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 when you run the second propeller, what are the two possible frequencies (in rpm) of the second propeller? (b). Suppose you increase the speed of the second propeller slightly and find that the beat frequency changes to 2.1 Hz. In part (a), which of the two answers was the correct one for the frequency of the second single-bladed propeller? How do you know?
> A 4.00-kg silver ingot is taken from a furnace, where its temperature is 750.0 °C, and placed on a large block of ice at 0.0° C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?
> An insulated beaker with negligible mass contains 0.250 kg of water at 75.0° C. How many kilograms of ice at -20.0° C must be dropped into the water to make the final temperature of the system 40.0 °C?
> A laboratory technician drops a 0.0850-kg sample of unknown solid material, at 100.0 °C, into a calorimeter. The calorimeter can, initially at 19.0° C, is made of 0.150 kg of copper and contains 0.200 kg of water. The final temperature of the calorimeter
> An asteroid with a diameter of 10 km and a mass of 2.60 × 1015 kg impacts the earth at a speed of 32.0 km/s, landing in the Pacific Ocean. If 1.00% of the asteroid’s kinetic energy goes to boiling the ocean water (assume an initial water temperature of 1
> Evaporation of sweat is an important mechanism for temperature control in some warm-blooded animals. (a). What mass of water must evaporate from the skin of a 70.0-kg man to cool his body 1.00C ? The heat of vaporization of water at body temperature (3
> Camels require very little water because they are able to tolerate relatively large changes in their body temperature. While humans keep their body temperatures constant to within one or two Celsius degrees, a dehydrated camel permits its body temperatur
> What is the amount of heat input to your skin when it receives the heat released (a). by 25.0 g of steam initially at 100.0 °C, when it is cooled to skin temperature 134.0° C2? (b). By 25.0 g of water initially at 100.0 °C, when it is cooled to 34.0° C
> What must the initial speed of a lead bullet be at 25.0 °C so that the heat developed when it is brought to rest will be just sufficient to melt it? Assume that all the initial mechanical energy of the bullet is converted to heat and that no heat flows f
> A welder using a tank of volume 0.0750 m3 fills it with oxygen (molar mass 32.0 g/mol) at a gauge pressure of 3.00 × 105 Pa and temperature of 37.00 C. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is
> An open container holds 0.550 kg of ice at -15.0° C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 800.0 J/min for 500.0 min. (a). After how many minutes does the ice start to melt? (b). After how m
> How much heat is required to convert 18.0 g of ice at -10.0° C to steam at 100.0 °C? Express your answer in joules, calories, and Btu.
> An ice-cube tray of negligible mass contains 0.290 kg of water at 18.0° C. How much heat must be removed to cool the water to 0.00 °C and freeze it? Express your answer in joules, calories, and Btu.
> Before going in for his annual physical, a 70.0-kg man whose body temperature is 37.0° C consumes an entire 0.355-L can of a soft drink (mostly water) at 12.0 °C. (a). What will his body temperature be after equilibrium is attained? Ignore any heating by
> A 6.00-kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -20.0° C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibri
> In a container of negligible mass, 0.200 kg of ice at an initial temperature of -40.0° C is mixed with a mass m of water that has an initial temperature of 80.0 °C. No heat is lost to the surroundings. If the final temperature of the system is 28.0° C, w
> A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at 20.0°C. A 0.250-kg block of iron at 85.0°C is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings.
> A copper calorimeter can with mass 0.100 kg contains 0.160 kg of water and 0.0180 kg of ice in thermal equilibrium at atmospheric pressure. If 0.750 kg of lead at 255° C is dropped into the calorimeter can, what is the final temperature? Assume that no h
> A blacksmith cools a 1.20-kg chunk of iron, initially at 650.0° C, by trickling 15.0 °C water over it. All of the water boils away, and the iron ends up at 120.0 ° C. How much water did the blacksmith trickle over the iron?
> One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0°C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached
> A submerged scuba diver hears the sound of a boat horn directly above her on the surface of the lake. At the same time, a friend on dry land 22.0 m from the boat also hears the horn (Fig. E16.7). The horn is 1.2 m above the surface of the water. What is
> A 500.0-g chunk of an unknown metal, which has been in boiling water for several minutes, is quickly dropped into an insulating Styrofoam beaker containing 1.00 kg of water at room temperature (20.0 °C). After waiting and gently stirring for 5.00 minutes
> You have 750 g of water at 10.0° C in a large insulated beaker. How much boiling water at 100.0°C must you add to this beaker so that the final temperature of the mixture will be 75° C?
> A 15.0-g bullet traveling horizontally at 865 m/s passes through a tank containing 13.5 kg of water and emerges with a speed of 534 m/s. What is the maximum temperature increase that the water could have as a result of this event?
> A technician measures the specific heat of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat transferred to the liquid for 120 s at a constant rate of 65.0 W. The mass of the liquid is 0.780 kg, and
> A 25,000-kg subway train initially traveling at 15.5 m/s slows to a stop in a station and then stays there long enough for its brakes to cool. The station’s dimensions are 65.0 m long by 20.0 m wide by 12.0 m high. Assuming all the work done by the brake
> While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change
> Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawbacks are that energy is wasted because the tank loses heat when it is not in use and that you can run out of ho
> You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is 28.4 N. You carefully add 1.25 × 104 J of heat energy to the sample and find that its temperature rises 18.0C . What is the sampl
> 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
> 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.
> 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?
