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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.
When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist airways. Consequently, an adult human exhales about 25 mg of evaporated water with each breath. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation
The burner on an electric stove has a power output of 2.0 kW.A 750 g stainless steel teakettle is filled with 20°C water and placed on the already hot burner. If it takes 3.0 min for the water to reach a boil, what volume of water, in cm3, was in the kettle?Stainless steel is mostly iron, so you
A 5.0-m-diameter garden pond is 30 cm deep. Solar energy is incident on the pond at an average rate of 400 W/m2. If the water absorbs all the solar energy and does not exchange energy with its surroundings, how many hours will it take to warm from 15°C to 25°C?
A 5.0 g ice cube at -20°C is in a rigid, sealed container from which all the air has been evacuated. How much heat is required to change this ice cube into steam at 200°C? Steam has CV = 1500 J/kg K and CP = 1960 J/kg K.
What maximum power can be radiated by a 10-cm-diameter solid lead sphere? Assume an emissivity of 1.
You are boiling pasta and absentmindedly grab a copper stirring spoon rather than your wooden spoon. The copper spoon has a 20 mm × 1.5 mm rectangular cross section, and the distance from the boiling water to your 35°C hand is 18 cm. How long does it take the spoon to transfer 25 J of energy to
A 10 m × 14 m house is built on a 12-cm-thick concrete slab. What is the heat-loss rate through the slab if the ground temperature is 5°C while the interior of the house is 22°C?
The ends of a 20-cm-long, 2.0-cm-diameter rod are maintained at 0°C and 100°C by immersion in an ice-water bath and boiling water. Heat is conducted through the rod at 4.5 × 104 J per hour. Of what material is the rod made?
A monatomic gas follows the process 1 †’ 2 †’ 3 shown in Figure EX19.32. How much heat is needed for(a) Process 1 †’ 2(b) Process 2 †’ 3? p (atm) 3- 2- 100°C isotherm 3 -V (cm³) 300 100 200 FIGURE EX19.32
A gas cylinder holds 0.10 mol of O2 at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the volume is doubled. What are the final(a) Pressure(b) Temperature?
A gas cylinder holds 0.10 mol of O2 at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the pressure is halved. What are the final(a) Volume(b) Temperature?
The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5.a. What is the specific heat ratio g?b. By what factor does the temperature increase?
A container holds 1.0 g of oxygen at a pressure of 8.0 atm.a. How much heat is required to increase the temperature by 100°C at constant pressure?b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant volume?
A container holds 1.0 g of argon at a pressure of 8.0 atm.a. How much heat is required to increase the temperature by 100°C at constant volume?b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant pressure?
A 65 cm3 block of iron is removed from an 800°C furnace and immediately dropped into 200 mL of 20°C water. What fraction of the water boils away?
A 500 g metal sphere is heated to 300°C, then dropped into a beaker containing 300 cm3 of mercury at 20.0°C. A short time later the mercury temperature stabilizes at 99.0°C. Identify the metal.
A 50.0 g thermometer is used to measure the temperature of 200 mL of water. The specific heat of the thermometer, which is mostly glass, is 750 J/kg K, and it reads 20.0°C while lying on the table. After being completely immersed in the water, the thermometer’s reading stabilizes at 71.2°C.
A 750 g aluminum pan is removed from the stove and plunged into a sink filled with 10.0 L of water at 20.0°C. The water temperature quickly rises to 24.0°C. What was the initial temperature of the pan in °C and in °F?
30 g of copper pellets are removed from a 300°C oven and immediately dropped into 100 mL of water at 20°C in an insulated cup. What will the new water temperature be?
An experiment measures the temperature of a 500 g substance while steadily supplying heat to it. Figure EX19.20 shows the results of the experiment. What are the(a) Specific heat of the solid phase,(b) Specific heat of the liquid phase,(c) Melting and boiling temperatures,(d) Heats of fusion and
Two cars collide head-on while each is traveling at 80 km/h.Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car? You can assume that each car’s specific heat is that of iron.
One way you keep from overheating is by perspiring.Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water’s heat of vaporization at 35°C is a somewhat larger 24 × 105 J/kg because at lower temperatures more
What is the maximum mass of ethyl alcohol you could boil with 1000 J of heat, starting from 20°C?
How much heat is needed to change 20 g of mercury at 20°C into mercury vapor at the boiling point?
a. 100 J of heat energy are transferred to 20 g of mercury. By how much does the temperature increase?b. How much heat is needed to raise the temperature of 20 g of water by the same amount?
A rapidly spinning paddle wheel raises the temperature of 200 mL of water from 21°C to 25°C. How much(a) Heat is transferred(b) Work is done in this process?
How much heat energy must be added to a 6.0-cm-diameter copper sphere to raise its temperature from -50°C to 150°C?
The gas cylinder in Figure Q19.11 is well insulated on all sides.The piston can slide without friction. Many small masses on top of the piston are removed one by one until the total mass is reduced by 50%.a. During this process, are(i) Î”T,(ii) W,(iii) Q greater than, less than, or equal
500 J of work are done on a system in a process that decreases the system’s thermal energy by 200 J. How much heat energy is transferred to or from the system?
The gas cylinder in Figure Q19.10 is well insulated except for the bottom surface, which is in contact with a block of ice. The piston can slide without friction. The initial gas temperature is 7 0°C.a. During the process that occurs until the gas reaches a new equilibrium, are(i)
A gas is compressed from 600 cm3 to 200 cm3 at a constant pressure of 400 kPa. At the same time, 100 J of heat energy is transferred out of the gas. What is the change in thermal energy of the gas during this process?
The gas cylinder in Figure Q19.9 is a rigid container that is well insulated except for the bottom surface, which is in contact with a block of ice. The initial gas temperature is > 0°C.a. During the process that occurs until the gas reaches a new equilibrium, are(i) Î”T,(ii)
Draw a first-law bar chart (see Figure 19.12) for the gas process in Figure EX19.9.Figure 19.12 -Isotherm FIGURE EX19.9 (a) Isothermal process: AEh = 0 (b) Isochoric process: W = 0 (c) Adiabatic process: Q = 0 Eth i + W + Q = Enf En i + W + Q Enf Ehi + W + Q = Enf 0- Energy that enters the system
Figure Q19.8 shows two different processes taking an ideal gas from state i to state f.a. Is the temperature change Î”T during process A larger than, smaller than, or equal to the change during process B? Explain.b. Is the heat energy added during process A greater than, less than, or
Draw a first-law bar chart (see Figure 19.12) for the gas process in Figure EX19.8.Figure 19.12 Adiabat Isotherms -V FIGURE EX19.8 (a) Isothermal process: AEh = 0 (b) Isochoric process: W = 0 (c) Adiabatic process: Q = 0 Eth i + W + Q = Enf En i + W + Q Enf Ehi + W + Q = Enf 0- Energy that enters
Figure Q19.7 shows two different processes taking an ideal gas from state i to state f. Is the work done on the gas in process A greater than, less than, or equal to the work done in process B? Explain. A FIGURE Q19.7
Figure Q19.6 shows an adiabatic process.a. Is the final temperature higher than, lower than, or equal to the initial temperature?b. Is any heat energy added to or removed from the system in this process? Explain. Pr Pi Vr V; FIGURE Q19.6
Draw a first-law bar chart (see Figure 19.12) for the gas process in Figure EX19.6.Figure 19.12 FIGURE EX19.6 (a) Isothermal process: AEh = 0 (b) Isochoric process: W = 0 (c) Adiabatic process: Q = 0 Eth i + W + Q = Enf En i + W + Q Enf Ehi + W + Q = Enf 0- Energy that enters the system as heat
Why is the molar specific heat of a gas at constant pressure larger than the molar specific heat at constant volume?
500 J of work must be done to compress a gas to half its initial volume at constant temperature. How much work must be done to compress the gas by a factor of 10, starting from its initial volume?
You need to raise the temperature of a gas by 10°C. To use the least amount of heat energy, should you heat the gas at constant pressure or at constant volume? Explain.
A 2000 cm3 container holds 0.10 mol of helium gas at 300°C. How much work must be done to compress the gas to 1000 cm3 at (a) Constant pressure(b) Constant temperature?
Two containers hold equal masses of nitrogen gas at equal temperatures. You supply 10 J of heat to container A while not allowing its volume to change, and you supply 10 J of heat to container B while not allowing its pressure to change. Afterward, is temperature TA greater than, less than, or
80 J of work are done on the gas in the process shown in Figure EX19.3. What is V1in cm3? p (kPa) 300- 200- 100- VI 2V1 FIGURE EX19.3 3V1
Do (a) Temperature,(b) Heat,(c) Thermal energy describe a property of a system, an interaction of the system with its environment, or both? Explain.
How much work is done on the gas in the process shown in Figure EX19.2? p (kPa) 400- 200- (cm³) 0+ 100 200 300 FIGURE EX19.2
When a space capsule returns to earth, its surfaces get very hot as it passes through the atmosphere at high speed. Has the space capsule been heated? If so, what was the source of the heat? If not, why is it hot?
How much work is done on the gas in the process shown in Figure EX19.1? p (kPa) 400- 200- V (cm') 0+ 100 200 300 FIGURE EX19.1
14 g of nitrogen gas at STP are pressurized in an isochoric process to a pressure of 20 atm. What are (a) The final temperature,(b) The work done on the gas,(c) The heat transfer to the gas,(d) The pressure ratio pmax/pmin?(e) Show the process on a pV diagram, using proper scales on both axes.
14 g of nitrogen gas at STP are adiabatically compressed to a pressure of 20 atm. What are(a) The final temperature,(b) The work done on the gas,(c) The heat transfer to the gas,(d) The compression ratio Vmax/Vmin ?(e) Show the process on a pV diagram, using proper scales on both axes.
Two containers of a diatomic gas have the same initial conditions. One container, heated at constant pressure, has a temperature increase of 20°C. The other container receives the same quantity of heat energy, but at constant volume. What is its temperature increase?
Figure P19.62 shows a thermodynamic process followed by 120 mg of helium. a. Determine the pressure (in atm), temperature (in °C), and volume (in cm3) of the gas at points 1, 2, and 3. Put your results in a table for easy reading.b. How much work is done on the gas during each of the three
Two cylinders each contain 0.10 mol of a diatomic gas at 300 K and a pressure of 3.0 atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0 atm.a. What are the final temperature and volume of each?b. Show both processes on a single pV diagram.
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled.a. What are the gas volume and temperature after the expansion?b. How much heat energy is transferred to the gas to cause this expansion?The gas pressure is then decreased at
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T1, and V1, what are(a) The final temperature,(b) The work done on the gas,(c) The heat energy transferred to the gas?
Radiation from the head is a major source of heat loss from the human body. Model a head as a 20-cm-diameter, 20-cm-tall cylinder with a flat top. If the body’s surface temperature is 35°C, what is the net rate of heat loss on a chilly 5°C day? All skin, regardless of color, is effectively
FIGURE EX17.4 is a snapshot graph at t = 0 s of two waves moving to the right at 1.0 m/s. The string is fixed at x = 8.0 m. Draw four snapshot graphs, stacked vertically, showing the string at t = 2, 4, 6, and 8 s. D (cm) at t = 0 s 3- 2- 1.0 m/s 1- -x (m) i 8 0- 2 3 4 3 6 -1- 1.0 m/s -2- -31
If you pour liquid into a tall, narrow glass, you may hear sound with a steadily rising pitch. What is the source of the sound? And why does the pitch rise as the glass fills?
FIGURE EX17.5 shows a standing wave oscillating at 100 Hz on a string. What is the wave speed? 50 cm FIGURE EX17.5
A flute filled with helium will, until the helium escapes, play notes at a much higher pitch than normal. Why?
FIGURE EX17.6 shows a standing wave on a 2.0-m-long string that has been fixed at both ends and tightened until the wave speed is 40 m/s. What is the frequency? FIGURE EX17.6
FIGURE EX17.7 shows a standing wave on a string that is oscillating at 100 Hz.a. How many antinodes will there be if the frequency is increased to 200 Hz?b. If the tension is increased by a factor of 4, at what frequency will the string continue to oscillate as a standing wave that looks like the
FIGURE Q17.8 is a snapshot graph of two plane waves passing through a region of space. Each wave has a 2.0 mm amplitude and the same wavelength. What is the net displacement of the medium at points a, b, and c? Wave 1 9, a Wave 2 FIGURE O17.8
a. What are the three longest wavelengths for standing waves on a 240-cm-long string that is fixed at both ends?b. If the frequency of the second-longest wavelength is 50 Hz, what is the frequency of the third-longest wavelength?
FIGURE Q17.9 shows the circular waves emitted by two in phase sources. Are a, b, and c points of maximum constructive interference, maximum destructive interference, or in between? 2 9, FIGURE Q17.9
Standing waves on a 1.0-m-long string that is fixed at both ends are seen at successive frequencies of 36 Hz and 48 Hz.a. What are the fundamental frequency and the wave speed?b. Draw the standing-wave pattern when the string oscillates at 48 Hz.
A trumpet player hears 5 beats per second when she plays a note and simultaneously sounds a 440 Hz tuning fork. After pulling her tuning valve out to slightly increase the length of her trumpet, she hears 3 beats per second against the tuning fork. Was her initial frequency 435 Hz or 445 Hz?
The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.
A heavy piece of hanging sculpture is suspended by a 90-cm long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?
A carbon dioxide laser is an infrared laser. A CO2 laser with a cavity length of 53.00 cm oscillates in the m = 100,000 mode.What are the wavelength and frequency of the laser beam?
Microwaves pass through a small hole into the €œmicrowave cavity€ of FIGURE EX17.13. What frequencies between 10 GHz and 20 GHz will create standing waves in the cavity? 10 cm Microwaves FIGURE EX17.13
What are the three longest wavelengths for standing sound waves in a 121-cm-long tube that is (a) Open at both ends(b) Open at one end, closed at the other?
FIGURE EX17.15 shows a standing sound wave in an 80-cm- long tube. The tube is filled with an unknown gas. What is the speed of sound in this gas? Molecule f= 500 Hz FIGURE EX17.15 80 cm
The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0°C helium. What is its frequency when filled with 0°C air?
We can make a simple model of the human vocal tract as an open-closed tube extending from the opening of the mouth to the diaphragm. What is the length of this tube if its fundamental frequency equals a typical speech frequency of 250 Hz? The speed of sound in the warm air is 350 m/s.
The lowest note on a grand piano has a frequency of 27.5 Hz.The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?
A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20°C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s. Does the fundamental frequency increase or decrease? By how much?
A violin string is 30 cm long. It sounds the musical note A (440 Hz) when played without fingering. How far from the end of the string should you place your finger to play the note C (523 Hz)?
A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an
Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart.The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm.a. What is the wavelength of the sound?b. If the distance
Two loudspeakers in a 20°C room emit 686 Hz sound waves along the x-axis.a. If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum destructive?b. If the speakers are out of phase, what is the smallest distance
Noise-canceling headphones are an application of destructive interference. Each side of the headphones uses a microphone to pick up noise, delays it slightly, then rebroadcasts the noise next to your ear where it can interfere with the incoming sound wave of the noise. Suppose you are sitting 1.8 m
What is the thinnest film of MgF2 (n = 1.39) on glass that produces a strong reflection for orange light with a wavelength of 600 nm?
A very thin oil film (n = 1.25) floats on water (n = 1.33).What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nm?
FIGURE EX17.28 shows the circular wave fronts emitted by two wave sources.a. Are these sources in phase or out of phase? Explain.b. Make a table with rows labeled P, Q, and R and columns labeled r1, r2, Î”r, and C/D. Fill in the table for points P, Q, and R, giving the distances as
Two in-phase loudspeakers, which emit sound in all directions, are sitting side by side. One of them is moved sideways by 3.0 m, then forward by 4.0 m. Afterward, constructive interference is observed 1/4 and 3/4 of the distance between the speakers along the line that joins them. What is the
Two in-phase speakers 2.0 m apart in a plane are emitting 1800 Hz sound waves into a room where the speed of sound is 340 m/s. Is the point 4.0 m in front of one of the speakers, perpendicular to the plane of the speakers, a point of maximum constructive interference, maximum destructive
Two out-of-phase radio antennas at x = ± 300 m on the x-axis are emitting 3.0 MHz radio waves. Is the point (x, y) = (300 m, 800 m) a point of maximum constructive interference, maximum destructive interference, or something in between?
Two strings are adjusted to vibrate at exactly 200 Hz. Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time.What is the new frequency of the string that was tightened?
A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork (the note C). She can match the frequency of the tuning fork by pulling out the “tuning joint” to lengthen her flute slightly. What was her initial frequency?
Traditional Indonesian music uses an ensemble called a gamelan that is based on tuned percussion instruments some what like gongs. In Bali, the gongs are often grouped in pairs that are slightly out of tune with each other. When both are played at once, the beat frequency lends a distinctive
Two microwave signals of nearly equal wavelengths can generate a beat frequency if both are directed onto the same microwave detector. In an experiment, the beat frequency is 100 MHz. One microwave generator is set to emit microwaves with a wavelength of 1.250 cm. If the second generator emits the
A 2.0-m-long string vibrates at its second-harmonic frequency with a maximum amplitude of 2.0 cm. One end of the string is at x = 0 cm. Find the oscillation amplitude at x = 10, 20, 30, 40, and 50 cm.
A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?
Tendons are, essentially, elastic cords stretched between two fixed ends. As such, they can support standing waves. A woman has a 20-cm-long Achilles tendon—connecting the heel to a muscle in the calf—with a cross-section area of 90 mm2. The density of tendon tissue is 1100 kg/m3. For a
Biologists think that some spiders “tune” strands of their web to give enhanced response at frequencies corresponding to those at which desirable prey might struggle. Orb spider web silk has a typical diameter of 20 μm, and spider silk has a density of 1300 kg/m3. To have a fundamental
A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s. If the string’s linear density is 0.600 g/m and the tension is 150 N, how long is the vibrating section of the violin string?
A violinist places her finger so that the vibrating section of a 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20°C room hears a note with a wavelength of 40 cm. What is the tension in the string?
A steel wire is used to stretch the spring of FIGURE P17.42. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0 cm. What stretch of the spring produces a standing wave with two antinodes? Steel wire

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