P9.26 A cube of wood having an edge dimension of 20.0 cm and a density of 650. kg/m3 floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level? (b) What mass of lead should be placed on the cube so that the top of the cube will be just level with the water surface?A light spring of force constant k = 160 N/m rests vertically on the bottom of a large beaker of water (Fig. P9.28a). A 500-kg block of wood (density = 650 kg/m3) is connected to the spring, and the blockspring system is allowed to come to static equilibrium (Fig. P9.28b). What is the elongation L, of the spring? Figure P9.28 A sample of an unknown material appears to weigh 300. N in air and 200. N when immersed in alcohol of specific gravity 0.700. What are (a) the volume and (b) the density of the material?An object weighing 300 N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 265 N. Immersed in oil, the object appears to weigh 275 N. Find (a) the density of the object and (b) the density of the oil.A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m3) rests on a scale. A 2.00-kg block of iron is suspended from a spring scale and is completely submerged in the oil (Fig. P9.31). Find the equilibrium readings of both scales. Figure P9.31 Wafer flowing through a garden hose of diameter 2.74 cm fills a 25.0-L bucket in 1.50 min. (a) What is the speed of the water leaving the end of the hose? (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle?45P 46P A hypodermic syringe contain a medicine with the density of water (Fig. P9.37). The barrel of the syringe has a cross-sectional area of in the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F of magnitude 2.00 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicines How speed through the needle. Assume the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal. Figure P9.37 When a person inhales, air moves down the bronchus (windpipe) at 15 cm/s. The average How speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.A jet airplane in level flight has a mass of 8.66 104 kg, and the two wings have an estimated total area of at is the pressure difference between the surfaces of the wings? (b) If the speed of air under the wings is 225 m/s, what is the speed of the air over the wings? Assume air has a density of 1.29 kg/m3. (c) Explain why all aircraft have a ceiling, a maximum operational altitude.An airplane has a mass M, and the two wings have a total area A. During level flight, the pressure on the lower wing surface is P1. Determine the pressure P2 on the upper wing surface.51P 52P A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure P9.43. If the hole has a diameter of 3.50 mm, what is the height h of the water level in the tank? Figure P9.43 A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is 2.50 103m3/min, determine (a) the speed at which the water levels the hole and (b) the diameter of the hole.The inside diameters of the larger portions of the horizontal pipe depicted in Figure P9.45 are 2.50 era. Water flows to the right at a rate of 1.80 104 m3/s. Determine the inside diameter of the constriction. Figure P9.45 Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2 096 in. (a) At what minimum pressure must the water be pumped to arrive at the village? (b) If 4 500 m3 are pumped per day what is the speed of the water in the pipe? (c) What additional pressure is necessary to deliver this flow? Note: You may assume the free-fall acceleration and the density of air are constant over the given range of elevations.Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches 40.0 m (Fig. P9.47). (a) Consider the rising stream as a series of separate drops. Analyze the free-fall motion of one of the drops to determine the speed at which the water leaves the ground. (b) Treat the rising stream as an ideal fluid in streamline flow. Use Bernoullis equation to determine the speed of the water as it leaves ground level. (c) What is the pressure (above atmospheric pressure) in the heated underground chamber 175 m below the vent? You may assume the chamber is large compared with the geyser vent.The Venturi tube shown in Figure P9.48 may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline ( = 7.00 102 kg/m2) through a nose having an outlet radius of 1.20 cm. If the difference in pressure is measured to be P1, P2; = 1.20 kPa and the radius of the inlet tube to the meter is 2.40 cm, find (a) the speed of the gasoline as it leaves the hose and (b) the fluid flow rate in cubic meters per second. Figure P9.48 59P 60P A certain fluid has a density of 1.080 kg/m3 and is observed to rise to a height of 2.1 cm in a 1.0-mm-diaimeter tube the contact angle between the wall and the fluid is zero. Calculate the surface tension of the fluid.Whole blood has a surface tension of 0.058 N/m and a density of 1 050 kg/m3. To what height can whole blood rise in a capillary blood vessel that has a radius of 2.0 106 m if the contact angle is zero?63P 64P 65P 66P Spherical panicles of a protein of density 1.8 g/cm3 are shaken up in a solution of 20C water. The solution is allowed to stand for 1.0 h. If the depth of water in the tube is 5.0 cm, find the radius of the largest particles that remain in solution at the end of the hour.A hypodermic needle is 3.0 era in length and 0.30 mm in diameter. What pressure difference between the input and output of the needle is required so that the flow rate of water through it will be 1 g/s? (Use 1.0 103 Pa s as the viscosity of water).69P 70P The aorta in humans has a diameter of about 2.0 cm, and at certain times the blood speed through it is about 55 cm/s. Is the blood flow turbulent? The density of whole blood is 1 050 kg/m3, and its coefficient of viscosity is 2.7 108 N s/m2.72P 73P Glycerin in water diffuses along a horizontal column that has a cross-sectional area of 2.0 cm2. The concentration gradient is 3.0 102 kg/m4, and the diffusion rate is found to be 5.7 1015 kg/s. Determine the diffusion coefficient.75P Small spheres of diameter 1.00 mm fall through 20C water with a terminal speed of 1.10 cm/s. Calculate the density of the spheres.An iron block of volume 0.20 m5 is suspended from a spring scale and immersed in a flask of water. Then the iron block is removed, and an aluminum block of the same volume replaces it. (a) In which case is the buoyant force the greatest, for the iron block or the aluminum block? (b) In which case does the spring scale read the largest value? (c) Use the known densities of these materials to calculate the quantities requested in parts (a) and (b). Are your calculations consistent with your previous answers to parts (a) and (b)?The true weight of an object can be measured in a vacuum, where buoyant forces are absent. A measurement in air, however, is disturbed by buoyant forces. An object of volume V is weighed in air on an equal-arm balance with the use of counterweights of density . Representing the density of air as air and the balance reading as Fg, show that the true weight Fg is Fg=Fg+(v-Fgg)airg As a first approximation. Earth's continents may be thought of as granitr blocks floating in a denser rock (called peridotitc) in the same way that ice floats in water. (a) Show that a formula describing this phenomenon is gt = pd where g is the density of granite (2.8 103 kg/m3), p is the density of peridotite (3.3 103 kg/m3), t is the thickness of a continent, and d is the depth to which a continent floats in the peridotite. (b) If a continent sinks 5.0 km into the peridotite layer (this surface may be thought of as the ocean floor), what is the thickness of the continent?80AP 81AP Superman attempts to drink water through a very long vertical straw as in Figure P9.82. With his great strength, he achieves maximum possible suction. The walls of the straw dont collapse. (a) Find the maximum height through which he can lift the water. (b) Still thirsty, the Man of Steel repeats his attempt on the Moon, which has no atmosphere. Find the difference between the water levels inside and outside the straw. Figure P9.82 83. The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H2O above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of mm of H2O because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height lo which the fluid rises is observed, as shown in Figure P9.83. If the fluid ruses to a height of 160. mm, we write its gauge pressure as 160. mm H2O. (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions ran be investigated by means of the Queckensted test. In this procedure, the veins in the patients neck are compressed lo make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the level of the fluid. What might account for this phenomenon?A Hydrometer is an instrument used to determine liquid density. A simple one is sketched in Figure P9.84. The bulb of a syringe is squeezed and released to lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. (Assume the rod is cylindrical.) The rod. of length L and average density 0, floats partially immersed in the liquid of density . A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by =0LLh Figure P9.84 85AP A helium-filled balloon, whose envelope has a mass of 0.25 kg, is lied to a 2.0-m-long, 0.050-kg string. The. balloon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equilibrium, as in Figure P9.86. Determine the value of h. Hint: Only that part of the string above the floor contributes to the load being supported by the balloon. Figure P9.86 A light spring of constant A = 90.0 N/m is attached vertically to a table (Fig. P9.87a). A 2.00-g balloon is filled with helium (density = 0.179 kg/m3) to a volume of 5 00 m3 and is then connected to the spring, causing the spring to stretch as shown in Figure P9.87b. Determine the extension distance L when the balloon is in equilibrium.A U-tube open at both ends is partially filled with water (Fig. P9.88a). Oil ( = 750 kg/m3) is then poured into the right arm and forms a column L = 5.00 cm high (Fig. P9.88b). (a) Determine the difference h in the heights of the two liquid surfaces, (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. P9.88c). Determine the speed of the air being blown across the left arm. Assume the density of air is 1.29 kg/m3. Figure P9.88 In about 1657. Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P9.89). Two teams of eight horses each could pull the hemispheres apart only on some trials and then with greatest difficulty, with the resulting sound likened to a cannon firing. Find the force F required to pull the thin-walled evacuated hemispheres apart in terms of R, the radius of the hemispheres, P the pressure inside the hemispheres, and atmospheric pressure P0. Figure P9.89 Oil having a density of 930 kg/m3 floats on water. A rectangular block of wood 4.00 cm high and with a density of 960 kg/m3 floats partly in the oil and partly in the water. The oil completely covers the block. How far below the interface between the two liquids is the bottom of the block?91AP 10.1QQ If you quickly plunge a room-temperature mercury thermometer into very hot water, the mercury level will (a) go up briefly before reaching a final reading, (b) go down briefly before reaching a final reading, or (c) not change.If you are asked to make a very sensitive glass thermometer, which of the following working fluids would you choose? (a) mercury (b) alcohol (c) gasoline (d) glycerin Two spheres are made of the same metal and have the same radius, but one is hollow and the other is solid. The spheres are taken through the same temperature increase. Which sphere expands more? (a) solid sphere, (b) hollow sphere, (c) they expand by the same amount, or (d) not enough information to say.10.5QQ 10.6QQ 1WUE 2WUE 3WUE An electrician is wiring new electrical outlets in a house and has stored a 50.0-m length of copper wire outside where the temperature is 15.0C. When the wire is brought inside and warmed to 23.0C, by what amount in centimeters will the wires length increase due to the temperature change? (See Section 10.3.)5WUE A cylinder of volume 50.0 cm3 made of Pyrex glass is full to the brim with acetone. If the cylinder and acetone are warmed by 30.0C, (a) what is the change in volume of the glass? (b) Of the acetone? (c) Will any acetone spill out of the cylinder? (See Section 10.3.)One way to cool a gas is to let it expand. When a certain gas under a pressure of 5.00 106 Ha at 25.0C is allowed to expand to 3.00 times its original volume, its final pressure is 1.07 106 Pa. (a) What is the initial temperature of the gas in Kelvin? (b) What is the final temperature of the system? (See Section 10.4.)A container holds 0.500 m3 of oxygen at an absolute pressure of 4.00 atm. A valve is opened, allowing the gas to drive a piston, increasing the volume of the gas until the pressure drops to 1.00 atm. If the temperature remains constant, what new volume does the gas occupy?Suppose 26.0 g of neon gas are stored in a tank at a temperature of 152C. (a) What is the temperature of the gas on the Kelvin scale? (See Section 10.2.) (b) How many moles of gas are in the tank? (See Section 10.4.) (c) What is the internal energy of the gas? (See Section 10.5.)10WUE (a) Why does an ordinary glass dish usually break when placed on a hot stove? (b) Dishes made of Pyrex glass dont break as easily. What characteristic of Pyrex prevents breakage?Some thermometers are made of a mercury column in a glass tube. Based on the operation of these common thermometers, which has the larger coefficient of linear expansion, glass or mercury? (Dont answer this question by looking in a table.)4CQ Objects deep beneath the surface of the ocean are subjected to extremely high pressures, as we saw in Topic 9. Some bacteria in these environments have adapted to pressures as much as a thousand times atmospheric pressure. How might such bacteria be affected if they were rapidly moved to the surface of the ocean?Why do vapor bubbles in a pot of boiling water get larger as they approach the surface?Markings to indicate length are placed on a steel tape in a room that is at a temperature of 22C. Measurements are then made with the same tape on a day when the temperature is 27C. Are the measurements too long, too short, or accurate?Metal lids on glass jars can often be loosened by running hot water over them. Why does that work?Suppose the volume of an ideal gas is doubled while the pressure is reduced by half. Does the internal energy of the gas increase, decrease, or remain the same? Explain.An automobile radiator is filled to the brim with water when the engine is cool. What happens to the water when the engine is running and the water has been raised to a high temperature?When the metal ring and metal sphere in Figure CQ10.14 are both at room temperature, the sphere can barely be passed through the ring, (a) After the sphere is warmed in a flame, it cannot be passed through the ring. Explain, (b) What if the ring is warmed and the sphere is left at room temperature? Does the sphere pass through the ring? Figure CQ10.14 1P The pressure in a constant-volume gas thermometer is 0.700 atm at 1.00 102C and 0.512 atm at 0C. (a) What is the temperature when the pressure is 0.040 0 atm? (b) What is the pressure at 450C?3P Death Valley holds the record for the highest recorded temperature in the United States. On July 10, 1913, at a place called Furnace Creek Ranch, the temperature rose to 134F. The lowest U.S. temperature ever recorded occurred at Prospect Creek Camp in Alaska on January 23, 1971, when the temperature plummeted to 79.8F. (a) Convert these temperatures to the Celsius scale, (b) Convert the Celsius temperatures to Kelvin.Show that the temperature 40 is unique in that it has the same numerical value on the Celsius and Fahrenheit scales.6P Show that if the temperature on the Celsius scale changes by TC, the Fahrenheit temperature changes by TF=95TC The temperature difference between the inside and the outside of a home on a cold winter day is 57.0F. Express this difference on (a) the Celsius scale and (b) the Kelvin scale.9P 10P 11P A grandfather clock is controlled by a swinging brass pendulum that is 1.3 m long at a temperature of 20.0C. (a) What is the length of the pendulum rod when the temperature drops to 0.0C? (b) If a pendulums period is given by T=2L/g, where L is its length, does the change in length of the rod cause the clock to run fast or slow?A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion = 1.30 104 (C)1). At room temperature (20.0C), the frames have circular lens holes 2.20 cm in radius. To what temperature must the frames be heated if lenses 2.21 cm in radius are to be inserted into them?A spherical steel ball bearing has a diameter of 2.540 cm at 25.00C. (a) What is its diameter when its temperature is raised to 100.0C? (b) What temperature change is required to increase its volume by 1.000%?A brass ring of diameter 10.00 cm at 20.0C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0C. Assuming the average coefficients of linear expansion are constant, (a) to what temperature must the combination be cooled to separate the two metals? Is that temperature attainable? (b) What if the aluminum rod were 10.02 cm in diameter?16P Lead has a density of 11.3 103 kg/m3 at 0C. (a) What is the density of lead at 90C? (b) Based on your answer to part (a), now consider a situation in which you plan to invest in a gold bar. Would you be better off buying it on a warm day? Explain.The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of 4.00 106 m2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is 35.0C. (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to 10.0C, what is the tension in the wire? Take Youngs modulus for steel to be 20.0 1010 N/m2. (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 108 N/m2. At what temperature would the wire reach its elastic limit? (c) Explain how your answers to (a) and (b) would change if the Golden Gate Bridge were twice as long.An underground gasoline tank can hold 1.00 103 gallons of gasoline at 52.0F. If the tank is being filled on a day when the outdoor temperature (and the gasoline in a tanker truck) is 95.0F, how many gallons from the truck can be poured into the tank? Assume the temperature of the gasoline quickly cools from 95.0F to 52.0F upon entering the tank.Show that the coefficient of volume expansion, , is related to the coefficient of linear expansion, , through the expression = 3.A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0C. It is completely filled with turpentine at 20.0C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0C. (a) How much turpentine overflows? (b) What is the volume of the turpentine remaining in the cylinder at 80.0C? (c) If the combination with this amount of turpentine is then cooled back to 20.0C, how far below the cylinders rim does the turpentines surface recede?A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.700 m when the temperature is 21.2C, what is the measured length when the temperature rises to 29.4C? Note: Dont neglect the expansion of the tape.The hand in Figure P10.23 is stainless steel (coefficient of linear expansion = 17.3 106(C)1; Youngs modulus = 18 1010 N/m2). It is essentially circular with an initial mean radius of 5.0 mm, a height of 4.0 mm, and a thickness of 0.50 mm. If the band just fits snugly over the tooth when heated to a temperature of 80.0C, what is the tension in the hand when it cools to a temperature of 37C? Figure P10.23 The Trans-Alaskan pipeline is 1 300 km long, reaching from Prudhoe Bay to the port of Valdez, and is subject to temperatures ranging from 73C to +35C. (a) How much does the steel pipeline expand due to the difference in temperature? (b) How can one compensate for this expansion?The average coefficient of volume expansion for carbon tetrachloride is 5.81 104 (C)1. If a 50.0-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0C, how much will spill over when the temperature rises to 30.0C?The density or gasoline is 7.30 102 kg/m3 at 0C. Its average coefficient of volume expansion is 9.60 104(C)1 and note that 1.00 gal = 0.003 80 m3. (a) Calculate the mass of 10.0 gal of gas at 0C. (b) If 1.000 m3 of gasoline at 0C is warmed by 20.0C, calculate its new volume. (c) Using the answer to part (b), calculate the density of gasoline at 20.0C. (d) Calculate the mass of 10.0 gal of gas at 20.0C. (e) How many extra kilograms of gasoline would you get if you bought 10.0 gal of gasoline at 0C rather than at 20.0C from a pump that is not temperature compensated?Figure P10.27 shows a circular steel casting with a gap. If the casting is heated, (a) does the width of the gap increase or decrease? (b) The gap width is 1.600 cm when the temperature is 30.0C. Determine the gap width when the temperature is 190C.The concrete sections of a certain superhighway are designed to have a length of 25.0 m. The sections are poured and cured at 10.0C. What minimum spacing should the engineer leave between the sections to eliminate buckling if the concrete is to reach a temperature of 50.0C?29P A 20.0-L tank of carbon dioxide gas (CO2) is at a pressure of 9.50 105 Pa and temperature of 19.0C (a) Calculate the temperature of the gas in Kelvin. (b) Use the ideal gas law to calculate the number of moles of gas in the tank. (c) Use the periodic table to compute the molecular weight of carbon dioxide, expressing it in grams per mole. (d) Obtain the number of grains of carbon dioxide in the tank. (e) A fire breaks out, raising the ambient temperature by 224.0 K while 82.0 g of gas leak out of the tank. Calculate the new temperature and the number of moles of gas remaining in the tank. (f) Using a technique analogous to that in Example 10.6b, find a symbolic expression for the final pressure, neglecting the change in volume of the tank. (g) Calculate the final pressure in the tank as a result of the fire and leakage.(a) An ideal gas occupies a volume of 1.0 cm3 at 20.C and atmospheric pressure. Determine the number of molecules of gas in the container, (b) If the pressure of the 1.0-cm3 volume is reduced to 1.0 1011 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container?An automobile tire is inflated with air originally at 10.0C and normal atmospheric pressure. During the process, the air is compressed to 28.0% of its original volume and the temperature is increased to 40.0C. (a) What is the tire pressure in pascals? (b) After the car is driven at high speed, the tires air temperature rises to 85.0C and the tires interior volume increases by 2.00%. What is the new tire pressure (absolute) in pascals?33P Gas is contained in an 8.00-L vessel at a temperature of 20.0C and a pressure of 9.00 atm. (a) Determine the number of moles of gas in the vessel. (b) How many molecules are in the vessel?35P The density of helium gas at 0C is 0 = 0.179 kg/m3. The temperature is then raised to T = 10C but the pressure is kept constant. Assuming the helium is an ideal gas, calculate the new density f of the gas.An air bubble has a volume of 1.50 cm3 when it is released by a submarine 1.00 102 m below the surface of a lake. What is the volume of the bubble when it reaches the surface? Assume the temperature and the number of air molecules in the bubble remain constant during its ascent.The ideal gas law can be recast in terms of the density of a gas. (a) Use dimensional analysis to find an expression for the density of a gas in terms of the number of moles n, the volume V, and the molecular weight M in kilograms per mole, (b) With the expression found in part (a), show that P=MRT for an ideal gas. (c) Find the density of the carbon dioxide atmosphere at the surface of Venus, where the pressure is 90.0 atm and the temperature is 7.00 102 K. (d) Would an evacuated steel shell of radius 1.00 m and mass 2.00 102 kg rise or fall in such an atmosphere? Why?What is the average kinetic energy of a molecule of oxygen at a temperature of 300. K?A sealed cubical container 20.0 cm on a side contains three times Avogadros number of molecules at a temperature of 20.0C. Find the force exerted by the gas on one of the walls of the container.41P 42P 43P A 7.00-L vessel contains 3.50 moles of ideal gas at a pressure of 1.60 106 Pa. Find (a) the temperature of the gas and (b) the average kinetic energy of a gas molecule in the vessel. (c) What additional information would you need if you were asked to find the average speed of a gas molecule?45P 46P Inside the wall of a house, an L-shaped section of hot-water pipe consists of three parts: a straight horizontal piece h = 28.0 cm long, an elbow, and a straight, vertical piece = 134 cm long (Fig. P10.51). A stud and a second- story floorboard hold the ends of this section of copper pipe stationary. Find the magnitude and direction of the displacement of the pipe elbow when the water flow is turned on, raising the temperature of the pipe from 18.0C to 46.5C. Figure P10.51 The active element of a certain laser is made of a glass rod 30.0 cm long and 1.50 cm in diameter. Assume the average coefficient of linear expansion of the glass is 9.00 106 (C)1. If the temperature of the rod increases by 65.0C, what is the increase in (a) its length, (b) its diameter, and (c) its volume?A popular brand of cola contains 6.50 g of carbon dioxide dissolved in 1.00 L of soft drink. If the evaporating carbon dioxide is trapped in a cylinder at 1.00 atm and 20.0C, what volume does the gas occupy?50AP 51AP A 1.5-m-long glass tube that is closed at one end is weighted and lowered to the bottom of a freshwater lake. When the tube is recovered, an indicator mark shows that water rose to within 0.40 m of the closed end. Determine the depth of the lake. Assume constant temperature.53AP A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P10.58). (a) If n moles of an ideal gas are in the cylinder at a temperature of T, use Newtons second law for equilibrium to show that the height h at which the piston is in equilibrium under its own weight is given by h=nRTmg+P0A where P0 is the atmospheric pressure. (b) Is the pressure inside the cylinder less than, equal to, or greater than atmospheric pressure? (c) If the gas in the cylinder is warmed, how would the answer for h be affected? Figure P10.58 55AP 56AP A liquid with a coefficient of volume expansion of just fills a spherical flask of volume V0 at temperature Ti (Fig. P10.61). The flask is made of a material that has a coefficient of linear expansion of . The liquid is free to expand into a capillary of cross-sectional area A at the top. (a) Show that if the temperature increases by T, the liquid rises in the capillary by the amount h = (V0/A)( 3)T. (b) For a typical system, such as a mercury thermometer, why is it a approximation to neglect the expansion of the flask? Figure P10.61 Before beginning a long trip on a hot day, a driver inflates an automobile tire to a gauge pressure of 1.80 atm at 300. K. At the end of the trip, the gauge pressure has increased to 2.20 atm. (a) Assuming the volume has remained constant, what is the temperature of the air inside the tire? (b) What percentage of the original mass of air in the tire should be released so the pressure returns to its original value? Assume the temperature remains at the value found in part (a) and the volume of the tire remains constant as air is released.Two concrete spans of a 250-m-long bridge are placed end to end so that no room is allowed for expansion (Fig. P10.63a). If the temperature increases by 20.0C, what is the height y to which the spans rise when they buckle (Fig. P10.63b)?An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m (Fig. P10.64). The cylinder is Filled with 5.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0C. (a) If the lid has a cross-sectional area of 0.010 0 m2 and negligible mass, how high will the lid rise when the temperature is raised to 250C? (b) What is the pressure of the gas at 250C? Figure P10.64 A bimetallic strip of length L is made of two ribbons of different metals bonded together. (a) First assume the strip is originally straight. As the strip is warmed, the metal with the greater average coefficient of expansion expands more than the other, forcing the strip into an arc, with the outer radius having a greater circumference (Fig. P10.65). Derive an expression for the angle of bending, , as a function of the initial length of the strips, their average coefficients of linear expansion, the change in temperature, and the separation of the centers of the strips (r = r2 r1). (b) Show that the angle of bending goes to zero when T goes to zero and also when the two average coefficients of expansion become equal. (c) What happens if the strip is cooled? Figure P10.65 A 250-m-long bridge is improperly designed so that it cannot expand with temperature. It is made of concrete with = 12 106 (C)1. (a) Assuming the maximum change in temperature at the site is expected to be 20C, find the change in length the span would undergo if it were free to expand. (b) Show that the stress on an object with Youngs modulus Y when raised by T with its ends Firmly fixed is given by a Y T. (c) If the maximum stress the bridge can withstand without crumbling is 2.0 107 Pa, will it crumble because of this temperature increase? Youngs modulus for concrete is about 2.0 1010 Pa.63AP Two small containers, each with a volume of 1.00 102cm3, contain helium gas at 0C and 1.00 atm pressure. The two containers are joined by a small open tube of negligible volume, allowing gas to flow from one container to the other. What common pressure will exist in the two containers if the temperature of one container is raised to 1.00 102 C while the other container is kept at 0C?11.1QQ 11.2QQ Will an ice cube wrapped in a wool blanket remain frozen for (a) less time, (b) the same length of time, or (c) a longer time than an identical ice cube exposed to air at room temperature?Two rods of the same length and diameter are made from different materials. The rods are to connect two regions of different temperature so that energy will transfer through the rods by heat. They can be connected in series, as in Figure 11.7a (page 363), or in parallel, as in Figure 11.7b. In which case is the rate of energy transfer by heat larger? (a) When the rods are in series. (b) When the rods are in parallel. (c) The rate is the same in both cases.Stars A and B have the same temperature, but star A has twice the radius of star B. (a) What is the ratio of star As power output to star Bs output due to electromagnetic radiation? The emissivity of both stars can be assumed to be 1. (b) Repeat the question if the stars have the same radius, but star A has twice the absolute temperature of star B. (c) Whats the ratio if star A has both twice the radius and twice the absolute temperature of star B?1WUE Physics Review An athlete lifts a 175-kg barbell through a vertical displacement of 2.00 m, requiring 4.30 s for the lift. (a) Calculate the average mechanical power he must deliver to the barbell during the lift. (b) For a short period he lifts the barbell at a constant speed of 0.600 m/s. What instantaneous power does he deliver so the barbell during the time? (See Section 5.6)3WUE Convert 3.50 103 cal to the equivalent number of (a) kilo-calories (also known as Calories, used to describe the energy content of food) and (b) joules.5WUE 6WUE A large room in a house holds 975 kg of dry air at 30.0C. A woman opens a window briefly and a cool breeze brings in an additional 50.0 kg of dry air at 18.0C. At what temperature will the two air masses come into thermal equilibrium, assuming they form a closed system? (The specific heat of dry air is 1 006 J/kg C, although that value will cancel out of the calorimetry equation.)A wooden wall 4.00 cm thick made of pine with thermal conductivity 0.12 W/m K) has an area of 48.0 m2. If the temperature inside is 25C and the temperature out-side is 14C, at what rate is thermal energy transferred through the wall by conduction? (See Section 11.5.)A granite ball of radius 2.00 m and emissivity 0.450 is heated to 135C. (a) Convert the given temperature to Kelvin. (b) What is the surface area of the ball? (c) If the ambient temperature is 25.0C, what net power does the ball radiate?Rub the palm of your hand on a metal surface for 30 to 45 seconds. Place the palm of your other hand on an unrubbed portion of the surface and then on the rubbed portion. The rubbed portion will feel warmer. Now repeat this process on a wooden surface. Why does the temperature difference between the rubbed and unrubbed portions of the wood surface seem larger than for the metal surface?In winter, why did the pioneers store an open barrel of water alongside their produce?In warm climates that experience an occasional hard freeze, fruit growers will spray the fruit trees with water, hoping that a layer of ice will form on the fruit. Why would such a layer be advantageous?4CQ On a clear, cold night, why does frost tend to form on the tops, rather than the sides, of mailboxes and cars?The U.S. penny is now made of copper-coated zinc. Can a calorimetric experiment be devised to test for the metal content in a collection of pennies? If so, describe the procedure.Cups of water for coffee or tea can be warmed with a coil that is immersed in the water and raised to a high temperature by means of electricity. (a) Why do the instructions warn users not to operate the coils in the absence of water? (b) Can the immersion coil be used to warm up a cup of stew?8CQ A tile floor may feel uncomfortably cold to your bare feet, but a carpeted floor in an adjoining room at the same temperature feels warm. Why?On a very hot day, its possible to cook an egg on the hood of a tar. Would you select a black car or a white car on which to cook your egg? Why?Concrete has a higher specific heat than does soil. Use this fact to explain (partially) why a city has a higher average temperature than the surrounding countryside. Would you expect evening breezes to blow from city to country or from country to city? Explain.You need to pick up a very hot cooking pot in your kitchen. You have a pair of hot pads. Should you soak them in cold water or keep them dry in order to pick up the pot most comfortably?A poker is a stiff, nonflammable rod used to push burning logs around in a fireplace. Suppose it is to be made of a single material. For best functionality and safety, should the poker be made from a material with (a) high specific heat and high thermal conductivity, (b) low specific heat and low thermal conductivity, (c) low specific heat and high thermal conductivity, (d) high specific heat and low thermal conductivity, or (e) low specific heat and low density?Star A has twice the radius and twice the absolute temperature of star B. What is the ratio of the power output of star A to that of star B? The emissivity of both stars can be assumed to be 1. (a) 4 (b) 8 (c) 16 (d) 32 (e) 64 15CQ The highest recorded waterfall in the world is found at Angel Falls in Venezuela. Its longest single waterfall has a height of 807 m. If water at the top of the falls is at 15.0C, what is the maximum temperature of the water at the bottom of the falls? Assume all the kinetic energy of the water as it reaches the bottom goes into raising the waters temperature.The temperature of a silver bar rises by 10.0C when it absorbs 1.23 kJ of energy by heat. The mass of the bar is 525 g. Determine the specific heal of silver from these data.Lake Erie contains roughly 4.00 1011 m3 of water. (a) How much energy is required to raise the temperature of that volume of water from 11.0C to 12.0C? (b) How many years would it take to supply this amount of energy by using the 1.00 104-MW exhaust energy of an electric power plant?An aluminum rod is 20.0 cm long at 20.0C and has a mass of 0.350 kg. If 1.00 104 J of energy is added to the rod by heat, what is the change in length of the rod?A 3.00-g copper coin at 25.0C drops 50.0 m to the ground. (a) Assuming 60.0% of the change in gravitational potential energy of the coin-Earth system goes into increasing the internal energy of the coin, determine the coins final temperature. (b) Does the result depend on the mass of the coin? Explain.6P A 75-kg sprinter accelerates from rest to a speed of 11.0 m/s in 5.0 s. (a) Calculate the mechanical work done by the sprinter during this time. (b) Calculate the average power the sprinter must generate. (c) If the sprinter converts food energy to mechanical energy with an efficiency of 25%, at what average rate is he burning Calories? (d) What happens to the other 75% of the food energy being used?A sprinter of mass m accelerates uniformly from rest to velocity v in t seconds. (a) Write a symbolic expression for the instantaneous mechanical power P required by the sprinter in terms of force F and velocity v. (b) Use Newtons second law and a kinematic equation for the velocity at any time to obtain an expression for the instantaneous power in terms of m, a, and t only. (c) If a 75.0-kg sprinter reaches a speed of 11.0 m/s in 5.00 s, calculate the sprinters acceleration, assuming it to be constant. (d) Calculate the 75.0-kg sprinters instantaneous mechanical power as a function of time t and (e) give the maximum rate at which he burns Calories during the sprint, assuming 25% efficiency of conversion form food energy to mechanical energy.9P 10P 11P A 1.5-kg copper block is given an initial speed of 3.0 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest. (a) If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in temperature. (b) What happens to the remaining energy?A certain steel railroad rails 13 yd in length and weighs 70.0 lb/yd How much thermal energy is required to increase the length of such a rail by 3.0 mm? .Note: Assume the steel has the same specific heal as iron.14P What mass of water at 25.0C must be allowed to conic to thermal equilibrium with a 1.85-kg cube of aluminum initially at 1.50 102C to lower the temperature of the aluminum to 65.0C? Assume any water turned to steam subsequently recondenses.Lead pellets, each of mass 1.00 g, are heated to 200.C. How many pellets must be added to 0.500 kg of water that is initially at 20.0C to make the equilibrium temperature 25.0C? Neglect any energy transfer to or from the container.17P In a showdown on the streets of Laredo, the good guy drops a 5.00-g silver bullet at a temperature of 20.0C into a 100-cm3 cup of water at 90.0C. Simultaneously, the bad guy drops a 5.00-g copper bullet at the same initial temperature into an identical cup of water. Which one ends the showdown with the coolest cup of water in the West? Neglect any energy transfer into or away from the container.19P A 1.50-kg iron horseshoe initially at 600C is dropped into a bucket containing 20.0 kg of water at 25.0C. What is the final temperature of the water-horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away.A student drops two metallic objects into a 120-g steel container holding 150 g of water at 25C. One object is a 200-g cube of copper that is initially at 85C, and the other is a chunk of aluminum that is initially at 5.0C. To the surprise of the student, the water reaches a final temperature of 25C, precisely where it started. What is the mass of the aluminum chunk?When a driver brakes an automobile, the friction between the brake drams and the brake shoes converts the cars kinetic energy to thermal energy. If a 1 500-kg automobile traveling at 30 m/s comes to a halt, how much does the temperature rise in each of the four 8.0-kg iron brake drums? (The specific heat of iron is 448J/kg C.)Equal 0.400-kg masses of lead and tin at 60.0C are placed in 1.00 kg of water at 20.0C. (a) What is the equilibrium temperature of the system? (b) If an alloy is half lead and half tin by mass, what specific heat would you anticipate for the alloy? (c) How many atoms of tin NSn, are in 0.400 kg of tin, and how many atoms of lead NPb are in 0.400 kg of lead? (d) Divide the number NSn of tin atoms by the number NPb of lead atoms and compare this ratio with the specific heat of tin divided by the specific beat of lead. What conclusion can be drawn?24P A 75-g ice cube al 0C is placed in 825 g of water at 25C. What is the final temperature of the mixture?26P 27P 28P 29P 30P 31P 32P A high-end gas stove usually has at least one burner rated at 14 000 Btu/h. (a) If you place a 0.25-kg aluminum pot containing 2.0 liters of water at 20.C on this burner, how long will it take to bring the water to a boil, assuming all the heat from the burner goes into the pot? (b) Once boiling begins how much time is required to boil all the water out of the pot?34P Steam at 100.C is added to ice at 0C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 10. g and the mass of ice is 50. g. (b) Repeat with steam of mass 1.0 g and ice of mass 50. g.The excess internal energy of metabolism is exhausted through a variety of channels, such as through radiation and evaporation of perspiration. Consider another pathway for energy loss: moisture in exhaled breath. Suppose you breathe out 22.0 breaths per minute, each with a volume of 0.600 L. Suppose also that you inhale dry air and exhale air at 37C containing water vapor with a vapor pressure of 3.20 kPa. The vapor comes from the evaporation of liquid water in your body. Model the water vapor as an ideal gas. Assume its latent heat of evaporation at 37C is the same as its heat of vaporization at 100.C. Calculate the rate at which you lose energy by exhaling humid air.A 3.00-g lead bullet at 30.0C is fired at a speed of 2.40 102 m/s into a large, fixed block of ice at 0C, in which it becomes embedded. (a) Describe the energy transformations that occur as the bullet is cooled. What is the final temperature of the bullet? (b) What quantity of ice melts?A glass windowpane in a home is 0.62 cm thick and has dimensions of 1.0 m 2.0 in. On a certain day, the indoor temperature is 25C and the outdoor temperature is 0C. (a) What is the rate at which energy is transferred by heat through the glass? (b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant?A pond with a flat bottom has a surface area of 820 m2 and a depth of 2.0 m. On a warm day, the surface water is at a temperature of 25C while the bottom of the pond is at 12C. Find the rate at which energy is transferred by conduction from the surface to the bottom of the pond.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.A steam pipe is covered with 1.50-cm-thick insulating material of thermal conductivity 0.200 cal/cm C s. How much energy is lost every second when the steam is at 200.C and the surrounding air is at 20.0C? The pipe has a circumference of 800. cm and a length of 50.0 m. Neglect losses through the ends of the pipe.The average thermal conductivity of the walls (including windows) and roof of a house in Figure P11.46 is 4.8 104 kW/m C, and their average thickness is 21.0 cm. The house is heated with natural gas, with a heat of combustion (energy released per cubic meter of gas burned) of 9 300 kcal/m3. How many cubic meters of gas must be burned each day to maintain an inside temperature of 25.0C if the outside temperature is 0.0C? Disregard surface air layers, radiation, and energy loss by heat through the ground. Figure P11.46 Consider two cooking pots of the same dimensions, each containing the same amount of water at the same initial temperature. The bottom of the first pot is made of copper, while the bottom of the second pot is made of aluminum. Both pots are placed on a hot surface having a temperature of 145C. The water in the copper-bottomed pot boils away completely in 425 s. How long does it take the water in the aluminum-bottomed pot to boil away completely?A thermopane window consists of two glass panes, each 0.50 cm thick, with a 1.0-cm-thick sealed layer of air in between. (a) If the inside surface temperature is 23C and the outside surface temperature is 0.0C, determine the rate of energy transfer through 1.0 m2 of the window. (b) Compare your answer to (a) with the rate of energy transfer through 1.0 m2 of a single 1.0-cm-thick pane of glass. Disregard surface air layers.A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100.C and that of the far end of the aluminum rod is held at 0C. If the copper rod is 0.15 m long, what must be the length of the aluminum rod so that the temperature at the junction is 50.C?A Styrofoam box has a surface area of 0.80 m and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0C, and the outside temperature is 25C. If it takes 8.0 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of the Styrofoam.A rectangular glass window pane on a house has a width of 1.0 m, a height of 2.0 m, and a thickness of 0.40 cm. Find the energy transferred through the window by conduction in 12 hours on a day when the inside temperature of the house is 22C and the outside temperature is 2.0C. Take surface air layers into consideration.48P Measurements on two stars indicate that Star X has a surface temperature of 5 727C and Star Y has a surface temperature of 11 727C. If both stars have the same radius, what is the ratio of the luminosity (total power output) of Star Y to the luminosity of Star X? Both stars can be considered to have an emissivity of 1.0.The filament of a 75-W light bulb is at a temperature of 3300 K. Assuming the filament has an emissivity e = 1.0, find its surface area.The bottom of a copper kettle has a 10.0-cm radius and is 2.00 mm thick. The temperature of the outside surface is 102C, and the water inside the kettle is boiling at 1 atm of pressure. Find the rate at which energy is being transferred through the bottom of the kettle.A family comes home from a long vacation with laundry to do and showers to take. The water heater has been turned off during the vacation. If the heater has a capacity of 50.0 gallons and a 4800-W heating element, how much time is required to raise the temperature of the water from 20.0C to 60.0C? Assume the heater is well insulated and no water is withdrawn from the tank during that time.A 0.040.-kg ice cube floats in 0.200 kg of water in a 0.100-kg copper cup; all are at a temperature of 0C. A piece of lead at 98C is dropped into the cup, and the final equilibrium temperature is 12C. What is the mass of the lead?The surface area of an unclothed person is 1.50 m2, and his skin temperature is 33.0C. The person is located in a dark room with a temperature of 20.0C, and the emissivity of the skin is e = 0.95. (a) At what rate is energy radiated by the body? (b) What is the significance of the sign of your answer?A 200-g block of copper at a temperature of 90C is dropped into 400 g of mater at 27C. The mater is contained in a 300-g glass container. What is the final temperature of the mixture?56AP A student measures the following data in a calorimetry experiment designed to determine the specific heat of aluminum: Initial temperature of water and calorimeter: 70.0C Mass of water: 0.400 kg Mass of calorimeter: 0.040 kg Specific heat of calorimeter: 0.63 kJ/kg C Initial temperature of aluminum: 27.0C Mass of aluminum: 0.200 kg Final temperature of mixture: 66.3C Use these data to determine the specific heat of aluminum. Explain whether your result is within 15% of the value listed in Table 11.1.58AP A class of 10 students; taking an exam has a power output per student of about 200 W. Assume the initial temperature of the room is 20C and that its dimensions are 6.0 m by 15.0 m by 3.0 m. What is the temperature of the room at the end of 1.0 h if all the energy remains in the air in the room and none is added by an outside source? The specific heat of air is 837J/kg C, and its density is about 1.3 103 g/cm3.A class of 10 students taking an exam has a power output per student of about 200 W. Assume the initial temperature of the room is 20C and that its dimensions are 6.0 m by 15.0 m by 3.0 m. What is the temperature of the room at the end of 1.0 h if all the energy remains in the air in the room and none is added by an outside source? The specific heat of air is 837 J/kg C, and its density is about 1.3 103 g/cm3.A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P11.63). One end of the compound bar is maintained at 80.0C, and the opposite end is at 30.0C. Find the temperature at the junction when the energy flow reaches a steady state. Figure P11.63 An iron plate is held against an iron, wheel so that a sliding frictional force of 50. N acts between the two pieces of metal. The relative speed at which the two surfaces slide over each other is 40. m/s. (a) Calculate the rate at which mechanical energy is converted to internal energy. (b) The plate and the wheel have masses of 5.0 kg each, and each receives 50% of the internal energy. If the system is run as described for 10. s and each object is then allowed to reach a uniform internal temperature, what is the resultant temperature increase?

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