If the root-mean-square speed of the atoms of an ideal gas is to be doubled, by what factor must the Kelvin temperature of the gas be increased? Explain.
> In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a). On a cold winter day when the temperature is -20° C, what amount of heat is needed to warm to
> While running, a 70-kg student generates thermal energy at a rate of 1200 W. For the runner to maintain a constant body temperature of 37 C, this energy must be removed by perspiration or other mechanisms. If these mechanisms failed and the energy could
> (a). In a liquid with density 1300 kg/m3, longitudinal waves with frequency 400 Hz are found to have wavelength 8.00 m. Calculate the bulk modulus of the liquid. (b). A metal bar with a length of 1.50 m has density 6400 kg/m3. Longitudinal sound waves t
> In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. (a). How much heat must be added to the water to raise its temperature from 20.0 C to 80.
> The shock-wave cone created by a space shuttle at one instant during its reentry into the atmosphere makes an angle of 58.0 with its direction of motion. The speed of sound at this altitude is 331 m/s. (a). What is the Mach number of the shuttle at thi
> A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a). What is the angle a of the shock-wave cone? (b). How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of
> An aluminum tea kettle with mass 1.10 kg and containing 1.80 kg of water is placed on a stove. If no heat is lost to the surroundings, how much heat must be added to raise the temperature from 20.0 °C to 85.0 °C?
> A stationary police car emits a sound of frequency 1200 Hz that bounces off a car on the highway and returns with a frequency of 1250 Hz. The police car is right next to the highway, so the moving car is traveling directly toward or away from it. (a). H
> The siren of a fire engine that is driving northward at 30.0 m/s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m/s. (a). What is the frequency of the siren’s sound that the fire engine’s driver hear
> Two swift canaries fly toward each other, each moving at 15.0 m/s relative to the ground, each warbling a note of frequency 1750 Hz. (a). What frequency note does each bird hear from the other one? (b). What wavelength will each canary measure for the
> While sitting in your car by the side of a country road, you are approached by your friend, who happens to be in an identical car. You blow your car’s horn, which has a frequency of 260 Hz. Your friend blows his car’s horn, which is identical to yours, a
> Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0° C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their tempe
> A railroad train is traveling at 30.0 m/s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m/s and (a). approaching th
> (a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2 atmosphere), Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2 atmosphere), a
> A swimming duck paddles the water with its feet once every 1.6 s, producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.32 m/s, and the crests of the waves ahead of the duck are spa
> (a) A sound source producing 1.00-kHz waves moves toward a stationary listener at one-half the speed of sound. What frequency will the listener hear? (b). Suppose instead that the source is stationary and the listener moves toward the source at one-half
> Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35.0 m/s. A listener is between the two whistles and is moving toward the right with a speed of 15.0 m/s (Fig. E16.
> A railroad train is traveling at 25.0 m/s in still air. The frequency of the note emitted by the locomotive whistle is 400 Hz. What is the wavelength of the sound waves (a). in front of the locomotive and (b). behind the locomotive? What is the frequen
> As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0 °C and 150.0 °C. Assume that the coefficients of expa
> In Example 16.18 (Section 16.8), suppose the police car is moving away from the warehouse at 20 m/s. What frequency does the driver of the police car hear reflected from the warehouse?
> A machinist bores a hole of diameter 1.35 cm in a steel plate that is at 25.0° C. What is the cross-sectional area of the hole (a). at 25.0° C and (b) when the temperature of the plate is increased to 175 °C? Assume that the coefficient of linear expansi
> The motors that drive airplane propellers are, in some cases, tuned by using beats. The whirring motor produces a sound wave having the same frequency as the propeller. (a). If one single-bladed propeller is turning at 575 rpm and you hear 2.0-Hz beats
> A violinist is tuning her instrument to concert A (440 Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of 3 Hz, which increases to 4 Hz when she tightens her violin string s
> Two guitarists attempt to play the same note of wavelength 64.8 cm at the same time, but one of the instruments is slightly out of tune and plays a note of wavelength 65.2 cm instead. What is the frequency of the beats these musicians hear when they play
> Convert the following Celsius temperatures to Fahrenheit: (a) -62.8 C, the lowest temperature ever recorded in North America (February 3, 1947, Snag, Yukon); (b). 56.7 C, the highest temperature ever recorded in the United States (July 10, 1913, Death V
> Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone arranged as shown in Fig. E16.39. For what frequencies does their sound at the speakers produce (a). constructive interferenc
> Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 Hz. You are 8.00 m from A. What is the closest you can be to B and be at a point of destructive inte
> The rate at which radiant energy from the sun reaches the earth’s upper atmosphere is about 1.50 kW/m2. The distance from the earth to the sun is 1.50 × 1011 m, and the radius of the sun is 6.96 × 108 m. (a). What is the rate of radiation of energy per
> Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 12.0 m to the right of speaker A. The frequency of the waves emitted by each speaker is 688 Hz. You are standing between the speakers, along the
> Rods of copper, brass, and steel—each with crosssectional area of 2.00 cm2—are welded together to form a Y-shaped figure. The free end of the copper rod is maintained at 100.0° C, and the free ends of the brass and steel rods at 0.0 °C. Assume that there
> One experimental method of measuring an insulating material’s thermal conductivity is to construct a box of the material and measure the power input to an electric heater inside the box that maintains the interior at a measured temperature above the outs
> A carpenter builds a solid wood door with dimensions 2.00 m × 0.95 m × 5.0 cm. Its thermal conductivity is k = 0.120 W/m ∙ K. The air films on the inner and outer surfaces of the door have the same combined thermal resistance as an additional 1.8-cm thic
> The rate of effusion—that is, leakage of a gas through tiny cracks—is proportional to vrms. If tiny cracks exist in the material that’s used to seal the space between two glass panes, how many times greater is the rate of He leakage out of the space betw
> Estimate the ratio of the thermal conductivity of Xe to that of He. (a) 0.015; (b) 0.061; (c) 0.10; (d) 0.17.
> At very low temperatures the molar heat capacity of rock salt varies with temperature according to Debye’s T3 law: where k = 1940 J/mol ∙ K and u = 281 K. (a). How much heat is required to raise the temperature of 1
> In the troposphere, the part of the atmosphere that extends from earth’s surface to an altitude of about 11 km, the temperature is not uniform but decreases with increasing elevation. (a). Show that if the temperature variation is appr
> A metal wire, with density r and Young’s modulus Y, is stretched between rigid supports. At temperature T, the speed of a transverse wave is found to be v1. When the temperature is increased to T +
> Calculate the integral in Eq. (18.31), 0 ∞ v2 f (v2) dv, and compare this result to 1v22av as given by Eq. (18.16). (Hint: You may use the tabulated integral where n is a positive integer and a is a positive constant.) 1.3.5. .•
> The size of an oxygen molecule is about 2.0 × 10-10 m. Make a rough estimate of the pressure at which the finite volume of the molecules should cause noticeable deviations from ideal gas behavior at ordinary temperatures (T = 300 K).
> Two loudspeakers, A and B (see Fig. E16.35), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 206 Hz. Consider a point P b
> A hot-air balloon stays aloft because hot air at atmospheric pressure is less dense than cooler air at the same pressure. If the volume of the balloon is 500.0 m3 and the surrounding air is at 15.0°C, what must the temperature of the air in the balloon b
> The derivation of the ideal-gas equation included the assumption that the number of molecules is very large, so that we could compute the average force due to many collisions. However, the ideal-gas equation holds accurately only at low pressures, where
> A group of students drove from their university (near sea level) up into the mountains for a skiing weekend. Upon arriving at the slopes, they discovered that the bags of potato chips they had brought for snacks had all burst open. What caused this to ha
> Unwrapped food placed in a freezer experiences dehydration, known as “freezer burn.” Why?
> The coolant in an automobile radiator is kept at a pressure higher than atmospheric pressure. Why is this desirable? The radiator cap will release coolant when the gauge pressure of the coolant reaches a certain value, typically 15 lb/in.2 or so. Why not
> The dark areas on the moon’s surface are called maria, Latin for “seas,” and were once thought to be bodies of water. In fact, the maria are not “seas” at all, but plains of solidified lava. Given that there is no atmosphere on the moon, how can you expl
> Hydrothermal vents are openings in the ocean floor that discharge very hot water. The water emerging from one such vent off the Oregon coast, 2400 m below the surface, is at 279 0C. Despite its high temperature, the water doesn’t boil. Why not?
> Ice is slippery to walk on, and especially slippery if you wear ice skates. What does this tell you about how the melting temperature of ice depends on pressure? Explain.
> In a gas that contains N molecules, is it accurate to say that the number of molecules with speed v is equal to f (v)? Is it accurate to say that this number is given by Nf (v)? Explain your answers.
> Two loudspeakers, A and B (Fig. E16.35), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of
> In the ideal-gas equation, could an equivalent Celsius temperature be used instead of the Kelvin one if an appropriate numerical value of the constant R is used? Why or why not?
> A gas storage tank has a small leak. The pressure in the tank drops more quickly if the gas is hydrogen or helium than if it is oxygen. Why?
> Imagine a special air filter placed in a window of a house. The tiny holes in the filter allow only air molecules moving faster than a certain speed to exit the house, and allow only air molecules moving slower than that speed to enter the house from out
> The temperature of an ideal gas is directly proportional to the average kinetic energy of its molecules. If a container of ideal gas is moving past you at 2000 m/s, is the temperature of the gas higher than if the container was at rest? Explain your reas
> The kinetic-molecular model contains a hidden assumption about the temperature of the container walls. What is this assumption? What would happen if this assumption were not valid?
> Comment on the following statement: When two gases are mixed, if they are to be in thermal equilibrium, they must have the same average molecular speed. Is the statement correct? Why or why not?
> The proportions of various gases in the earth’s atmosphere change somewhat with altitude. Would you expect the proportion of oxygen at high altitude to be greater or less than at sea level compared to the proportion of nitrogen? Why?
> In addition to the normal cooking directions printed on the back of a box of rice, there are also “high-altitude directions.” The only difference is that the “high-altitude directions” suggest increasing the cooking time and using a greater volume of boi
> A student asserts that a suitable unit for specific heat is/. Is she correct? Why or why not?
> Glider pilots in the Midwest know that thermal updrafts are likely to occur in the vicinity of freshly plowed fields. Why?
> Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away (Fig. E16.34). (a). At what distance d will the sound from the speakers first produce
> In coastal regions in the winter, the temperature over the land is generally colder than the temperature over the nearby ocean; in the summer, the reverse is usually true. Explain. (Hint: The specific heat of soil is only 0.2–0.8 times as great as that o
> When a freshly baked apple pie has just been removed from the oven, the crust and filling are both at the same temperature. Yet if you sample the pie, the filling will burn your tongue but the crust will not. Why is there a difference? (Hint: The filling
> A jet airplane is flying at a constant altitude at a steady speed vS greater than the speed of sound. Describe what observers at points A, B, and C hear at the instant shown in Fig. Q16.25, when the shock wave has just reached point B. Explain. Fig. Q16
> When you first step out of the shower, you feel cold. But as soon as you are dry you feel warmer, even though the room temperature does not change. Why?
> Does an aircraft make a sonic boom only at the instant its speed exceeds Mach 1? Explain.
> Old-time kitchen lore suggests that things cook better (evenly and without burning) in heavy cast-iron pots. What desirable characteristics do such pots have?
> If you wait at a railroad crossing as a train approaches and passes, you hear a Doppler shift in its sound. But if you listen closely, you hear that the change in frequency is continuous; it does not suddenly go from one high frequency to another low fre
> Desert travelers sometimes keep water in a canvas bag. Some water seeps through the bag and evaporates. How does this cool the water inside the bag?
> Why is a hot, humid day in the tropics generally more uncomfortable for human beings than a hot, dry day in the desert?
> Before giving you an injection, a physician swabs your arm with isopropyl alcohol at room temperature. Why does this make your arm feel cold? (Hint: The reason is not the fear of the injection! The boiling point of isopropyl alcohol is 82.4 0C.)
> A steel tank is completely filled with 1.90 m3 of ethanol when both the tank and the ethanol are at 32.0 °C. When the tank and its contents have cooled to 18.0° C, what additional volume of ethanol can be put into the tank?
> A large church has part of the organ in the front of the church and part in the back. A person walking rapidly down the aisle while both segments are playing at once reports that the two segments sound out of tune. Why?
> The climate of regions adjacent to large bodies of water (like the Pacific and Atlantic coasts) usually features a narrower range of temperature than the climate of regions far from large bodies of water (like the prairies). Why?
> Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 860 Hz. Point P is 12.0 m from A and 13.4 m from B. Is the interference at P constructive or destructive
> An organist in a cathedral plays a loud chord and then releases the keys. The sound persists for a few seconds and gradually dies away. Why does it persist? What happens to the sound energy when the sound dies away?
> A small metal band is slipped onto one of the tines of a tuning fork. As this band is moved closer and closer to the end of the tine, what effect does this have on the wavelength and frequency of the sound the tine produces? Why?
> A small fraction of the energy in a sound wave is absorbed by the air through which the sound passes. How does this modify the inverse-square relationship between intensity and distance from the source? Explain.
> The units of specific heat c are J/kg ∙ K, but the units of heat of fusion Lf or heat of vaporization Lv are simply J/kg. Why do the units of Lf and Lv not include a factor of (K)-1 to account for a temperature change?
> If the pressure amplitude of a sound wave is halved, by what factor does the intensity of the wave decrease? By what factor must the pressure amplitude of a sound wave be increased in order to increase the intensity by a factor of 16? Explain.
> Which has a more direct influence on the loudness of a sound wave: the displacement amplitude or the pressure amplitude? Explain.
> Two bodies made of the same material have the same external dimensions and appearance, but one is solid and the other is hollow. When their temperature is increased, is the overall volume expansion the same or different? Why?
> A glass flask whose volume is 1000.00 cm3 at 0.0 °C is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0 °C, 8.95 cm3 of mercury overflow. If the coefficient of volume expansion of mercury is 18.0 × 10-5 K-1, c
> Lane dividers on highways sometimes have regularly spaced ridges or ripples. When the tires of a moving car roll along such a divider, a musical note is produced. Why? Explain how this phenomenon could be used to measure the car’s speed.
> In a popular and amusing science demonstration, a person inhales helium and then his voice becomes high and squeaky. Why does this happen? (Warning: Inhaling too much helium can cause unconsciousness or death.)
> Symphonic musicians always “warm up” their wind instruments by blowing into them before a performance. What purpose does this serve?
> If you heat the air inside a rigid, sealed container until its Kelvin temperature doubles, the air pressure in the container will also double. Is the same thing true if you double the Celsius temperature of the air in the container? Explain.
> Would you expect the pitch (or frequency) of an organ pipe to increase or decrease with increasing temperature? Explain.
> The hero of a western movie listens for an oncoming train by putting his ear to the track. Why does this method give an earlier warning of the approach of a train than just listening in the usual way?
> Section 18.1 states that ordinarily, pressure, volume, and temperature cannot change individually without one affecting the others. Yet when a liquid evaporates, its volume changes, even though its pressure and temperature are constant. Is this inconsist
> The statistical quantities “average value” and “root-mean-square value” can be applied to any distribution. Figure P18.82 shows the scores of a class of 150 students on a 100-point q
> The vapor pressure of water (see Exercise 18.44) decreases as the temperature decreases. The table lists the vapor pressure of water at various temperatures: Exercise 18.44: The vapor pressure is the pressure of the vapor phase of a substance when it i
> A steel cylinder with rigid walls is evacuated to a high degree of vacuum; you then put a small amount of helium into the cylinder. The cylinder has a pressure gauge that measures the pressure of the gas inside the cylinder. You place the cylinder in var
> You blow across the open mouth of an empty test tube and produce the fundamental standing wave of the air column inside the test tube. The speed of sound in air is 344 m/s and the test tube acts as a stopped pipe. (a). If the length of the air column in
> A vertical cylinder of radius r contains an ideal gas and is fitted with a piston of mass m that is free to move (Fig. P18.79). The piston and the walls of the cylinder are frictionless, and the entire cylinder is placed in a constant-temperature bath. T
> Calculate the integral in Eq. (18.30), 0 ∞
> (a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval v to v +
> (a). Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300 K. (b). Calculate the moment of inertia of an oxygen molecule (O2) for rotation about either the y- or z-axis shown in Fig. 18.18b. Treat the molecu
> (a). The temperature near the top of Jupiter’s multicolored cloud layer is about 140 K. The temperature at the top of the earth’s troposphere, at an altitude of about 20 km, is about 220 K. Calculate the rms speed of hydrogen molecules in both these envi
> (a). Show that a projectile with mass m can “escape” from the surface of a planet if it is launched vertically upward with a kinetic energy greater than mgRp, where g is the acceleration due to gravity at the planet’s surface and Rp is the planet’s radiu
