Symphonic musicians always “warm up” their wind instruments by blowing into them before a performance. What purpose does this serve?
> 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.
> 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.
> 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.)
> 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
> The surface of the sun has a temperature of about 5800 K and consists largely of hydrogen atoms. (a). Find the rms speed of a hydrogen atom at this temperature. (The mass of a single hydrogen atom is 1.67 × 10-27 kg.) (b). The escape speed
> It is possible to make crystalline solids that are only one layer of atoms thick. Such “two-dimensional” crystals can be created by depositing atoms on a very flat surface. (a). If the atoms in such a two-dimensional crystal can move only within the pla
> (a). What is the total random translational kinetic energy of 5.00 L of hydrogen gas (molar mass 2.016 g/mol) with pressure 1.01 × 105 Pa and temperature 300 K? (Hint: Use the procedure of Problem 18.67 as a guide.) Problem 18.67: You blow up a spheri
> A commonly used potential-energy function for the interaction of two molecules (see Fig. 18.8) is the Lennard-Jones 6-12 potential: where r is the distance between the centers of the molecules and U0 and R0 are positive constants. The corresponding for
> A pipe closed at both ends can have standing waves inside of it, but you normally don’t hear them because little of the sound can get out. But you can hear them if you are inside the pipe, such as someone singing in the shower. (a). Show that the wavele
> Consider a sound wave in air that has displacement amplitude 0.0200 mm. Calculate the pressure amplitude for frequencies of (a). 150 Hz; (b). 1500 Hz; (c). 15,000 Hz. In each case compare the result to the pain threshold, which is 30 Pa.
> (a). Compute the increase in gravitational potential energy for a nitrogen molecule (molar mass 28.0 g/mol) for an increase in elevation of 400 m near the earth’s surface. (b). At what temperature is this equal to the average kinetic energy of a nitroge
> You blow up a spherical balloon to a diameter of 50.0 cm until the absolute pressure inside is 1.25 atm and the temperature is 22.0 °C. Assume that all the gas is N2, of molar mass 28.0 g/mol. (a). Find the mass of a single N2 molecule. (b). How much tr
> Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 2.00 atm, then the root-mean-square speed of the helium atoms is vrms = 176 m/s. By how much (in atmospheres) must the pressure be increased to increase the vrms of the He at
> A sealed box contains a monatomic ideal gas. The number of gas atoms per unit volume is 5.00 × 1020 atoms/cm3, and the average translational kinetic energy of each atom is 1.80 × 10-23 J. (a). What is the gas pressure? (b). If the gas is neon (molar ma
> You have two identical containers, one containing gas A and the other gas B. The masses of these molecules are mA = 3.34 × 10-27 kg and mB = 5.34 × 10-26 kg. Both gases are under the same pressure and are at 10.0° C. (a). Which molecules (A or B) have g
> A person at rest inhales 0.50 L of air with each breath at a pressure of 1.00 atm and a temperature of 20.0 °C. The inhaled air is 21.0% oxygen. (a). How many oxygen molecules does this person inhale with each breath? (b). Suppose this person is now re
> Estimate the number of atoms in the body of a 50-kg physics student. Note that the human body is mostly water, which has molar mass 18.0 g/mol, and that each water molecule contains three atoms.
> During your mechanical engineering internship, you are given two uniform metal bars A and B, which are made from different metals, to determine their thermal conductivities. Measuring the bars, you determine that both have length 40.0 cm and uniform cros
> At a chemical plant where you are an engineer, a tank contains an unknown liquid. You must determine the liquid’s specific heat capacity. You put 0.500 kg of the liquid into an insulated metal cup of mass 0.200 kg. Initially the liquid and cup are at 20.
> As a physicist, you put heat into a 500.0-g solid sample at the rate of 10.0 kJ/min while recording its temperature as a function of time. You plot your data as shown in Fig. P17.111. (a). What is the latent heat of fusion for this solid? (b). What are
> The longest pipe found in most medium-size pipe organs is 4.88 m (16 ft) long. What is the frequency of the note corresponding to the fundamental mode if the pipe is (a). open at both ends, (b). open at one end and closed at the other?
> The icecaps of Greenland and Antarctica contain about 1.75% of the total water (by mass) on the earth’s surface; the oceans contain about 97.5%, and the other 0.75% is mainly groundwater. Suppose the icecaps, currently at an average temperature of about
> You have probably seen people jogging in extremely hot weather. There are good reasons not to do this! When jogging strenuously, an average runner of mass 68 kg and surface area 1.85 m2 produces energy at a rate of up to 1300 W, 80% of which is converted
> A metal sphere with radius 3.20 cm is suspended in a large metal box with interior walls that are maintained at 30.0° C. A small electric heater is embedded in the sphere. Heat energy must be supplied to the sphere at the rate of 0.660 J/s to maintain th
> A physicist uses a cylindrical metal can 0.250 m high and 0.090 m in diameter to store liquid helium at 4.22 K; at that temperature the heat of vaporization of helium is 2.09 × 104 J/kg. Completely surrounding the metal can are walls maintained at the te
> A light, plastic sphere with mass m = 9.00 g and density r = 4.00 kg/m3 is suspended in air by thread of negligible mass. (a). What is the tension T in the thread if the air is at 5.00oC and p = 1.00 atm? The molar mass of air is 28.8 g/mol. (b). How mu
> (a) When the air temperature is below 0° C, the water at the surface of a lake freezes to form an ice sheet. Why doesn’t freezing occur throughout the entire volume of the lake? (b). Show that the thickness of the ice sheet formed on the surface of a la
> The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 75-kg (165-lb) person of height 1.83 m (6 ft) has a body surface area of approximately 2.0 m2. (a). What is the net amount of heat this person could
> A brass rod 12.0 cm long, a copper rod 18.0 cm long, and an aluminum rod 24.0 cm long—each with cross-sectional area 2.30 cm3—are welded together end to end to form a rod 54.0 cm long, with copper as the middle section. The free end of the brass section
> A large tank of water has a hose connected to it (Fig. P18.59). The tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the value 3.50 m, the absolute pressure p of the compressed air is 4.2
> Compute the ratio of the rate of heat loss through a single-pane window with area 0.15 m2 to that for a double-pane window with the same area. The glass of a single pane is 4.2 mm thick, and the air space between the two panes of the double-pane window i
> Many opera singers (and some pop singers) have a range of about 2 1 2 octaves or even greater. Suppose a soprano’s range extends from A below middle C (frequency 220 Hz) up to E-flat above high C (frequency 1244 Hz). Although the vocal tract is quite c
> A 250-kg weight is hanging from the ceiling by a thin copper wire. In its fundamental mode, this wire vibrates at the frequency of concert A (440 Hz). You then increase the temperature of the wire by 40°C . (a). By how much will the fundamental frequenc
> You propose a new temperature scale with temperatures given in M. You define 0.0 M to be the normal melting point of mercury and 100.0 M to be the normal boiling point of mercury. (a). What is the normal boiling point of water in M? (b). A temperatur
> Animals in cold climates often depend on two layers of insulation: a layer of body fat (of thermal conductivity 0.20 W/m ∙ K) surrounded by a layer of air trapped inside fur or down. We can model a black bear (Ursus americanus) as a sphere 1.5 m in diame
> In a container of negligible mass, 0.0400 kg of steam at 100 °C and atmospheric pressure is added to 0.200 kg of water at 50.0 °C. (a). If no heat is lost to the surroundings, what is the final temperature of the system? (b). At the final temperature,
> A Styrofoam bucket of negligible mass contains 1.75 kg of water and 0.450 kg of ice. More ice, from a refrigerator at -15.0 °C, is added to the mixture in the bucket, and when thermal equilibrium has been reached, the total mass of ice in the bucket is 0
> A copper calorimeter can with mass 0.446 kg contains 0.0950 kg of ice. The system is initially at 0.0° C. (a). If 0.0350 kg of steam at 100.0 °C and 1.00 atm pressure is added to the can, what is the final temperature of the calorimeter can and its cont
> A thirsty nurse cools a 2.00-L bottle of a soft drink (mostly water) by pouring it into a large aluminum mug of mass 0.257 kg and adding 0.120 kg of ice initially at -15.0 °C. If the soft drink and mug are initially at 20.0 °C, what is the final temperat
> You have 1.50 kg of water at 28.0° C in an insulated container of negligible mass. You add 0.600 kg of ice that is initially at -22.0° C. Assume that no heat exchanges with the surroundings. (a) After thermal equilibrium has been reached, has all of the
> In a household hot-water heating system, water is delivered to the radiators at 70.0° C (158.0 °F) and leaves at 28.0 °C (82.4 °F). The system is to be replaced by a steam system in which steam at atmospheric pressure condenses in the radiators and the c
