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 of 510 kcal/h. How long would you have to exercise to “work off” one doughnut? (b). If the energy in the doughnut could somehow be converted into the kinetic energy of your body as a whole, how fast could you move after eating the doughnut? Take your mass to be 60 kg, and express your answer in m/s and in km/h.
> (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
> The African bombardier beetle (Stenaptinus insignis) can emit a jet of defensive spray from the movable tip of its abdomen (Fig. P17.91). The beetle’s body has reservoirs containing two chemicals; when the beetle is disturbed, these che
> The human vocal tract is a pipe that extends about 17 cm from the lips to the vocal folds (also called “vocal cords”) near the middle of your throat. The vocal folds behave rather like the reed of a clarinet, and the vocal tract acts like a stopped pipe.
> (a) By how much would the body temperature of the bicyclist in Problem 17.89 increase in an hour if he were unable to get rid of the excess heat? (b). Is this temperature increase large enough to be serious? To find out, how high a fever would it be equ
> If the air temperature is the same as the temperature of your skin (about 30°C), your body cannot get rid of heat by transferring it to the air. In that case, it gets rid of the heat by evaporating water (sweat). During bicycling, a typical 70-kg person’
> The molar heat capacity of a certain substance varies with temperature according to the empirical equation How much heat is necessary to change the temperature of 3.00 mol of this substance from 27°C to 227°C? (Hint: Use Eq. (17.
> (a). A typical student listening attentively to a physics lecture has a heat output of 100 W. How much heat energy does a class of 140 physics students release into a lecture hall over the course of a 50-min lecture? (b). Assume that all the heat energy
> A person of mass 70.0 kg is sitting in the bathtub. The bathtub is 190.0 cm by 80.0 cm; before the person got in, the water was 24.0 cm deep. The water is at 37.0° C. Suppose that the water were to cool down spontaneously to form ice at 0.0 °C, and that
> 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 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
> 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?
> 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
