A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120.0° C to 10.0° C?
> Suppose that a steel hoop could be constructed to fit just around the earth’s equator at 20.0 °C. What would be the thickness of space between the hoop and the earth if the temperature of the hoop were increased by 0.500°C ?
> You cool a 100.0-g slug of red-hot iron (temperature 745° C) by dropping it into an insulated cup of negligible mass containing 85.0 g of water at 20.0 °C. Assuming no heat exchange with the surroundings, (a). what is the final temperature of the water
> Shivering is your body’s way of generating heat to restore its internal temperature to the normal 37 °C, and it produces approximately 290 W of heat power per square meter of body area. A 68-kg, 1.78-m-tall woman has approximately 1.8 m2 of surface area.
> A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and 7.0 g of fat. Average food energy values are 4.0 kcal/g for protein and carbohydrates and 9.0 kcal/g for fat. (a). During heavy exercise, an average person uses energy at a rate
> A steel ring with a 2.5000-in. inside diameter at 20.0° C is to be warmed and slipped over a brass shaft with a 2.5020-in. outside diameter at 20.0 °C. (a) To what temperature should the ring be warmed? (b) If the ring and the shaft together are cooled
> The fundamental frequency of a pipe that is open at both ends is 524 Hz. (a). How long is this pipe? If one end is now closed, find (b). the wavelength and (c). the frequency of the new fundamental.
> A Foucault pendulum consists of a brass sphere with a diameter of 35.0 cm suspended from a steel cable 10.5 m long (both measurements made at 20.0° C). Due to a design oversight, the swinging sphere clears the floor by a distance of only 2.00 mm when the
> (a) Equation (17.12) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount L when its temperature changes by T, the stress is equal to where F is the tens
> On a cool (4.0 °C) Saturday morning, a pilot fills the fuel tanks of her Pitts S-2C (a two-seat aerobatic airplane) to their full capacity of 106.0 L. Before flying on Sunday morning, when the temperature is again 4.0 °C, she checks the fuel level and fi
> A metal rod that is 30.0 cm long expands by 0.0650 cm when its temperature is raised from 0.0°C to 100.0 °C. A rod of a different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third rod, also 30.0 cm long, is made
> A surveyor’s 30.0-m steel tape is correct at 20.0 °C. The distance between two points, as measured by this tape on a day when its temperature is 5.00° C, is 25.970 m. What is the true distance between the points?
> You are making pesto for your pasta and have a cylindrical measuring cup 10.0 cm high made of ordinary glass [
> (a) Equation (16.30) can be written as where c is the speed of light in vacuum, 3.00 × 108 m/s. Most objects move much slower than this (v/c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding err
> A long tube contains air at a pressure of 1.00 atm and a temperature of 77.00C. The tube is open at one end and closed at the other by a movable piston. A tuning fork that vibrates with a frequency of 500 Hz is placed near the open end. Resonance is prod
> A long, closed cylindrical tank contains a diatomic gas that is maintained at a uniform temperature that can be varied. When you measure the speed of sound v in the gas as a function of the temperature T of the gas, you obtain these results: (a). Expla
> A turntable 1.50 m in diameter rotates at 75 rpm. Two speakers, each giving off sound of wavelength 31.3 cm, are attached to the rim of the table at opposite ends of a diameter. A listener stands in front of the turntable. (a). What is the greatest beat
> Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if (a). the pipe is open a
> A police siren of frequency fsiren is attached to a vibrating platform. The platform and siren oscillate up and down in simple harmonic motion with amplitude Ap and frequency fp. (a). Find the maximum and minimum sound frequencies that you would hear at
> Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils and then listen to the frequency of the sound reflected from their prey to determine the prey’s speed. (The “horseshoe” that gives the bat its name is a depression around the nostrils tha
> A 2.00-MHz sound wave travels through a pregnant woman’s abdomen and is reflected from the fetal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflected sound is then mixed with the transmitted
> The sound source of a ship’s sonar system operates at a frequency of 18.0 kHz. The speed of sound in water (assumed to be at a uniform 200C) is 1482 m/s. (a). What is the wavelength of the waves emitted by the source? (b). What is the difference in fre
> A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of 8.00 Hz?
> Two identical loudspeakers are located at points A and B, 2.00 m apart. The loudspeakers are driven by the same amplifier and produce sound waves with a frequency of 784 Hz. Take the speed of sound in air to be 344 m/s. A small microphone is moved out fr
> The frequency of the note F4 is 349 Hz. (a). If an organ pipe is open at one end and closed at the other, what length must it have for its fundamental mode to produce this note at 20.0 C? (b). At what air temperature will the frequency be 370 Hz, corres
> An organ pipe has two successive harmonics with frequencies 1372 and 1764 Hz. (a). Is this an open or a stopped pipe? Explain. (b). What two harmonics are these? (c). What is the length of the pipe?
> A uniform 165-N bar is supported horizontally by two identical wires A and B (Fig. P16.62). A small 185-N cube of lead is placed threefourths of the way from A to B. The wires are each 75.0 cm long and have a mass of 5.50 g. If both of them are simultane
> A person is playing a small flute 10.75 cm long, open at one end and closed at the other, near a taut string having a fundamental frequency of 600.0 Hz. If the speed of sound is 344.0 m/s, for which harmonics of the flute will the string resonate? In eac
> A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 m on a winter day at a temperature of -15 °C. How much more interior space does the dome have in the summer, when the temperature is 35 °C?
> The sound from a trumpet radiates uniformly in all directions in 20 C air. At a distance of 5.00 m from the trumpet the sound intensity level is 52.0 dB. The frequency is 587 Hz. (a). What is the pressure amplitude at this distance? (b). What is the dis
> A soprano and a bass are singing a duet. While the soprano sings an A-sharp at 932 Hz, the bass sings an A-sharp but three octaves lower. In this concert hall, the density of air is 1.20 kg/m3 and its bulk modulus is 1.42 × 105 Pa. In order for their not
> A vertical cylindrical tank contains 1.80 mol of an ideal gas under a pressure of 0.300 atm at 20.0 0C. The round part of the tank has a radius of 10.0 cm, and the gas is supporting a piston that can move up and down in the cylinder without friction. The
> A balloon of volume 750 m3 is to be filled with hydrogen at atmospheric pressure (1.01 × 105 Pa). (a). If the hydrogen is stored in cylinders with volumes of 1.90 m3 at a gauge pressure of 1.20 × 106 Pa, how many cylinders are required? Assume that the
> A flask with a volume of 1.50 L, provided with a stopcock, contains ethane gas (C2H6) at 300 K and atmospheric pressure (1.013 × 105 Pa). The molar mass of ethane is 30.1 g/mol. The system is warmed to a temperature of 550 K, with the stopcock open to th
> An automobile tire has a volume of 0.0150 m3 on a cold day when the temperature of the air in the tire is 5.0 0C and atmospheric pressure is 1.02 atm. Under these conditions the gauge pressure is measured to be 1.70 atm (about 25 lb/in.2). After the car
> At the surface of Venus the average temperature is a balmy 460°C due to the greenhouse effect (global warming!), the pressure is 92 earth-atmospheres, and the acceleration due to gravity is 0.894gearth. The atmosphere is nearly all CO2 (molar mass 44.0 g
> Titan, the largest satellite of Saturn, has a thick nitrogen atmosphere. At its surface, the pressure is 1.5 earth-atmospheres and the temperature is 94 K. (a). What is the surface temperature in °C? (b). Calculate the surface density in Titan’s atmosp
> During a test dive in 1939, prior to being accepted by the U.S. Navy, the submarine Squalus sank at a point where the depth of water was 73.0 m. The temperature was 27.0 0C at the surface and 7.0 0C at the bottom. The density of seawater is 1030 kg/m3.
> A cylinder 1.00 m tall with inside diameter 0.120 m is used to hold propane gas (molar mass 44.1 g/mol) for use in a barbecue. It is initially filled with gas until the gauge pressure is 1.30 × 106 Pa at 22.00 C. The temperature of the gas remains consta
> Aluminum rivets used in airplane construction are made slightly larger than the rivet holes and cooled by “dry ice” (solid CO2) before being driven. If the diameter of a hole is 4.500 mm, what should be the diameter of
> In an evacuated enclosure, a vertical cylindrical tank of diameter D is sealed by a 3.00-kg circular disk that can move up and down without friction. Beneath the disk is a quantity of ideal gas at temperature T in the cylinder (Fig. P18.50). Initially th
> If deep-sea divers rise to the surface too quickly, nitrogen bubbles in their blood can expand and prove fatal. This phenomenon is known as the bends. If a scuba diver rises quickly from a depth of 25 m in Lake Michigan (which is fresh water), what will
> (a). Calculate the change in air pressure you will experience if you climb a 1000-m mountain, assuming that the temperature and air density do not change over this distance and that they were 22°C and 1.2 kg/m3, respectively, at the bottom of the mountai
> A physics lecture room at 1.00 atm and 27.0°C has a volume of 216 m3. (a). Use the ideal-gas law to estimate the number of air molecules in the room. Assume that all of the air is N2. Calculate (b). the particle density—that is, the number of N2 molecu
> To measure the specific heat in the liquid phase of a newly developed cryoprotectant, you place a sample of the new cryoprotectant in contact with a cold plate until the solution’s temperature drops from room temperature to its freezing point. Then you m
> In another experiment, you place a layer of this cryoprotectant between one 10 cm × 10 cm cold plate maintained at -40° C and a second cold plate of the same size maintained at liquid nitrogen’s boiling temperature (77 K). Then you measure the rate of he
> Careful measurements show that the specific heat of the solid phase depends on temperature (Fig. P17.117). How will the actual time needed for this cryoprotectant to come to equilibrium with the cold plate compare with the time predicted by using the val
> You place 35 g of this cryoprotectant at 22°C in contact with a cold plate that is maintained at the boiling temperature of liquid nitrogen (77 K). The cryoprotectant is thermally insulated from everything but the cold plate. Use the values in the table
> What is one reason the noble gases are preferable to air (which is mostly nitrogen and oxygen) as an insulating material? (a). Noble gases are monatomic, so no rotational modes contribute to their molar heat capacity; (b). noble gases are monatomic, so
> For cranial ultrasound, why is it advantageous to use frequencies in the kHZ range rather than the MHz range? (a). The antinodes of the standing waves will be closer together at the lower frequencies than at the higher frequencies; (b). there will be n
> In some applications of ultrasound, such as its use on cranial tissues, large reflections from the surrounding bones can produce standing waves. This is of concern because the large pressure amplitude in an antinode can damage tissues. For a frequency of
> Because the speed of ultrasound in bone is about twice the speed in soft tissue, the distance to a structure that lies beyond a bone can be measured incorrectly. If a beam passes through 4 cm of tissue, then 2 cm of bone, and then another 1 cm of tissue
> After a beam passes through 10 cm of tissue, what is the beam’s intensity as a fraction of its initial intensity from the transducer? (a). 1 × 10-11; (b). 0.001; (c). 0.01; (d). 0.1.
> If the deepest structure you wish to image is 10.0 cm from the transducer, what is the maximum number of pulses per second that can be emitted? (a). 3850; (b). 7700; (c). 15,400; (d). 1,000,000.
> A hollow cylinder has length L, inner radius a, and outer radius b, and the temperatures at the inner and outer surfaces are T2 and T1. (The cylinder could represent an insulated hot-water pipe.) The thermal conductivity of the material of which the cyli
> Consider a poor lost soul walking at 5 km/h on a hot day in the desert, wearing only a bathing suit. This person’s skin temperature tends to rise due to four mechanisms: (i) energy is generated by metabolic reactions in the body at a rate of 280 W, and a
> The dark area in Fig. P18.83 that appears devoid of stars is a dark nebula, a cold gas cloud in interstellar space that contains enough material to block out light from the stars behind it. A typical dark nebula is about 20 light-years in diameter and co
> A long spring such as a Slinky™ is often used to demonstrate longitudinal waves. (a). Show that if a spring that obeys Hooke’s law has mass m, length L, and force constant k′ the speed of longitudinal waves on the spring is v = L
> Figure P16.75 shows the pressure fluctuation p of a nonsinusoidal sound wave as a function of x for t = 0. The wave is traveling in the +x-direction. (a). Graph the pressure fluctuation p as a function of t for x = 0. Show at least two cycles of oscilla
> (a). Which has more atoms: a kilogram of hydrogen or a kilogram of lead? Which has more mass? (b). Which has more atoms: a mole of hydrogen or a mole of lead? Which has more mass? Explain your reasoning.
> A baby’s mouth is 30 cm from her father’s ear and 1.50 m from her mother’s ear. What is the difference between the sound intensity levels heard by the father and by the mother?
> A rigid, perfectly insulated container has a membrane dividing its volume in half. One side contains a gas at an absolute temperature T0 and pressure p0, while the other half is completely empty. Suddenly a small hole develops in the membrane, allowing t
> A beaker of water at room temperature is placed in an enclosure, and the air pressure in the enclosure is slowly reduced. When the air pressure is reduced sufficiently, the water begins to boil. The temperature of the water does not rise when it boils; i
> The atmosphere of the planet Mars is 95.3% carbon dioxide (CO2) and about 0.03% water vapor. The atmospheric pressure is only about 600 Pa, and the surface temperature varies from -30 0C to -100 0C. The polar ice caps contain both CO2 ice and water ice.
> The discussion in Section 18.4 concluded that all ideal monatomic gases have the same heat capacity CV. Does this mean that it takes the same amount of heat to raise the temperature of 1.0 g of each one by 1.0 K? Explain your reasoning.
> (a). If you apply the same amount of heat to 1.00 mol of an ideal monatomic gas and 1.00 mol of an ideal diatomic gas, which one (if any) will increase more in temperature? (b). Physically, why do diatomic gases have a greater molar heat capacity than m
> The temperature of an ideal monatomic gas is increased from 25 0C to 50 0C. Does the average translational kinetic energy of each gas atom double? Explain. If your answer is no, what would the final temperature be if the average translational kinetic ene
> Consider two specimens of ideal gas at the same temperature. Specimen A has the same total mass as specimen B, but the molecules in specimen A have greater molar mass than they do in specimen B. In which specimen is the total kinetic energy of the gas gr
> In deriving the ideal-gas equation from the kineticmolecular model, we ignored potential energy due to the earth’s gravity. Is this omission justified? Why or why not?
> When energy shortages occur, magazine articles sometimes urge us to keep our homes at a constant temperature day and night to conserve fuel. They argue that when we turn down the heat at night, the walls, ceilings, and other areas cool off and must be re
> We’re lucky that the earth isn’t in thermal equilibrium with the sun (which has a surface temperature of 5800 K). But why aren’t the two bodies in thermal equilibrium?
> The intensity due to a number of independent sound sources is the sum of the individual intensities. (a). When four quadruplets cry simultaneously, how many decibels greater is the sound intensity level than when a single one cries? (b). To increase th
> (a). Normal body temperature. The average normal body temperature measured in the mouth is 310 K. What would Celsius and Fahrenheit thermometers read for this temperature? (b). Elevated body temperature. During very vigorous exercise, the body’s tempera
> Some folks claim that ice cubes freeze faster if the trays are filled with hot water, because hot water cools off faster than cold water. What do you think?
> It is well known that a potato bakes faster if a large nail is stuck through it. Why? Does an aluminum nail work better than a steel one? Why or why not? (Note: Don’t try this in a microwave oven!) There is also a gadget on the market to hasten the roast
> If you are riding in a supersonic aircraft, what do you hear? Explain. In particular, do you hear a continuous sonic boom? Why or why not?
> A person pours a cup of hot coffee, intending to drink it five minutes later. To keep the coffee as hot as possible, should she put cream in it now or wait until just before she drinks it? Explain.
> In case 1, a source of sound approaches a stationary observer at speed u. In case 2, the observer moves toward the stationary source at the same speed u. If the source is always producing the same frequency sound, will the observer hear the same frequenc
> A cold block of metal feels colder than a block of wood at the same temperature. Why? A hot block of metal feels hotter than a block of wood at the same temperature. Again, why? Is there any temperature at which the two blocks feel equally hot or cold? W
> Stars other than our sun normally appear featureless when viewed through telescopes. Yet astronomers can readily use the light from these stars to determine that they are rotating and even measure the speed of their surface. How do you think they can do
> Can you think of circumstances in which a Doppler effect would be observed for surface waves in water? For elastic waves propagating in a body of water deep below the surface? If so, describe the circumstances and explain your reasoning. If not, explain
> A sound source and a listener are both at rest on the earth, but a strong wind is blowing from the source toward the listener. Is there a Doppler effect? Why or why not?
> When water is placed in ice-cube trays in a freezer, why doesn’t the water freeze all at once when the temperature has reached C? In fact, the water freezes first in a layer adjacent to the sides of the tray. Why?
> For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0 × 10-5 Pa. Calculate the (a). intensity; (b). sound intensity level; (c). displacement amplitude of this sound wave a
> Two vibrating tuning forks have identical frequencies, but one is stationary and the other is mounted at the rim of a rotating platform. What does a listener hear? Explain.
> If the pressure of an ideal monatomic gas is increased while the number of moles is kept constant, what happens to the average translational kinetic energy of one atom of the gas? Is it possible to change both the volume and the pressure of an ideal gas
> When a car is driven some distance, the air pressure in the tires increases. Why? Should you let out some air to reduce the pressure? Why or why not?
> A piece of aluminum foil used to wrap a potato for baking in a hot oven can usually be handled safely within a few seconds after the potato is removed from the oven. The same is not true of the potato, however! Give two reasons for this difference.
> Use the concepts of the kinetic-molecular model to explain: (a). why the pressure of a gas in a rigid container increases as heat is added to the gas and (b). why the pressure of a gas increases as we compress it, even if we do not change its temperatu
> Does the sound intensity level b obey the inverse-square law? Why?
> In some household air conditioners used in dry climates, air is cooled by blowing it through a water-soaked filter, evaporating some of the water. How does this cool the air? Would such a system work well in a high-humidity climate? Why or why not?
> A newspaper article about the weather states that “the temperature of a body measures how much heat the body contains.” Is this description correct? Why or why not?
> (a). Does a sound level of 0 dB mean that there is no sound? (b). Is there any physical meaning to a sound having a negative intensity level? If so, what is it? (c). Does a sound intensity of zero mean that there is no sound? (d). Is there any physica
> The inside of an oven is at a temperature of 200° C (392 °F). You can put your hand in the oven without injury as long as you don’t touch anything. But since the air inside the oven is also at 200 °C, why isn’t your hand burned just the same?
> Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0° R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numeri
> Why is it sometimes possible to loosen caps on screw-top bottles by dipping the capped bottle briefly into hot water?
> Why do frozen water pipes burst? Would a mercury thermometer break if the temperature went below the freezing temperature of mercury? Why or why not?
> In most modern wind instruments the pitch is changed by using keys or valves to change the length of the vibrating air column. The bugle, however, has no valves or keys, yet it can play many notes. How might this be possible? Are there restrictions on wh
> Many automobile engines have cast-iron cylinders and aluminum pistons. What kinds of problems could occur if the engine gets too hot? (The coefficient of volume expansion of cast iron is approximately the same as that of steel.)
> Explain why it would not make sense to use a full-size glass thermometer to measure the temperature of a thimbleful of hot water.
> When sound travels from air into water, does the frequency of the wave change? The speed? The wavelength? Explain your reasoning.
