For diatomic carbon dioxide gas (CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (a). the most probable speed vmp; (b). the average speed vav; (c). the root-mean-square speed vrms.
> 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.
> What is the rate of energy radiation per unit area of a blackbody at (a) 273 K and (b) 2730 K?
> One end of an insulated metal rod is maintained at 100.0 C, and the other end is maintained at 0.00 °C by an ice–water mixture. The rod is 60.0 cm long and has a cross-sectional area of 1.25 cm2. The heat conducted by the rod melts 8.50 g of ice in 10.0
> How fast (as a percentage of light speed) would a star have to be moving so that the frequency of the light we receive from it is 10.0% higher than the frequency of the light it is emitting? Would it be moving away from us or toward us? (Assume it is mov
> A car alarm is emitting sound waves of frequency 520 Hz. You are on a motorcycle, traveling directly away from the parked car. How fast must you be traveling if you detect a frequency of 490 Hz?
> A sound wave in air at 200 C has a frequency of 320 Hz and a displacement amplitude of 5.00 × 10-3 mm. For this sound wave calculate the (a). pressure amplitude (in Pa); (b). intensity (in W/m2); (c). sound intensity level (in decibels).
> On the planet Arrakis a male ornithoid is flying toward his mate at 25.0 m/s while singing at a frequency of 1200 Hz. If the stationary female hears a tone of 1240 Hz, what is the speed of sound in the atmosphere of Arrakis?
> In the situation described in Exercise 17.42, the man’s metabolism will eventually return the temperature of his body (and of the soft drink that he consumed) to 37.0 °C. If his body releases energy at a rate of 7.00 × 103 kJ/day (the basal metabolic rat
> Two organ pipes, open at one end but closed at the other, are each 1.14 m long. One is now lengthened by 2.00 cm. Find the beat frequency that they produce when playing together in their fundamentals.
> The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.00 C in summer to -100 0C in winter. Over the course of a Martian year, what are
> At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at 20.00C? (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element. The
> Calculate the mean free path of air molecules at 3.50 × 10-13 atm and 300 K. (This pressure is readily attainable in the laboratory; see Exercise 18.23.) As in Example 18.8, model the air molecules as spheres of radius 2.0 × 10-10 m. Exercise 18.23: Mo
> A 75.0-cm-long wire of mass 5.625 g is tied at both ends and adjusted to a tension of 35.0 N. When it is vibrating in its second overtone, find (a). the frequency and wavelength at which it is vibrating and (b). the frequency and wavelength of the soun
> You have a stopped pipe of adjustable length close to a taut 62.0-cm, 7.25-g wire under a tension of 4110 N. You want to adjust the length of the pipe so that, when it produces sound at its fundamental frequency, this sound causes the wire to vibrate in
> A nail driven into a board increases in temperature. If we assume that 60% of the kinetic energy delivered by a 1.80-kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature incre
> A fan at a rock concert is 30 m from the stage, and at this point the sound intensity level is 110 dB. (a). How much energy is transferred to her eardrums each second? (b). How fast would a 2.0-mg mosquito have to fly (in mm/s) to have this much kineti
> A large organic molecule has a mass of 1.41 × 10-21 kg. What is the molar mass of this compound?
> How many moles are in a 1.00-kg bottle of water? How many molecules? The molar mass of water is 18.0 g/mol.
> In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7 × 109 people)?
> (a). If two sounds differ by 5.00 dB, find the ratio of the intensity of the louder sound to that of the softer one. (b). If one sound is 100 times as intense as another, by how much do they differ in sound intensity level (in decibels)? (c). If you in
> At point A, 3.0 m from a small source of sound that is emitting uniformly in all directions, the sound intensity level is 53 dB. (a). What is the intensity of the sound at A? (b). How far from the source must you go so that the intensity is one-fourth
> The Sacramento City Council adopted a law to reduce the allowed sound intensity level of the much-despised leaf blowers from their current level of about 95 dB to 70 dB. With the new law, what is the ratio of the new allowed intensity to the previously a
> A large cylindrical tank contains 0.750 m3 of nitrogen gas at 27 0C and 7.50 × 103Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.410 m3 and the t
> At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5 °C and the air density is 0.364 kg/m3. What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the s
> With the assumption that the air temperature is a uniform 0.0°C, what is the density of the air at an altitude of 1.00 km as a percentage of the density at the surface?
> You live on a busy street, but as a music lover, you want to reduce the traffic noise. (a). If you install special sound reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity 1in
> An experimenter using a gas thermometer found the pressure at the triple point of water (0.01°C) to be 4.80 × 104 Pa and the pressure at the normal boiling point (100°C) to be 6.50 × 104 Pa. (a). Assuming that the pressure varies linearly with temperatu
> A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3 of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m3.
> A copper cylinder is initially at 20.0° C. At what temperature will its volume be 0.150% larger than it is at 20.0 °C?
> You are trying to overhear a juicy conversation, but from your distance of 15.0 m, it sounds like only an average whisper of 20.0 dB. How close should you move to the chatterboxes for the sound level to be 60.0 dB?
> The Humber Bridge in England has the world’s longest single span, 1410 m. Calculate the change in length of the steel deck of the span when the temperature increases from -5.0 °C to 18.0 °C.
> A U.S. penny has a diameter of 1.9000 cm at 20.0 C. The coin is made of a metal alloy (mostly zinc) for which the coefficient of linear expansion is 2.6 × 10-5 K-1. What would its diameter be on a hot day in Death Valley (48.0°C)? On a cold night in the
> One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5° C. You could use the building as a sort of giant thermometer on a ho
> A constant-volume gas thermometer registers an absolute pressure corresponding to 325 mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?
> You put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped 10.0 K. What is its temperature change in (a) F° and (b) C° ?
> (a). Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other. (b). Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other.
> At a temperature of 27.0C, what is the speed of longitudinal waves in (a). hydrogen (molar mass 2.02 g/mol); (b). helium (molar mass 4.00 g/mol); (c). argon (molar mass 39.9 g/mol)? See Table 19.1 for values of γ. (d). Compare your answer
> (a). By what factor must the sound intensity be increased to raise the sound intensity level by 13.0 dB? (b). Explain why you don’t need to know the original sound intensity.
> The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?
> Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a). the midday temperature at the surface of the moon (400 K); (b). the temperature at the tops of the clouds in the atmosphere of Saturn (95 K); (c). the temperature at
> (a). Whale communication. Blue whales apparently communicate with each other using sound of frequency 17 Hz, which can be heard nearly 1000 km away in the ocean. What is the wavelength of such a sound in seawater, where the speed of sound is 1531 m/s? (
> A loud factory machine produces sound having a displacement amplitude of 1.00 µm, but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maximum pressure amplitude of the sound waves is limited to 10.0 Pa. Und
> (a). On January 22, 1943, the temperature in Spearfish, South Dakota, rose from -4.0° F to 45.0 °F in just 2 minutes. What was the temperature change in Celsius degrees? (b). The temperature in Browning, Montana, was 44.0° F on January 23, 1916. The nex
> Example 16.1 (Section 16.1) showed that for sound waves in air with frequency 1000 Hz, a displacement amplitude of 1.2 × 10-8 m produces a pressure amplitude of 3.0 × 10-2 Pa. Water at 200C has a bulk modulus of 2.2 × 109 Pa, and the speed of sound in wa
> The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume e = 1 for these surfaces. Find the radii of the following stars (assumed to be spherical): (a). Rigel, the bright blue star in t
> The operating temperature of a tungsten filament in an incandescent light bulb is 2450 K, and its emissivity is 0.350. Find the surface area of the filament of a 150-W bulb if all the electrical energy consumed by the bulb is radiated by the filament as
> The emissivity of tungsten is 0.350. A tungsten sphere with radius 1.50 cm is suspended within a large evacuated enclosure whose walls are at 290.0 K. What power input is required to maintain the sphere at 3000.0 K if heat conduction along the supports i
> A spherical pot contains 0.75 L of hot coffee (essentially water) at an initial temperature of 95° C. The pot has an emissivity of 0.60, and the surroundings are at 20.0° C. Calculate the coffee’s rate of heat loss by radiation.
> Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate. Typically, the diameter of this membrane is about 8.4 mm in humans. (a). How much energy is delivered to the eardrum each second when someone whispers (20 dB) a s
> A picture window has dimensions of 1.40 m × 2.50 m and is made of glass 5.20 mm thick. On a winter day, the temperature of the outside surface of the glass is -20.0 °C, while the temperature of the inside surface is a comfortable 19.5° C. (a). At what r
> You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 190.0 J/s from a furnace at 400.0 °C to a container of boiling water under 1 atmosphere. What must the rod’s diameter be?
> A pot with a steel bottom 8.50 mm thick rests on a hot stove. The area of the bottom of the pot is 0.150 m2. The water inside the pot is at 100.0° C, and 0.390 kg are evaporated every 3.00 min. Find the temperature of the lower surface of the pot, which
> A long rod, insulated to prevent heat loss along its sides, is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an ice–water mixture at the other (Fig. E17.62). The rod consists of a 1.00-m sec
> The blood plays an important role in removing heat from the body by bringing this energy directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. Assume that the blood is br
> An electric kitchen range has a total wall area of 1.40 m2 and is insulated with a layer of fiberglass 4.00 cm thick. The inside surface of the fiberglass has a temperature of 175 C, and its outside surface is at 35.0 C. The fiberglass has a thermal co
> A carpenter builds an exterior house wall with a layer of wood 3.0 cm thick on the outside and a layer of Styrofoam insulation 2.2 cm thick on the inside wall surface. The wood has k = 0.080 W/m ∙ K, and the Styrofoam has k = 0.027 W /m ∙ K. The interior
> Suppose that the rod in Fig. 17.24a is made of copper, is 45.0 cm long, and has a cross-sectional area of 1.25 cm2. Let TH = 100.0 C and TC = 0.0 C. (a). What is the final steady-state temperature gradient along the rod? (b). What is the heat curre
> Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is 0.300 m and the length of the copper section is 0.800 m. Each segment has cross-sectional area 0.00500 m2. The free end of the brass segme
> Calculate the volume of 1.00 mol of liquid water at 20°C (at which its density is 998 kg/m3), and compare that with the volume occupied by 1.00 mol of water at the critical point, which is 56 × 10-6 m3. Water has a molar mass of 18.0 g/mol.
> What must be the stress (F/A) in a stretched wire of a material whose Young’s modulus is Y for the speed of longitudinal waves to equal 30 times the speed of transverse waves?
