Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Physics
Give an example of entrainment not mentioned in the text.Many entrainment devices have a constriction, called a Venturi, such as shown in Figure 12.24. How does this bolster entrainment? Figure 12.24 A tube with a narrow segment designed to enhance entrainment is called a Venturi. These are very commonly used in carburetors and aspirators.Some chimney pipes have a T-shape, with a crosspiece on top that helps draw up gases whenever there is even a slight breeze. Explain how this works in terms of Bernoulli's principle.Is there a limit to the height to which an entrainment device can raise a fluid? Explain your answer.Why is it preferable for airplanes to take off into the wind rather than with the wind?Roofs are sometimes pushed off vertically during a tropical cyclone, and buildings sometimes explode outward when hit by a tornado. Use Bernoulli's principle to explain these phenomena.Why does a sailboat need a keel?It is dangerous to stand close to railroad tracks when a rapidly moving commuter train passes. Explain why atmospheric pressure would push you toward the moving train.Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.A perfume bottle or atomizer sprays a fluid that is in the bottle. (Figure 12.25.) How does the fluid rise up in the vertical tube in the bottle? Figure 12.25 Atomizer: perfume bottle with tube to carry up through the bottle. (credit: Antonia Foy, Flickr)If you lower the window on a car while moving, an empty plastic bag can sometimes fly out the window. Why does this happen?Based on Bernoulli's equation, what are three forms of energy in a fluid? (Note that these forms are conservative, unlike heat transfer and other dissipative forms not included in Bernoulli's equation.)Water that has emerged from a hose into the atmosphere has a gauge pressure of zero. Why? When you put your hand in front of the emerging stream you feel a force, yet the water's gauge pressure is zero. Explain where the force comes from in terms of energy.The old rubber boot shown in Figure 12.26 has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of leak 1? Explain your responses in terms of energy.Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.Explain why the viscosity of a liquid decreases with temperature—that is, how might increased temperature reduce the effects of cohesive forces in a liquid? Also explain why the viscosity of a gas increases with temperature—that is, how does increased gas temperature create more collisions between atoms and molecules?When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why.Why does flow decrease in your shower when someone flushes the toilet?Plumbing usually includes air-filled tubes near water faucets, as shown in Figure 12.27. Explain why they are needed and how they work. Figure 12.27 The vertical tube near the water tap remains full of air and serves a useful purpose.Doppler ultrasound can be used to the speed of blood in the body. If there is a partial constriction of an artery, where would you expect blood speed to be greatest, at or nearby the constriction? What are the two distinct causes of higher resistance in the constriction?Sink drains often have a device such as that shown in Figure 12.28 to help speed the flow of water. How does this work? Figure 12.28 You will find devices such as this in many drains. They significantly increase flow rate.Some ceiling fans have decorative wicker reeds on their blades. Discuss whether these fans are as quiet and efficient as those with smooth blades.What direction will a helium balloon move inside a car that is slowing down—toward the front or back? Explain your answer.Will identical raindrops fall more rapidly in 5° C air or 25° C air, neglecting any differences in air density? Explain your answer.If you took two marbles of different sizes, what would you expect to observe about the relative magnitudes of their terminal velocities?Why would you expect the rate of diffusion to increase with temperature? Can you give an example, such as the fact that you can dissolve sugar more rapidly in hot water?How are osmosis and dialysis similar? How do they differ?What is the average flow rate in cm3/S of gasoline to the engine of a car traveling at 100 km/h if it averages 10.0 km/L?The heart of a resting adult pumps blood at a rate of 5.00 L/min. (a) Convert this to cm3/s. (b) What is this rate in M3/s?Blood is pumped from the heart at a rate of 5.0 L/min into the aorta (of radius 1.0 cm). Determine the speed of blood through the aorta.Blood is flowing through an artery of radius 2 mm at a rate of 40 cm/s. Determine the flow rate and the volume that passes through the artery in a period of 30 s.The Huka Falls on the Waikato River is one of New Zealand's most visited natural tourist attractions (see Figure 12.29). On average the river has a flow rate of about 300,000 L/S. At the gorge, the river narrows to 20 m wide and averages 20 m deep. (a) What is the average speed of the river in the gorge? (b) What is the average speed of the water in the river downstream of the falls when it widens to 60 m and its depth increases to an average of 40 m? Figure 12.29 The Huka Falls in Taupo, New Zealand, demonstrate flow rate. (credit: RaviGogna, Flickr)A major artery with a cross-sectional area of 1.00 cm2 branches into 18 smaller arteries, each with an average cross-sectional area of 0.400 cm2. By what factor is the average velocity of the blood reduced when it passes into these branches?(a) As blood passes through the capillary bed in an organ, the capillaries join to form venules (small veins). If the blood speed increases by a factor of 4.00 and the total cross-sectional area of the venules is 10.0 cm2, what is the total cross-sectional area of the capillaries feeding these venules? (b) How many capillaries are involved if their average diameter is 10.0 m?The human circulation system has approximately 1109 capillary vessels. Each vessel has a diameter of about 8 m. Assuming cardiac output is 5 L/min, determine the average velocity of blood flow through each capillary vessel.(a) Estimate the time it would take to fill a private swimming pool with a capacity of 80,000 L using a garden hose delivering 60 L/min. (b) How long would it take to fill if you could divert a moderate size river, flowing at 5000 m3/s, into it?The flow rate of blood through 2.00106 -m-radius capillary is 3.80109 cm3/s. (a) What is the speed of the blood flow? (This small speed allows time for diffusion of materials to and from the blood.) (b) Assuming all the blood in the body passes through capillaries, how many of them must there be to carry a total flow of 90.0 cm3/s? (The large number obtained is an overestimate, but it is still reasonable.)(a) What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?The main uptake air duct of a forced air gas heater is 0.300 m in diameter. What is the average speed of air in the duct if it carries a volume equal to that of the house's interior every 15 min? The inside volume of the house is equivalent to a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high.Water is moving at a velocity of 2.00 m/s through a hose with an internal diameter of 1.60 cm. (a) What is the flow rate in liters per second? (b) The fluid velocity in this hose's nozzle is 15.0 m/s. What is the nozzle's inside diameter?Prove that the speed of an incompressible fluid through a constriction, such as in a Venturi tube, increases by a factor equal to the square of the factor by which the diameter decreases. (The converse applies for flow out of a constriction into a larger-diameter region.)Water emerges straight down from a faucet with a 1.80-cm diameter at a speed of 0.500 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.) (a) What is the flow rate in cm3/s? (b) What is the diameter of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.Unreasonable Results A mountain stream is 10.0 m wide and averages 2.00 m in depth. During the spring runoff, the flow in the stream reaches 100,000 m3/s. (a) What is the average velocity of the stream under these conditions? (b) What is unreasonable about this velocity? (c) What is unreasonable or inconsistent about the premises?Verify that pressure has units of energy per unit volume.Suppose you have a wind speed gauge like the pitot tube shown in Example 12.2(b). By what factor must wind speed increase to double the value of h in the manometer? Is this independent of the moving fluid and the fluid in the manometer?If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?Calculate the maximum height to which water could be squirted with the hose in Example 12.2 example if it: (a) Emerges from the nozzle. (b) Emerges with the nozzle removed, assuming the same flow rate.Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 220 m2? Typical air density in Boulder is 1.14 kg/m3, and the corresponding atmospheric pressure is 8.89104 N/m2. (Bernoulli's principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)(a) Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6.00 m/s parallel to its front surface and 3.50 m/s along its back surface. Take the density of air to be 1.29 kg/m3. (The calculation, based on Bernoulli's principle, is approximate due to the effects of turbulence.) (b) Discuss whether this force is great enough to be effective for propelling a sailboat.(a) What is the pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/S? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)(a) Using Bernoulli's equation, show that the measured fluid speed v for a pitot tube, like the one in Figure 12.7(b), is given by v=( 2gh)1/2 , where h is the height of the manometer fluid, is the density of the manometer fluid, is the density of the moving fluid, and g is the acceleration due to gravity. (Note that v is indeed proportional to the square root of h, as stated in the text.) (b) Calculate v for moving air if a mercury manometer's h is 0.200 m. Figure 12.7 Measurement of fluid speed based on Bernoulli's principle. (a) A manometer is connected to two that are close together and small enough not to disturb the flow. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there. Tube 2 has an opening on the side, and so the fluid has a speed V across the opening; thus, pressure there drops. The difference in pressure at the manometer is 12v22 , and so h is proportional to 12v22 . (b) This type of velocity measuring device is a Prandtl tube, also known as a pitot tube.Hoover Dam on the Colorado River is the highest dam in the United States at 221 m, with an output of 1300 MW. The dam generates electricity with water taken from a depth of 150 m and an average flow rate of 650 m3/s. (a) Calculate the power in this flow. (b) What is the ratio of this power to the facility's average of 680 MW?A frequently quoted rule of thumb in aircraft design is that wings should produce about 1000 N of lift per square meter of wing. (The fact that a wing has a top and bottom surface does not double its area.) (a) At takeoff, an aircraft travels at 60.0 m/s, so that the air speed relative to the bottom of the wing is 60.0 m/s. Given the sea level density of air to be 1.29 kg/m3, how fast must it move over the upper surface to create the ideal lift? (b) How fast must air move over the upper surface at a cruising speed of 245 m/s and at an altitude where air density is one-fourth that at sea level? (Note that this is not all of the aircraft's lift—some comes from the body of the plane, some from engine thrust, and so on. Furthermore, Bernoulli's principle gives an approximate answer because flow over the wing creates turbulence.)The left ventricle of a resting adult's heart pumps blood at a flow rate of 83.0 cm3/s, increasing its pressure by 110 mm Hg, its speed from zero to 30.0 cm/s, and its height by 5.00 cm. (All numbers are averaged over the entire heartbeat.) Calculate the total power output of the left ventricle. Note that most of the power is used to increase blood pressure.A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.750 us, with an output pressure of 3.00105 N/m2. (a) The water enters a hose with a 3.00-cm inside diameter and rises 2.50 m above the pump. What is its pressure at this point? (b) The hose goes over the foundation wall, losing 0.500 m in height, and widens to 4.00 cm in diameter. What is the pressure now? You may neglect frictional losses in both parts of the problem.(a) Calculate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information—air temperature is 20° C, the cart is moving at 0.400 m/s, its surface area is 2.50102 m2, and the thickness of the air layer is 6.00105 m. (b) What is the ratio of this force to the weight of the 0.300-kg cart?What force is needed to pull one microscope slide over another at a speed of 1.00 cm/s, if there is a 0.500-mm-thick layer of 20° C water between them and the contact area is 8.00 cm2?A glucose solution being administered with an IV has a flow rate of 4.00 cm3/min. What will the new flow rate be if the glucose is replaced by whole blood having the same density but a viscosity 2.50 times that of the glucose? All other factors remain constant.The pressure drop along a length of artery is 100 Pa, the radius is 10 mm, and the flow is laminar. The average speed of the blood is 15 mm/s. (a) What is the net force on the blood in this section of artery? (b) What is the power expended maintaining the flow?A small artery has a length of 1.1103 m and a radius of 2.5105 m. If the pressure drop across the artery is 1.3 kPa, what is the flow rate through the artery? (Assume that the temperature is 37° C.)Fluid originally flows through a tube at a rate of 100 cm3/s. To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the same as in the original conditions. (a) Pressure difference increases by a factor of 1.50. (b) A new fluid with 3.00 times greater viscosity is substituted. (c) The tube is replaced by one having 4.00 times the length. (d) Another tube is used with a radius 0.100 times the original. (e) Yet another tube is substituted with a radius 0.100 times the original and half the length, and the pressure difference is increased by a factor of 1.50.The arterioles (small arteries) leading to an organ, constrict in order to decrease flow to the organ. To shut down an organ, blood flow is reduced naturally to 1.00% of its original value. By what factor did the radii of the arterioles constrict? Penguins do this when they stand on ice to reduce the blood flow to their feet.Angioplasty is a technique in which arteries partially blocked with plaque are dilated to increase blood flow. By what factor must the radius of an artery be increased in order to increase blood flow by a factor of 10?(a) Suppose a blood vessel's radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs=6rv. Show that the terminal speed is given by v=2R2g9(s1), where R is the radius of the sphere, s is its density, and 1 is the density of the fluid and the coefficient of viscosity.Using the equation of the previous problem, find the viscosity of motor oil in which a steel ball of radius 0.8 mm falls with a terminal speed of 4.32 cm/s. The densities of the ball and the oil are 7.86 and 0.88 g/mL, respectively.A skydiver will reach a terminal velocity when the air drag equals their weight. For a skydiver with high speed and a large body, turbulence is a factor. The drag force then is approximately proportional to the square of the velocity. Taking the drag force to be FD=12Av2 and setting this equal to the person's weight, find the terminal speed for a person falling "spread eagle." Find both a formula and a number for vt, with assumptions as to size.A layer of oil 1.50 mm thick is placed between two microscope slides. Researchers find that a force of 5.50104 N is required to glide one over the other at a speed of 1.00 cm/s when their contact area is 6.00 cm2. What is the oil's viscosity? What type of oil might it be?(a) Verify that a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, assuming that all other factors remain constant, as stated in the text. (b) What increase in flow is obtained from a 5.00% increase in radius, again assuming all other factors remain constant?Example 12.8 dealt with the flow of saline solution in an IV system. (a) Verify that a pressure of 1.62104 N/m2 is created at a depth of 1.61 m in a saline solution, assuming its density to be that of sea water. (b) Calculate the new flow rate if the height of the saline solution is decreased to 1.50 m. (c) At what height would the direction of flow be reversed? (This reversal can be a problem when patients stand up.)When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in an artery has been reduced to 10.0% of its normal value by a blood clot and the average pressure difference has increased by 20.0%, by what factor has the clot reduced the radius of the artery?During a marathon race, a runner's blood flow increases to 10.0 times her resting rate. Her blood's viscosity has dropped to 95.0% of its normal value, and the blood pressure difference across the circulatory system has increased by 50.0%. By what factor has the average radii of her blood vessels increased?Water supplied to a house by a water main has a pressure of 3.00105 N/m2 early on a summer day when neighborhood use is low. This pressure produces a flow of 20.0 L/min through a garden hose. Later in the day, pressure at the exit of the water main and entrance to the house drops, and a flow of only 8.00 L/min is obtained through the same hose. (a) What pressure is now being supplied to the house, assuming resistance is constant? (b) By what factor did the flow rate in the water main increase in order to cause this decrease in delivered pressure? The pressure at the entrance of the water main is 5.00105 N/m2, and the original flow rate was 200 L/min. (c) How many more users are there, assuming each would consume 20.0 L/min in the morning?An oil gusher shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. Neglecting air resistance but not the resistance of the pipe, and assuming laminar flow, calculate the gauge pressure at the entrance of the 50.0-m-long vertical pipe. Take the density of the oil to be 900 kg/m3 and its viscosity to be 1.00 (N/m2) s (or 1.00 Pa s). Note that you must take into account the pressure due to the 50.0-m column of oil in the pipe.Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200.0 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is 8.00106 N/m2. (a) Calculate the resistance of the hose. (b) What is the viscosity of the concrete, assuming the flow is laminar? (c) How much power is being supplied, assuming the point of use is at the same level as the pump? You may neglect the power supplied to increase the concrete's velocity.Construct Your Own Problem Consider a coronary artery constricted by arteriosclerosis. Construct a problem in which you calculate the amount by which the diameter of the artery is decreased, based on an assessment of the decrease in flow rate.Consider a river that spreads out in a delta region on its way to the sea. Construct a problem in which you calculate the average speed at which water moves in the delta region, based on the speed at which it was moving up river. Among the things to consider are the size and flow rate of the river before it spreads out and its size once it has spread out. You can construct the problem for the river spreading out into one large river or into multiple smaller rivers.Verify that the flow of oil is laminar (barely) for an oil gusher that shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. The vertical pipe is 50 m long. Take the density of the oil to be 900 kg/m3 and its viscosity to be 1.00(N/m2) s (or 1.00Pa s).Show that the Reynolds number NRis unitless by substituting units for all the quantities in its definition and cancelling.Calculate the Reynolds numbers for the flow of water through (a) a nozzle with a radius of 0.250 cm and (b) a garden hose with a radius of 0.900 cm, when the nozzle is attached to the hose. The flow rate through hose and nozzle is 0.500 us. Can the flow in either possibly be laminar?A fire hose has an inside diameter of 6.40 cm. Suppose such a hose carries a flow of 40.0 LIS starting at a gauge pressure of 1.62106 N/m2. The hose goes 10.0 m up a ladder to a nozzle having an inside diameter of 3.00 cm. Calculate the Reynolds numbers for flow in the fire hose and nozzle to show that the flow in each must be turbulent.Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in wheelbarrows. The flow rate is 200.0 L/min through a 50.0-m-long, 8.00-cm-diameter hose, and the pressure at the pump is 8.00106 N/m2. Verify that the flow of concrete is laminar taking concrete's viscosity to be 48.0 (N/m2) s, and given its density is 2300 kg/m3.At what flow rate might turbulence begin to develop in a water main with a 0.200-m diameter? Assume a 20° C temperature.What is the greatest average speed of blood flow at 37° C in an artery of radius 2.00 mm if the flow is to remain laminar? What is the corresponding flow rate? Take the density of blood to be 1025 kg/m3.In Take-Home Experiment: Inhalation, we measured the average flow rate Q of air traveling through the trachea during each inhalation. Now calculate the average air speed in meters per second through your trachea during each inhalation. The radius of the trachea in adult humans is approximately 10-2 m. From the data above, calculate the Reynolds number for the air flow in the trachea during inhalation. Do you expect the air flow to be laminar or turbulent?Gasoline is piped underground from refineries to major users. The flow rate is 3.00102 m3/s (about 500 gal/ min), the viscosity of gasoline is 1.00103 (N/m2) s, and its density is 680 kg/m3. (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?Assuming that blood is an ideal fluid, calculate the critical flow rate at which turbulence is a certainty in the aorta. Take the diameter of the aorta to be 2.50 cm. (Turbulence will actually occur at lower average flow rates, because blood is not an ideal fluid. Furthermore, since blood flow pulses, turbulence may occur during only the high-velocity part of each heartbeat.)Unreasonable Results A fairly large garden hose has an internal radius of 0.600 cm and a length of 23.0 m. The nozzle-less horizontal hose is attached to a faucet, and it delivers 50.0 L/S. (a) What water pressure is supplied by the faucet? (b) What is unreasonable about this pressure? (c) What is unreasonable about the premise? (d) What is the Reynolds number for the given flow? (Take the viscosity of water as 1.005103(N/m2)s .)You can smell perfume very shortly after opening the bottle. To show that it is not reaching your nose by diffusion, calculate the average distance a perfume molecule moves in one second in air, given its diffusion constant D to be 1.00106 m2/s.What is the ratio of the average distances that oxygen will diffuse in a given time in air and water? Why is this distance less in water (equivalently, why is D less in water)?Oxygen reaches the veinless cornea of the eye by diffusing through its tear layer, which is 0.500-mm thick. How long does it take the average oxygen molecule to do this?(a) Find the average time required for an oxygen molecule to diffuse through a 0.200-mm-thick tear layer on the cornea. (b) How much time is required to diffuse 0.500 cm3 of oxygen to the cornea if its surface area is 1.00 cm2?Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.What does it mean to say that two systems are in thermal equilibrium?Give an example of a physical property that varies with temperature and describe how it is used to measure temperature.When a cold alcohol thermometer is placed in a hot liquid, the column of alcohol goes down slightly before going up. Explain why.If you add boiling water to a cup at room temperature, what would you expect the final equilibrium temperature of the unit to be? You will need to include 1he surroundings as pan of the system. Consider the zeroth law of thermodynamics.Thermal stresses caused by uneven cooling can easily break glass cookware. Explain why Pyrex®, a glass with a small coefficient at lineal expansion, is less susceptible.Water expands significantly when it freezes: a volume increase at about 9% occurs. As a result of this expansion and because of the formation and growth of crystals as water freezes anywhere from 10% to 30% of biological cells are burst when animal or plant material is frozen. Discuss the implications of this cell damage for the prospect of preserving human bodies by freezing so that they can he thawed at some future date when it is hoped that all diseases are curable.One method at getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block he hotter or colder than the peg during insertion? Explain your answer.Does it really help to run hot water over a tight metal lid on a glass jar before flying to open it? Explain your answer.Liquids and solids expand with increasing temperature, because the kinetic energy of a body's atoms and molecules increases. Explain why some materials shrink with increasing temperature.Find out the human population of Earth. Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth?
Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?A constant-volume gas thermometer contains a fixed amount of gas. What properly of the gas is measured to indicate its temperature?How is momentum related to the pressure exerted by a gas? Explain on the atomic and molecular level, considering the behavior of atoms and molecules.A pressure cooker contains water and steam in equilibrium at a pressure greater than atmospheric pressure. How does this greater pressure increase cooking speed?Why does condensation from most rapidly on the coldest object in a roomfor example, on a glass of ice water?What is the vapor pressure of solid carbon dioxide (dry ice) at _785 Figure 13.36 The phase diagram for carbon dioxide. The axes aha nonlinear, and the graph is not to scale. Dry ice is solid carbon dioxide and has a sublimation temperature ofCan carbon dioxide be liquefied at room temperature (20C) ? If so, how? If not, why not? (See Figure 13.36.) Figure 13.36 The phase diagram for carbon dioxide. The axes are nonlinear, and the graph is not to scale. Dry ice is solid carbon dioxide and has a sublimation temperature of -78.5°C .Oxygen cannot be liquefied at room temperature by placing it under a large enough pressure to force its molecules together. Explain why this is.What is the distinction between gas and vapor?Because humidity depends only on water's vapor pressure and temperature, are the saturation vapor densities listed in Table 13.5 valid in an atmosphere of helium at a pressure of 1.01105N/m2 , rather than air? Are those values affected by altitude on Earth?Why does a beaker of 40.0C water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker?Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)?What is me Fahrenheit temperature of a person with at 39.0°C fever?Frost damage to most plants occurs at temperatures of 28.0F or lower. What is this temperature on the Kelvin scale?To conserve energy, room temperatures are kept at 68.0F in the winter and 78.0F in the summer. What are these temperatures on me Celsius scale?A tungsten light bulb filament may operate a1 2900 K. What is its Fahrenheit temperature? What is this on me Celsius scale?The Surface temperature of the Sun is about 5750 K. What is this temperature on the Fahrenheit scale?One of the honest temperatures ever recorded on the surface at Earth was 134F in Death Valley, CA. What is this temperature in Celsius degrees? What is this temperature in Kelvin?(a) Suppose a cold front blows into your locale and drops the temperature by 40.0 Fahrenheit degrees. How many degrees Celsius does me temperature decrease when there is a 40.0F decrease in temperature? (b) Show that any change in temperature in Fahrenheit degrees is nine—?fths the change in Celsius degrees.(a) At what temperature do the Fahrenheit and Celsius scales have the same numerical value? (b) At what temperature do me Fahrenheit and Kelvin scales have the same numerical value?The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0C. What will its height be on a day when the temperature falls to 10.0C ? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's.How much taller does me Eiffel Tower become at the end of a day when the temperature has increased by 15C ? Its original height is 321 m and you can assume it is made of steel.What is the change in length of a 3.00mlong column of mercury if its temperature changes from 37.0C to 40.0C, assuming the mercury is unconstrained?How large an expansion gap should be left between steel railroad rails it they may reach a maximum temperature 350C greater than when they were laid? Their original length is 10.0 m.You are looking to purchase a small piece of land in Hong Kong. The price is “only” 60,000 per square meter! The land title says the dimensions are 20m30m. By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was 20C above normal?Global warming will produce rising sea levels partly due to melting ice team but alga due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate me change in length of a column of water 1.00 km high for a temperature increase of 1.00C. Note that this calculation is only approximate because ocean warming is not uniform with depth.Show that 60.0L of gasoline originally at 15.0C will expand to 61.1L when it warms to 35.0C, as claimed in Example 13.4.(a) Suppose a meter Stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0C. What is their difference in length at 22.0C ? (b) Repeat the calculation for two 30.0mlong surveyor's tapes.(a) If a 500mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 500C, how much will overflow when its temperature reaches 210C ? (b) How much less water would overflow under the same conditions?Most automobiles have a coolant reservoir to catch radiator fluid than may overflow when 1he engine is hot. A radiator is made of copper and is filled to its 16.0L capacity when at 10.0C. What volume of radiator fluid will overflow when the radiator and fluid reach their 95.0C operating temperature, given that the fluid’s volume coefficient of expansion is =400106/C ? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than 95.0C.A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in level if the 350cm3 of coffee is in a 7.00cmdiameter cup and decreases in temperature from 95.0C to 45.0C. (Most of me drop in level is actually due to escaping bubbles of air.)(a) The density of water at 0C is very nearly 1000kg/m3 (it is actually 999.84kg/m3 ), whereas the density of ice at 0C is 917kg/m3. Calculate the pressure necessary to keep ice from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature. (This problem gives you only an indication of how large the forces associated with freezing water might be.) (b) What are the implications of this result for biological cells that are frozen?Show that 3, by calculating the change in volume V of a cube with sides of length L.The gauge pressure in your car tires is 2.50105N/m2 at a temperature of 35.0C when you drive it onto a ferry heat to Alaska. What is their gauge pressure later, when their temperature has dropped to 40.0C ?Convert an absolute pressure of 7.00105N/m2 to gauge pressure in lb/in2. (This value was stated to be just less than 90.0lb/in2 in Example 13.9. Is it?)Suppose a gasfilled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0C. (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60.0C (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?Large helium-filled balloons are used to lift scienti?c equipment to high altitudes. (a) What is the pressure inside such a balloon if it starts out at sea level with a temperature of 10.0C and rises to an altitude where its volume is twenty times the original volume and its temperature is 50.0C ? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)Confirm mat the units of nRT are those of energy for each value of R : (a) 8.31J/molK, (b) 1.99cal/molK, and (c) 0.0821Latm/molK.In the text, it was shown that N/V=2.681025m3 for gas at STP. (a) Show that this quantity is equivalent to N/V=2.681019cm3, as stated. (b) About how many atoms are mere in one m3 (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of Mama and molecules?Calculate the number of moles in me 2.00L volume of air in the lungs of me average person. Note that me air is at 37.0C (body temperature).An airplane passenger has 100cm3 of air in his stomach just before the plane takes off from a sealevel airport. What volume will the air have at cruising altitude if cabin pressure drops to 7.50104N/m2 ?(a) What is me 1imlume (in km3) of Avogadro’s number of sand grains if each grain is a cube and has sides mat are 1.0 mm long? (b) How many kilometers of beaches in length would this cover it me beach averages 100 m in width and 10.0 m in depth? Neglect air spaces between grains.An expensive vacuum System can achieve a pressure as low as 1.00107N/m2 at 20C. How many atoms are there in a cubic centimeter at this pressure and temperature?The number density of gas atoms at a certain location in the space above our planet is about 1.001011m3, and the pressure is 2.751010N/m2 in this space. What is the temperature there?A bicycle tire has a pressure of 7.00105N/m2 at a temperature of 18.0C and contains 2.00L of gas. What will its pressure be if you let out an amount of air that has a volume of 100cm3 at atmospheric pressure? Assume tire temperature and volume remain constant.A high—pressure gas cylinder contains 50.13L of toxic gas at a pressure of 1.40107N/m2 and a temperature of 25.0C. Its value leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (78.5C) to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure it onetenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?Find the number of moles in 2.00L of gas at 35.0C and under 7.41107N/m2 of pressure.Calculate the depth to which Avogadro's number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume me space between balls adds an extra 25.0% to their volume and assume they are not crushed by their own weight.(a) What is me gauge pressure in a 25.0C car tire containing 3.60 mol of gas in a 30.0 L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and 25.0C ? Assume the temperature returns to 25.0C and me volume remains constant.(a) In the deep space between galaxies, me density of atoms is as low as 106atoms/m3, and me temperature is a frigid 2.7 K. What is me pressure? (b) What volume (in m3) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?Some incandescent light bulbs are filled with argon gas. What is vrms for argon atoms near the filament, assuming their temperature is 2500 K?Average atomic and molecular speeds (vrms) are large, even at low temperatures. What is vrms for helium atoms at 5.00 K, just one degree above helium's liquefaction temperature?(a) What is the average kinetic energy in joules of hydrogen atoms on the 5500C surface at the Sun? (b) What is the average kinetic energy of helium atoms in a region of the solar corona where me temperature is 6.00105K ?The escape velocity of any object from Earth is 11.2km/s. (a) Express this speed in m/s and km/h. (b) At what temperature would oxygen molecules (molecular mass is equal to 32.0g/mol ) have an average velocity vrms equal to Earth's escape velocity of 11.1km/s ?The escape velocity from the Moon is much smaller than from Earth and is only 2.38km/s. At what temperature would hydrogen molecules (molecular mass is equal to 2.01ftg/mol ) have an average velocity vrms equal to the Moon’s escape velocity?Nuclear fusion, the energy source at the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of me alums is high—that is, at high temperatures. Suppose you want me atoms in your fusion experiment to have average kinetic energies of 6.401014J. What temperature is needed?Suppose that the average velocity (vrms) of carbon dioxide molecules (molecular mass is equal to 44.0g/mol ) in a ?ame is found to be 1.05105m/s. What temperature does this represent?Hydrogen molecules (molecular mass is equal to 2.016g/mol ) have an average velocity vrmsequal to 193m/s. What is the temperature?Much of The 935 near the Sun is atomic hydrogen. Its temperature would have to be 1.5107K for the average velocity vrms to equal me escape velocity from the Sun. What is that velocity?There are two important isotopes of uranium 235U and 238U ; these isotopes are nearly identical chemically but have different atomic masses. Only 235U is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities vrms of uranium hexafluoride gas. UF6. (a) The molecular masses for 235UUF6 and 238UUF6 are 349.0g/mol and 352.0g/mol, respectively. What is the ratio of their average velocities? (b) At what temperature would their average velocities differ by 1.00m/s ? (c) Do your answers in this problem imply that this technique may be difficult?Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when me atmospheric pressure is 1.01105N/m2 ?(a) What is me vapor pressure of water at 20.0C ? (b) What percentage of atmospheric pressure does this correspond to? (c) What percent of 20.0C air is water vapor if it has 100% relative humidity? (The density of dry air at 20.0C is 1.20kg/m3 .)Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure. (a) What pressure is necessary to raise the boiling point to 120.0C ? (b) What gauge pressure does this correspond to?(a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is 8.59104N/m2 ? (b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is 7.00104N/m2 ?What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature at 70.0C ?At a spot in the high Andes, water boils at 80.0C, greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location?What is the relative humidity on a 25.0C day when the air contains 18.0g/m3 of water vapor?What is the density of water vapor in g/m3 on a hot dry day in me desert when the temperature is 40.0C and the relative humidity 15 6.00%?A deepsea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of 1.01105N/m2. (a) What is me partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of 2.00106N/m2, what percent oxygen should it be to have the same oxygen partial pressure as at sea level?The vapor pressure of water at 40.0C is 7.34103N/m2. Using the ideal gas law, calculate the density of water vapor in g/m3 that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature (51.1g/m3).Air in human lungs has a temperature of 37.0C and a saturation vapor density of 44.0g/m3. (a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss at water vapor by me person? (b) Calculate the partial pressure of water vapor having this density, and compare it with the vapor pressure of 6.31103N/m2.If the relative humidity is 90.0% on a muggy summer morning when the temperature is 20.0C, what will it be later in the day when the temperature is 30.0C, assuming the water vapor density remains constant?Late on an autumn day, the relative humidity is 45.0% and the temperature is 20.0C. What will the relative humidity be that evening when the temperature has dropped to 10.0C, assuming constant water vapor density?Atmospheric pressure amp Mt. Everest is 3.30104N/m2. (a) What is the partial pressure of oxygen there if it is 20.9% at me air? (b) What percent oxygen should a mountain climber breathe so that its partial pressure is the same as at sea level, where atmospheric pressure is 1.01105N/m2 ? (c) One of the most severe problems for those climbing very high mountains is the extreme drying of breathing passages. Why does this drying occur?What is the dew point (the temperature at which 100% relative humidity would occur) on a day when relative humidity is 39.0% at a temperature of 20.0C ?On a certain day the temperature is 25.0C and the relative humidity is 90.0%. How many grams of water must condense out of each cubic meter of air if the temperature falls to 15.0C ? Such a drop in temperature can, thus, produce heavy dew or fog.Integrated Concepts The boiling point of water increases with depth because pressure increases with depth. At what depth will fresh water have a boiling point of 150C, if the surface of the water is at sea level?Integrated Concepts (a) At what depth in fresh water is critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth?Integrated Concepts To get an idea of the small effect that temperature has on Archimedes’ principle, calculate the traction of a copper block's weight that is supported by the buoyant force in 0C water and compare this fraction with the fraction supported in 95.0C water.Integrated Concepts If you want to cook in water at 150C, you need a pressure cooker that can withstand the necessary pressure. (a) What pressure is required for the boiling point of water to be this high? (b) If the lid of the pressure cooker is a disk 25.0 cm in diameter, what force must it be able to withstand at this pressure?Unreasonable Results (a) How many moles per cubic meter of an ideal gas are there at a pressure of 1.001014N/m2 and at 0C ? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?Unreasonable Results (a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If 1he hole is 10.0% bigger in diameter than the 22.0C rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (2) Which premise is responsible?Unreasonable Results The temperature inside a supernova explosion is said to be 2.001013K. (a) What would the average velocity vrmsof hydrogen atoms be? (b) What is unreasonable about this velocity? (b) Which premise or assumption is responsible?Unreasonable Results Suppose the relative humidity is 80% on a day when the temperature is 30.0C. (a) What will the relative humidity be if the air cools to 25.0C and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible?How is heat transfer related to temperature?Describe a situation in which heat transfer occurs. What are the resulting forms of energy?When heal transfers into a system, is the energy stored as heat? Explain briefly.What three factors affect the heat transfer that is necessary to change an object's temperature?The brakes in a car increase in temperature by T when bringing the car to rest from a speed v. How much greater would T be if the car initially had twice the speed? You may assume the car to stop suf?ciently fast so that no heat transfers out at the brakes.Heat transfer can cause temperature and phase changes. What else can cause these changes?How does the latent heat of fusion of water help slow the decrease of air temperatures, perhaps preventing temperatures from falling significantly below 0C, in the vicinity of large bodies of water?What is me temperature of ice right after it is formed by freezing water?If you place 0C ice into 0C water in an insulated container, what will happen? Will some ice melt, will more water freeze, or will neither take place?What effect does condensation on a glass of ice water have on the rate at which the ice melts? Will the condensation speed up the melting process or slow it down?In my humid climates where there are numerous bodies of water, such as in Florida, it is unusual for temperatures to rise above about 35C(95F). In deserts, however, temperatures can rise far above this. Explain how the evaporation of water helps limit high temperatures in humid climates.In winters, if is often warmer in San Francisco than in nearby Sacramento, 150 km inland. In summers, it is nearly always hotter in Sacramento. Explain how the bodies of water surrounding San Francisco moderate its extreme temperatures.Putting a lid on a boiling pot greatly reduces the heat transfer necessary to keep it boiling. Explain why.Freeze-dried toads have been dehydrated in a vacuum. During the process, me food freezes and must be heated to facilitate dehydration. Explain both how the vacuum speeds up dehydration and why the food freezes as a result.When still air cools by radiating at night, it is unusual for temperatures to fall below the dew point. Explain why.In a physics classroom demonstration, an instructor inflates a balloon by mouth and then cools it in liquid nitrogen. When cold, the shrunken balloon has a small amount of light blue liquid in it, as well as some snow-like crystals. As it warms up, the liquid boils, and part of me crystals sublimate, with some crystals lingering for a while and then producing a liquid. Identify the blue liquid and the two solids in the cold balloon. Justify your identifications using data from Table 14.2.What are the main methods of heat transfer front the hot core of Earth to its surface? From Earth's surface to outer space? When our bodies get too warm, they respond by sweating and increasing blood circulation to the surface to transfer thermal energy away from the care. What effect will this have on a person in at 40.0C hot tub? Figure 14.30 shows a cutaway drawing of a thermos battle (also known as a Dewar flask), which is a device designed specifically to slow down all terms at heat transfer. Explain the functions of the various parts, such as the vacuum, the silvering of the walls, the thin-walled long glass neck, the rubber support, the air layer, and the stopper. Figure 14.30 The construction of a thermos bottle is designed to inhibit all methods of heat transfer.Some electric sieves have a flat ceramic surface with heating elements hidden beneath. A pot placed over a heating element will be heated, while it is safe to touch the surface only a few centimeters away. Why is ceramic, with a conductivity less than that of a metal but greater than that of a good insulator, an ideal choice for the stove top?Loosefitting white clothing covering most at the body is ideal for desert dwellers, both in the hot Sun and during cold evenings. Explain how such clothing is advantageous during both day and night.One way to make a fireplace more energy efficient is to have an external air supply for me combustion at its fuel. Another is to have room air circulate around the outside of the fire box and back into the room. Detail the methods of heat transfer involved in each.On cold, clear nights horses will sleep under the cover of large trees. How does this help them keep warm?When watching a daytime circus in a large, darkcolored tent, you sense significant heat transfer from the tent. Explain why this occurs.Satellites designed to observe me radiation from cold (3 K) dark space have sensors that are shaded from the Sun, Earth, and Moon and that are cooled to very low temperatures. Why must the sensors be at low temperature?Why are cloudy nights generally warmer than clear ones?Why are thermometers that are used in weather stations shielded from the sunshine? What does a thermometer measure if it is shielded from the sunshine and also if it is not?On average, would Earth be warmer or cooler without the atmosphere? Explain your answer.On a hot day, the temperature of an 80,000L swimming pool increases by 150C. What is the net heat transfer during this healing? Ignore any complications, such as loss of water by evaporation.Show that 1cal/gC=1kcal/kgC.To sterilize a 50.0g glass baby bottle, we must raise its temperature from 22.0C to 95.0C. How much heat 1Iansfer is required?The same heat transfer into identical masses of different substances produces different temperature changes. Calculate the final temperature when 1.00 kcal of heat transfers into 1.00 kg of the following, originally at 20.0C : (a) water; (b) concrete; (c) steel; and (d) mercury.Rubbing your hands together warms them by converting work into thermal energy. If a woman rubs her hands back and form for a total of 20 rubs, at a distance of 750 cm per rub, and with an average frictional force of 40.0 N, what is the temperature increase? The mass of tissues warmed is only 0.100 kg, mostly in the palms and fingers.A 0.250kg block at a pure material is heated from 20.0C to 65.0C by the addition of 4.35 kJ of energy. Calculate its speci?c heat and identify the Substance of which it is most likely composed.Suppose identical amounts of heat transfer into different masses of copper and water, causing identical changes in temperature. What is the ratio of the mass of copper to water?(a) The number of kilocalories in food is determined by calorimetry techniques in which the food is burned and the amount at heat transfer is measured. How many kilocalories per gram are there in a 5.00g peanut if the energy from burning it is transferred to 0.500 kg of water held in a 0.100kg aluminum cup, causing a 54.9C temperature increase? (b) Compare your answer to labeling information found on a package of peanuts and comment on whether the values are consistent.Following Vigorous exercise, the body temperature of an 80.0kg person is 40.0C. At what rate in watts must the person transfer thermal energy to reduce the body temperature to 37.0C in 30.0 min, assuming the body continues to produce energy at the rate of 150 W? (1watt=1joule/second or 1W=1J/s ).Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature it the cooling system fails (1 watt 2 1 joule/second or 1W=1J/s and 1MW=1megawatt ). (a) Calculate the rate of temperature increase in degrees Celsius per second (C/s) if the mass of the reactor core is 1.60105kg and it has an average specific heat of 0.3349kJ/kgC. (b) How long would it take to obtain a temperature increase of 2000C, which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than that calculated here because the heat transfer is concentrated in a smaller mass. Later, however, the temperature increase would slow down because the 5105-kg steel containment vessel would also begin to heat up.) Figure 14.32 Radioactive spentfuel pool at a nuclear power plant. Spent fuel stays hot for a long time. (credit: U.S. Department of Energy)How much heat transfer (in kilocalories) is required to thaw a 0.450kg package of frozen vegetables originally at if their heat of fusion is the same as that of water?A bag containing 0C ice is much more effective in absorbing energy than one containing the same amount at 0C water. a. How much heat transfer is necessary to raise the temperature of 0.800 kg of water from 0C to 30.0C ? b. How much heat transfer is required to first melt 0.800 kg of 0C ice and then raise its temperature? c. Explain how your answer supports the contention that the ice is more effective.(a) How much heat transfer is required to raise the temperature of a 0.750kg aluminum pot containing 2.50 kg of water from 30.0C to the boiling point and then boil away 0.750 kg of water? (b) How long does this take if the rate of heat transfer is 500 W 1watt=ljoule/second(lW=lJ/s) ?The formation of condensation on a glass of ice water causes the ice to melt faster than it would otherwise. If 8.00 g of condensation forms on a glass containing both water and 200 g of ice, how many grams of the ice will melt as a result? Assume no other heat transfer occurs.On a trip, you notice that a 3.50kg bag of ice lasts an average of one day in your cooler. What is the average power in watts entering the ice if it starts at 0°C and completely melts to 0C water in exactly one day 1watt=1joule/second (lW=1J/s) ?On a certain dry sunny day, a swimming pool’s temperature would rise by 1.50C if not for evaporation. What fraction of the water must evaporate to carry away precisely enough energy to keep the temperature constant?(a) How much heat transfer is necessary to raise the temperature of a 0.200kg piece of ice from 20.0C to 130C, including the energy needed for phase changes? (b) How much time is required for each stage, assuming a constant 20.0kJ/s rate of heat transfer? (c) Make a graph of temperature versus time for this process.In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf in Antarctica. It was approximately a rectangle 160 km long, 40.0 km wide, and 250 m thick. (a) What is the mass of this iceberg, given that the density of ice is 917kg/m3 ? (b) How much heat transfer (in joules) is needed to melt it? (c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100W/m2, 12.00 h per day?How many grams of coffee must evaporate from 350 g of coffee in a 100g glass cup to cool the coffee from 95.0C to 45.0C ? You may assume the coffee has the same thermal properties as water and that the average heat at vaporization is 2340kJ/kg(560cal/g). (You may neglect the change in mass of the coffee as it cools, which will give you an answer that is slightly larger than correct.)(a) It is difficult to extinguish a fire on a crude oil tanker, because each liter of crude oil releases 2.80107J of energy when burned. To illustrate this difficulty, calculate the number of liters of water that must be expended to absorb the energy released by burning 1.00 L of crude oil, it the water has its temperature raised from 20.0C to 100C, it boils, and the resulting steam is raised to 300C. (b) Discuss additional complications caused by the fact that crude oil has a smaller density than water.The energy released from condensation in thunderstorms can be very large. Calculate the energy released into the atmosphere for a small storm of radius 1 km, assuming that 1.0 cm of rain is precipitated uniformly over this area.To help prevent from damage, 4.00 kg at 0C water is sprayed onto a fruit tree. (a) How much heat transfer occurs as the water freezes? (b) How much would the temperature at the 200kg tree decrease if this amount of heat transferred from the tree? Take the specific heat to be 3.35kJ/kgC, and assume that no phase change occurs.A 0.250kg aluminum bowl holding 0.800 kg of soup at 25.0C is placed in a freezer. What is the final temperature if 377 kJ of energy is transferred from the bowl and soup, assuming the soup's thermal properties are the same as that of water? Explicitly show how you follow the steps in ProblemSolving Strategies for the Effects of Heat Transfer.A 0.0500kg ice cube at 30.0C is placed in 0.400 kg of 350C water in a very wellinsulated container. What is the final temperature?If you pour 0.0100 kg of 20.0C water onto a 1.20kg block of ice (which is initially at 15.0C ), what is the final temperature? You may assume that the water cools so rapidly that effects of the surroundings are negligible.Indigenous people sometimes cook in watertight baskets by placing hot rocks into water to bring it to a boil. What mass of 500C rock must be placed in 4.00 kg of 15.0C water to bring its temperature to 100C, if 0.0250 kg of water escapes as vapor from the initial sizzle? You may neglect the effects of the surroundings and take the average speci?c heat of the rocks to be that of granite.What would be the final temperature of the pan and water in Calculating the Final Temperature When Heat Is Transferred Between Two Bodies: Pouring Cold Water in a Hat Pan if 0.260 kg of water was placed in the pan and 0.0100 kg of the water evaporated immediately, leaving the remainder to come to a common temperature with the pan?In some countries, liquid nitrogen is used on dairy trucks instead of mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid nitrogen, which has a density at 808kg/m3. (a) Calculate the heat transfer necessary to evaporate this amount of liquid nitrogen and raise its temperature to 300C. (Use cp and assume it is constant over the temperature range.) This value is the amount of cooling the liquid nitrogen supplies. (b) What is this heat transfer rate in kilowatthours? (c) Compare the amount of cooling obtained from melting an identical mass at 0C ice with that from evaporating the liquid nitrogen.Some gun fanciers make their own bullets, which involves melting and casting the lead slugs. How much heat transfer is needed to raise the temperature and melt 0.500 kg of lead, starting from 25.0C ?(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is 120m2 and their inside surface is at 18.0C, while their outside surface is at 5.00C. (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly the windows transfer heat by conduction, calculate the rate of conduction in watts through a 3.00m2 window that is 0.635 cm thick (1/4 in) if the temperatures of the inner and outer surfaces are 5.00C and 10.0C, respectively. This rapid rate will not be maintainedthe inner surface will cool, and even result in frost formation.Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is 37.0C, the skin temperature is 34.0C, the thickness of the tissues between averages 1.00 cm, and the surface area is 1.40m2.Suppose you stand with one foot on ceramic flooring and one foot on a wool carpet, making contact over an area of 80.0cm2 with each foot. Both the ceramic and the carpet are 2.00 cm thick and are 10.0C on their bottom sides. At what rate must heat transfer occur from each foot to keep the top of the ceramic and carpet at 33.0C ?A man consumes 3000 kcal of food in one day. Converting most of it to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?(a) A firewalker runs across a bed of hot coals without sustaining burns. Calculate the heat transferred by conduction into the sole of one foot of a firewalker given that the bottom of the foot is a 3.00-mm-thick callus with a conductivity at the low end of the range for wood and its density is 300kg/m3. The area of contact is 25.0cm2, the temperature of the coals is 700C, and the time in contact is 1.00 s. (b) What temperature increase is produced in the 25.0cm3 of tissue affected? (c) What effect do you think this will have on the tissue, keeping in mind that a callus is made of dead cells?(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a 1.40m2 surface area? Assume that the animal’s skin temperature is 32.0C, that tile air temperature is 5.00C, and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?A walrus transfers energy by conduction through its blubber at the rate of 150 W when immersed in 1.00°C water. The walrus’s internal core temperature is 37.0°C, and it has a surface area of What is the average thickness of its blubber, which has the conductivity of fatty tissues without blood? Figure 14.33 Walrus on ice. (credit: Captain Budd Christman, NOAA Corps)Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of 10.0m2 and a thermal conductivity twice that of glass wool with the rate of heat conduction through a window that is 0.750 cm thick and that has an area of 2.00m2, assuming the same temperature difference across each.Suppose a person is covered head to foot by wool clothing with average thickness of 2.00 cm and is transferring energy by conduction through the clothing at the rate of 50.0 W. What is the temperature difference across the clothing, given the surface area is 1.40m2 ?Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through the same area and at the same rate as computed in Example 14.6, what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.One easy way to reduce heating (and cooling) costs is to add extra insulation in the attic of a house. Suppose the 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, then by what percentage would the heating cost of the house drop? Take the single story house to be of dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heat loss through windows and doors.(a) Calculate the rate of heat conduction through a double-paned window that has a 1.50m3 area and is made of two panes of 0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surface temperature is 15.0C, while that on the outside is 10.0C. (Hint: There are identical temperature drops across the two glass panes. First find these and then the temperature drop across the air gap. This problem ignores the increased heat transfer in the air gap due to convection.) (b) Calculate the rate of heat conduction through a 1.60-cm-thick window of the same area and with the same temperatures. Compare your answer with that for part (a).Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as two years.) Suppose you wish to install the extra insulation in Exercise 14.41. If energy cost 1.00 per million joules and the insulation was 4.00 per square meter, then calculate the simple payback time. Take the average T for the 120 day heating season to be 15.0C.For the human body, what is the rate of heat transfer by conduction through the body’s tissue with the following conditions: the tissue thickness is 3.00 cm, the change in temperature is 2.00C, and the skin area is 1.50m2. How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)At what wind speed does 10C air cause the same chill factor as still air at 29C ?At what temperature does still air cause the same chill factor as 5C air moving at 15m/s ?The “steam” above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 250 g of hot coffee initially at 90.0C if 2.00 g evaporates from it? The coffee is in a Styrofoam clip, so other methods of heat transfer can be neglected.(a) How many kilograms of water must evaporate from a 60.0-kg woman to lower her body temperature by 0.750C ? (b) Is this a reasonable amount of water to evaporate in the form of perspiration, assuming the relative humidity of the surrounding air is low?On a hot dry day, evaporation from a lake has just enough heat transfer to balance the 1.00kW/m2 of incoming heat from the Sun. What mass of water evaporates in 1.00 h from each square meter? Explicitly show how you follow the steps in the Problem-Solving Strategies for the Effects of Heat Transfer.One winter day, the climate control system of a large university classroom building malfunctions. As a result, 500m3 of excess cold air is brought in each minute. At what rate in kilowatts must heat transfer occur to warm this air by 10.0C (that is, to bring the air to room temperature)?The Kilauea volcano in Hawaii is the world’s most active, disgorging about 5105m3 of 1200C lava per day. What is the rate of heat transfer out of Earth by convection if this lava has a density of 2700kg/m3 and eventually cools to 30C ? Assume that the specific heat of lava is the same as that of granite. Figure 14.34 Lava flow on Kilauea volcano in Hawaii. (credit: J. R Eaton, U.S. Geological Survey)During heavy exercise, the body pumps 2.00 L of blood per minute to the surface, where it is cooled by 2.00C. What is the rate of heat transfer from this forced convection alone, assuming blood has the same specific heat as water and its density is 1050kg/m3 ?A person inhales and exhales 2.00 L of 37.0C air, evaporating 4.00102g of water from the lungs and breathing passages with each breath. (a) How much heat transfer occurs due to evaporation in each breath? (b) What is the rate of heat transfer in watts if the person is breathing at a moderate rate of 18.0 breaths per minute? (c) If the inhaled air had a temperature of 20.0C, what is the rate of heat transfer for warming the air? (d) Discuss the total rate of heat transfer as it relates to typical metabolic rates. Will this breathing be a major form of heat transfer for this person?A glass coffee pot has a circular bottom with a 9.00-cm diameter in contact with a heating element that keeps the coffee warm with a continuous heat transfer rate of 50.0 W (a) What is the temperature of the bottom of the pot, if it is 3.00 mm thick and the inside temperature is 60.0C ? (b) If the temperature of the coffee remains constant and all of the heat transfer is removed by evaporation, how many grams per minute evaporate? Take the heat of vaporization to be 2340kJ/kg.At what net rate does heat radiate from a 275m2 black roof on a night when the roof’s temperature is 30.0C and the surrounding temperature is 15.0C ? The emissivity of the roof is 0.900.(a) Cherry-red embers in a fireplace are at 850C and have an exposed area of 0.200m2 and an emissivity of 0.980. The surrounding room has a temperature of 18.0C. If 50% of the radiant energy enters the room, what is the net rate of radiant heat transfer in kilowatts? (b) Does your answer support the contention that most of the heat transfer into a room by a fireplace comes from infrared radiation?Radiation makes it impossible to stand close to a hot lava flow. Calculate the rate of heat transfer by radiation from 1.00m2 of 1200C fresh lava into 30.0C surroundings, assuming lava’s emissivity is 1.00.(a) Calculate the rate of heat transfer by radiation from a car radiator at 110C into a 50.0C environment, if the radiator has an emissivity of 0.750 and a 1.20m2 surface area. (b) Is this a significant fraction of the heat transfer by an automobile engine? To answer this, assume a horsepower of 200 hp (1.5 kW) and the efficiency of automobile engines as 25%.Find the net rate of heat transfer by radiation from a skier standing in the shade, given the following. She is completely clothed in white (head to foot, including a ski mask), the clothes have an emissivity of 0.200 and a surface temperature of 10.0C, the surroundings are at 15.0C, and her surface area is 1.60m2.Suppose you walk into a sauna that has an ambient temperature of 50.0C. (a) Calculate the rate of heat transfer to you by radiation given your skin temperature is 37.0C, the emissivity of skin is 0.98, and the surface area of your body is 1.50m2. (b) If all other forms of heat transfer are balanced (the net heat transfer is zero), at what rate will your body temperature increase if your mass is 75.0 kg?Thermography is a technique for measuring radiant heat and detecting variations in surface temperatures that may be medically, environmentally, or militarily meaningful.(a) What is the percent increase in the rate of heat transfer by radiation from a given area at a temperature of 34.0C compared with that at 33.0C, such as on a person’s skin? (b) What is the percent increase in the rate of heat transfer by radiation from a given area at a temperature of 34.0C compared with that at 20.0C, such as for warm and cool automobile hoods? Figure 14.35 Artist’s rendition of a thermograph of a patient’s upper body, showing the distribution of heat represented by different colors.The Sun radiates like a perfect black body with an emissivity of exactly 1. (a) Calculate the surface temperature of the Sun, given that it is a sphere with a 7.00108m radius that radiates 3.801026W into 3-K space. (b) How much power does the Sun radiate per square meter of its surface? (c) How much power in watts per square meter is that value at the distance of Earth, 1.501011m away? (This number is called the solar constant.)A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at 1200C, its surface is at 450C, and the surroundings are at 27.0C. (a) Calculate the rate at which energy is transferred by radiation from 1.00m2 of surface lava into the surroundings, assuming the emissivity is 1.00. (b) Suppose heat conduction to the surface occurs at the same rate. What is the thickness of the lava between the 450C surface and the 1200C interior, assuming that the lava’s conductivity is the same as that of brick?Calculate the temperature the entire sky would have to be in order to transfer energy by radiation at 1000W/m2 —about the rate at which the Sun radiates when it is directly overhead on a clear day. This value is the effective temperature of the sky, a kind of average that takes account of the fact that the Sun occupies only a small part of the sky but is much hotter than the rest. Assume that the body receiving the energy has a temperature of 27.0C.(a) A shirtless rider under a circus tent feels the heat radiating from the sunlit portion of the tent. Calculate the temperature of the tent canvas based on the following information: The shirtless rider’s skin temperature is 34.0C and has an emissivity of 0.970. The exposed area of skin is 0.400m2. He receives radiation at the rate of 20.0 W—half what you would calculate if the entire region behind him was hot. The rest of the surroundings are at 34.0C. (b) Discuss how this situation would change if the sun lit side of the tent was nearly pure white and if the rider was covered by a white tunic.Integrated Concepts One 30.0C day the relative humidity is 75.0%, and that evening the temperature drops to 20.0C, well below the dew point. (a) How many grams of water condense from each cubic meter of air? (b) How much heat transfer occurs by this condensation? (c) What temperature increase could this cause in dry air?Integrated Concepts Large meteors sometimes strike the Earth, converting most of their kinetic energy into thermal energy. (a) What is the kinetic energy of a 109kg meteor moving at 25.0km/s ? (b) If this meteor lands in a deep ocean and 80% of its kinetic energy goes into heating water, how many kilograms of water could it raise by 5.0C ? (c) Discuss how the energy of the meteor is more likely to be deposited in the ocean and the likely effects of that energy.Integrated Concepts Frozen waste from airplane toilets has sometimes been accidentally ejected at high altitude. Ordinarily it breaks up and disperses over a large area, but sometimes ¡t holds together and strikes the ground. Calculate the mass of 0C ice that can be melted by the conversion of kinetic and gravitational potential energy when a 20.0 kg piece of frozen waste is released at 12.0 km altitude while moving at 250m/s and strikes the ground at 100m/s (since less than 20.0 kg melts, a significant mess results).€69. Integrated Concepts (a) A large electrical power facility produces 1600 MW of “waste heat.” which is dissipated to the environment in cooling towers by warming air flowing through the towers by 500C. What is the necessary flow rate of air in m3/s ? (b) Is your result consistent with the large cooling towers used by many large electrical power plants?Integrated Concepts (a) Suppose you start a workout on a Stairmaster, producing power at the same rate as climbing 116 stairs per minute. Assuming your mass is 76.0 kg and your efficiency is 20.0%, how long will it take for your body temperature to rise 1.00C if all other forms of heat transfer in and out of your body are balanced? (b) Is this consistent with your experience in getting warm while exercising?Integrated Concepts A 76.0-kg person suffering from hypothermia comes indoors and shivers vigorously. How long does it take the heat transfer to increase the person’s body temperature by 2.00C if all other forms of heat transfer are balanced?Integrated Concepts In certain large geographic regions, the underlying rock is hot. Wells can be drilled and water circulated through the rock for heat transfer for the generation of electricity. (a) Calculate the heat transfer that can be extracted by cooling 1.00km3 of granite by 100C. (b) How long will it take for heat transfer at the rate of 300 MW, assuming no heat transfers back into the 1.00km3 of rock by its surroundings?Integrated Concepts Heat transfers from your lungs and breathing passages by evaporating water. (a) Calculate the maximum number of grams of water that can be evaporated when you inhale 1.50 L of 37C air with an original relative humidity of 40.0%. (Assume that body temperature is also 37C .) (b) How many joules of energy are required to evaporate this amount? (c) What is tile rate of heat transfer in watts from this method, if you breathe at a normal resting rate of 10.0 breaths per minute?Integrated Concepts (a) What is the temperature increase of water failing 55.0 m over Niagara Falls? (b) What fraction must evaporate to keep the temperature constant?Integrated Concepts Hot air rises because it has expanded. It then displaces a greater volume of cold air, which increases the buoyant force on it. (a) Calculate the ratio of the buoyant force to the weight of 50.0C air surrounded by 20.0C air. (b) What energy is needed to cause 1.00m3 of air to go from 20.0C to 50.0°C? (c) What gravitational potential energy is gained by this volume of air if it rises 1.00 m? Will this cause a significant cooling of the air?Unreasonable Results (a) What is the temperature increase of an 80.0 kg person who consumes 2500 kcal of food in one day with 95.0% of the energy transferred as heat to the body? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?Unreasonable Results A slightly deranged Arctic inventor surrounded by ice thinks it would be much less mechanically complex to cool a car engine by melting ice on it than by having a water-cooled system with a radiator, water pump, antifreeze, and so on. (a) If 80.0% of the energy in 1.00 gal of gasoline is converted into waste heat” in a car engine, how many kilograms of 0°C ice could it melt? (b) Is this a reasonable amount of ice to carry around to cool the engine for 1.00 gal of gasoline consumption? (c) What premises or assumptions are unreasonable?Unreasonable Results (a) Calculate the rate of heat transfer by conduction through a window with an area of 1.00 m2 that is 0.750 cm thick, if its inner surface is at 22.00C and its outer surface is at 35.00C (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?Unreasonable Results A meteorite 1.20 cm in diameter is so hot immediately after penetrating the atmosphere that it radiates 20.0 kW of power. (a) What is its temperature, if the surroundings are at 20.0C and it has an emissivity of 0.800? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?Construct Your Own Problem Consider a new model of commercial airplane having its brakes tested as a part of the initial flight permission procedure. The airplane is brought to takeoff speed and then stopped with the brakes alone. Construct a problem in which you calculate the temperature increase of the brakes during this process. You may assume most of the kinetic energy of the airplane is converted to thermal energy in the brakes and surrounding materials, and that little escapes. Note that the brakes are expected to become so hot in this procedure that they ignite and, in order to pass the test, the airplane must be able to withstand the fire for some time without a general conflagration.Construct Your Own Problem Consider a person outdoors on a cold night. Construct a problem in which you calculate the rate of heat transfer from the person by all three heat transfer methods. Make the initial circumstances such that at rest the person will have a net heat transfer and then decide how much physical activity of a chosen type is necessary to balance the rate of heat transfer. Among the things to consider are the size of the person, type of clothing, initial metabolic rate, sky conditions, amount of water evaporated, and volume of air breathed. Of course, there are many other factors to consider and your instructor may wish to guide you in the assumptions made as well as the detail of analysis and method of presenting your results.Describe the photo of the tea kettle at the beginning of this section in terms of heat transfer, work done, and internal energy. How is heat being transferred? What is the work done and what is doing it? How does use kettle maintain its internal energy?The first law of thermodynamics and the conservation of energy, as discussed in Conservation of Energy, ale cleanly related. How do they differ in the types of energy considered?Heat transfer Q and work done W are always energy in transit, whereas internal energy U is energy stored in a system. Give an example of each type of energy, and state specifically how it is either in transit or resides m a system.How do heat transfer and internal energy differ? In particular, which can be stored as such in a system and which cannot?If you run down some stairs and stop, what happens to your kinetic energy and your initial gravitational potential energy?Give an explanation of how food energy (calories) can be viewed as molecular potential energy (consistent with me atomic and molecular definition of internal energy).