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 the constellation Orion, which radiates energy at a rate of 2.7 × 1032 W and has surface temperature 11,000 K; (b). Procyon B (visible only using a telescope), which radiates energy at a rate of 2.1 × 1023 W and has surface temperature 10,000 K. (c). Compare your answers to the radius of the earth, the radius of the sun, and the distance between the earth and the sun. (Rigel is an example of a supergiant star, and Procyon B is an example of a white dwarf star.)
> 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.
> 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.
> 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 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?
> The vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. The relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water
> Solid water (ice) is slowly warmed from a very low temperature. (a). What minimum external pressure p1 must be applied to the solid if a melting phase transition is to be observed? Describe the sequence of phase transitions that occur if the applied pre
> For a gas of nitrogen molecules (N2), what must the temperature be if 94.7% of all the molecules have speeds less than (a). 1500 m/s; (b). 1000 m/s; (c). 500 m/s? Use Table 18.2. The molar mass of N2 is 28.0 g/mol. Table 18.2: sa/a v/U rms Fract
> (a). Calculate the specific heat at constant volume of water vapor, assuming the nonlinear triatomic molecule has three translational and three rotational degrees of freedom and that vibrational motion does not contribute. The molar mass of water is 18.0
> (a). Compute the specific heat at constant volume of nitrogen (N2) gas, and compare it with the specific heat of liquid water. The molar mass of N2 is 28.0 g/mol. (b). You warm 1.00 kg of water at a constant volume of 1.00 L from 20.00 C to 30.00 C in a
> Perfectly rigid containers each hold n moles of ideal gas, one being hydrogen (H2) and the other being neon (Ne). If it takes 300 J of heat to increase the temperature of the hydrogen by 2.50 0C, by how many degrees will the same amount of heat raise the
> How much heat does it take to increase the temperature of 1.80 mol of an ideal gas by 50.0 K near room temperature if the gas is held at constant volume and is (a) diatomic; (b) monatomic?
> Smoke particles in the air typically have masses of the order of 10-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a). Find the root mean- squa
> Oxygen (O2) has a molar mass of 32.0 g/mol. What is (a). the average translational kinetic energy of an oxygen molecule at a temperature of 300 K; (b). the average value of the square of its speed; (c). the root-mean-square speed; (d). the momentum of
> (a) A deuteron, 21 H, is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K. What is the rms speed of the deuterons? Is this a significan
> A 60.0-m-long brass rod is struck at one end. A person at the other end hears two sounds as a result of two longitudinal waves, one traveling in the metal rod and the other traveling in air. What is the time interval between the two sounds? (The speed of
> A container with volume 1.64 L is initially evacuated. Then it is filled with 0.226 g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. If the root-mean-square speed of the gas mo
> We have two equal-size boxes, A and B. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box A is at 50 0C while the gas in box B is at 10 0C. This is all we know about the gas in the boxes
> A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (a) the average kinetic energies of the three types of atoms and (b) the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under
> (a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m × 12.00 m × 4.00 m if the air is treated as an ideal gas at 1.00 atm? (b). What is the speed of a 2000-kg automobile if its kinetic energy equals t
> Consider an ideal gas at 270 C and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a). What is the length of an edge of each
> The Lagoon Nebula (Fig. E18.24) is a cloud of hydrogen gas located 3900 light-years from the earth. The cloud is about 45 light-years in diameter and glows because of its high temperature of 7500 K. (The gas is raised to this temperature by the stars tha
> Modern vacuum pumps make it easy to attain pressures of the order of 10-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a). At a pressure of 9.00 × 10-14 atm and an ordinary temperature of 300.0 K, how many molecul
> (a).Calculate the mass of nitrogen present in a volume of 3000 cm3 if the gas is at 22.0°C and the absolute pressure of 2.00 × 10-13 atm is a partial vacuum easily obtained in laboratories. (b).What is the density (in kg/m3) of the N2?
> With the assumptions of Example 18.4 (Section 18.1), at what elevation above sea level is air pressure 90% of the pressure at sea level?
> Three moles of an ideal gas are in a rigid cubical box with sides of length 0.300 m. (a). What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0° C? (b) What is the force when the temperature of the g
> (a). Show that the fractional change in the speed of sound (dv/v) due to a very small temperature change dT is given by dv/v = 1 2 dT/T. (Hint: Start with Eq. 16.10.) Eq. 16.10: U =
> 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. (a). What is the wavelength of these waves? (b). For 1000-Hz waves in air, w
> A sled with mass 12.00 kg moves in a straight line on a frictionless, horizontal surface. At one point in its path, its speed is 4.00 m/s; after it has traveled 2.50 m beyond this point, its speed is 6.00 m/s. Use the work–energy theorem to find the forc
> You throw a 3.00-N rock vertically into the air from ground level. You observe that when it is 15.0 m above the ground, it is traveling at 25.0 m/s upward. Use the work–energy theorem to find (a) the rock’s speed just as it left the ground and (b) its ma
> You are a member of an Alpine Rescue Team. You must project a box of supplies up an incline of constant slope angle a so that it reaches a stranded skier who is a vertical distance h above the bottom of the incline. The incline is slippery, but there is
> Use the work–energy theorem to solve each of these problems. You can use Newton’s laws to check your answers. (a) A skier moving at 5.00 m>s encounters a long, rough horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis
> Use the work–energy theorem to solve each of these problems. You can use Newton’s laws to check your answers. Neglect air resistance in all cases. (a) A branch falls from the top of a 95.0-m-tall redwood tree, starting from rest. How fast is it moving wh
> A 4.80-kg watermelon is dropped from rest from the roof of an 18.0-m-tall building and feels no appreciable air resistance. (a) Calculate the work done by gravity on the watermelon during its displacement from the roof to the ground. (b) Just before it s
> Using a cable with a tension of 1350 N, a tow truck pulls a car 5.00 km along a horizontal roadway. (a) How much work does the cable do on the car if it pulls horizontally? If it pulls at 35.0° above the horizontal? (b) How much work does the cable do on
> About 50,000 years ago, a meteor crashed into the earth near present-day Flagstaff, Arizona. Measurements from 2005 estimate that this meteor had a mass of about 1.4 × 108 kg (around 150,000 tons) and hit the ground at a speed of 12 km/s. (a) How much ki
> (a) In the Bohr model of the atom, the ground-state electron in hydrogen has an orbital speed of 2190 km/s. What is its kinetic energy? (Consult Appendix F.) (b) If you drop a 1.0-kg weight (about 2 lb) from a height of 1.0 m, how many joules of kinetic
> Adult cheetahs, the fastest of the great cats, have a mass of about 70 kg and have been clocked to run at up to 72 mi/h 132 m/s2. (a) How many joules of kinetic energy does such a swift cheetah have? (b) By what factor would its kinetic energy change if
> You are holding a briefcase by the handle, with your arm straight down by your side. Does the force your hand exerts do work on the briefcase when (a) you walk at a constant speed down a horizontal hallway and (b) you ride an escalator from the first to
> A 1.50-kg book is sliding along a rough horizontal surface. At point A it is moving at 3.21 m>s, and at point B it has slowed to 1.25 m/s. (a) How much work was done on the book between A and B? (b) If -0.750 J of work is done on the book from B to C, ho
> An airplane in flight is subject to an air resistance force proportional to the square of its speed v. But there is an additional resistive force because the airplane has wings. Air flowing over the wings is pushed down and slightly forward, so from Newt
