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

0.020 mol of gas undergoes the process shown in FIGURE EX18.37.a. What type of process is this?b. What is the final temperature in °C?c. What is the final volume V2? p (atm) 3- 2- 1- V (cm³) 400 0+ V2 FIGURE EX18.37 2.
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.36.a. What type of process is this?b. What is the final temperature in °C?c. How many moles of gas are there? p (atm) 3- 2 2- 1- V (cm³) 300 0+ 100 200 FIGURE EX18.36
0.0040 mol of gas undergoes the process shown in FIGURE EX18.35.a. What type of process is this?b. What are the initial and final temperatures in °C? p (atm) 3- 2- – V (cm³) 300 0+ 100 200 FIGURE EX18.35
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isothermal expansion to a volume of 200 cm3.a. What is the final pressure of the gas?b. Show the process on a pV diagram. Include a proper scale on both axes.
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isobaric heating to a temperature of 300°C.a. What is the final volume of the gas?b. Show the process on a pV diagram. Include a proper scale on both axes.
0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C.a. What is the final pressure of the gas?b. Show the process on a pV diagram. Include a proper scale on both axes.
A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303°C. The air above the piston is at 1.00 atm pressure.a. What is the gas pressure inside the cylinder?b. What will the height of the piston be
A rigid container holds hydrogen gas at a pressure of 3.0 atm and a temperature of 20°C. What will the pressure be if the temperature is lowered to -20°C?
A rigid, hollow sphere is submerged in boiling water in a room where the air pressure is 1.0 atm. The sphere has an open valve with its inlet just above the water level. After a long period of time has elapsed, the valve is closed. What will be the pressure inside the sphere if it is then placed
A gas with initial state variables p1, V1, and T1 is cooled in an isochoric process until p2 = 1/3 p1. What are(a) V2(b) T2?
A gas with initial state variables p1, V1, and T1 expands isothermally until V2 = 2V1. What are(a) T2(b) p2?
A gas at temperature T0 and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with three times the volume, after which the pressure is half the original pressure.What is the new temperature of the gas?
The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about 2 × 106 K. The gas pressure in the corona is about 0.03 Pa. Estimate the number density of particles in the solar corona.
A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C.a. How many moles of oxygen are in the cylinder?b. How many oxygen molecules are in the cylinder?c. What is the number density of the oxygen?d. What is the reading of a pressure gauge attached to the tank?
The total lung capacity of a typical adult is 5.0 L. Approximately 20% of the air is oxygen. At sea level and at a body temperature of 37°C, how many oxygen molecules do the lungs contain at the end of a strong inhalation?
A gas at 100°C fills volume V0. If the pressure is held constant, what is the volume if(a) The Celsius temperature is doubled(b) The Kelvin temperature is doubled?
A rigid container holds 2.0 mol of gas at a pressure of 1.0 atm and a temperature of 30°C.a. What is the container’s volume?b. What is the pressure if the temperature is raised to 130°C?
3.0 mol of gas at a temperature of -120°C fills a 2.0 L container. What is the gas pressure?
A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward,a. Has the mass density of the gas changed? If so, by what factor? If not, why not?b. Has the number of moles of gas changed? If so, by what factor? If not, why not?
What is the temperature in °F and the pressure in Pa at the triple point of(a) Water(b) Carbon dioxide?
A 60.00 L fuel tank is filled with gasoline on a –10°C day, then rolled into a storage shed where the temperature is 20°C. If the tank is not vented, what minimum volume needs to be left empty at filling time so that the tank doesn’t rupture as it warms?
Two students each build a piece of scientific equipment that uses a 655-mm-long metal rod. One student uses a brass rod, the other an invar rod. If the temperature increases by 5.0°C, how much more does the brass rod expand than the invar rod?
A surveyor has a steel measuring tape that is calibrated to be 100.000 m long (i.e., accurate to ± 1 mm) at 20°C. If she measures the distance between two stakes to be 65.175 m on a 3°C day, does she need to add or subtract a correction factor to get the true distance? How large, in mm, is the
A concrete bridge is built of 325-cm-long concrete slabs with an expansion joint between them. The slabs just touch on a 115°F day, the hottest day for which the bridge is designed. What is the gap between the slabs when the temperature is 0°F?
A demented scientist creates a new temperature scale, the “Z scale.” He decides to call the boiling point of nitrogen 0°Z and the melting point of iron 1000°Z.a. What is the boiling point of water on the Z scale?b. Convert 500°Z to degrees Celsius and to kelvins.
At what temperature does the numerical value in °F match the numerical value in °C?
A student is asked to sketch a pV diagram for a gas that goes through a cycle consisting of(a) An isobaric expansion,(b) A constant-volume reduction in temperature,(c) An isothermal process that returns the gas to its initial state. The student draws the diagram shown in FIGURE Q18.12. What, if
The lowest and highest natural temperatures ever recorded on earth are -129°F in Antarctica and 134°F in Death Valley. What are these temperatures in °C and in K?
The temperature increases from 300 K to 1200 K as a gas undergoes the process shown in FIGURE Q18.11. What is the final pressure? p (atm) 2- 0+ FIGURE Q18.11
What volume of aluminum has the same number of atoms as 10 cm3 of mercury?
A gas undergoes the process shown in FIGURE Q18.10. By what factor does the temperature change? FIGURE Q18.10
1.0 mol of gold is shaped into a sphere. What is the sphere’s diameter?
A gas is in a sealed container. By what factor does the gas pressure change if:a. The volume is doubled and the temperature is tripled?b. The volume is halved and the temperature is tripled?
An element in its solid phase has mass density 1750 kg/m3 and number density 4.39 × 1028 atoms/m3. What is the element’s atomic mass number?
a. A sample of water vapor in an enclosed cylinder has an initial pressure of 500 Pa at an initial temperature of -0.01°C.A piston squeezes the sample smaller and smaller, without limit. Describe what happens to the water as the squeezing progresses.b. Repeat part a if the initial temperature is
What is the number density of(a) Aluminum(b) Lead?
An aquanaut lives in an underwater apartment 100 m beneath the surface of the ocean. Compare the freezing and boiling points of water in the aquanaut’s apartment to their values at the surface.Are they higher, lower, or the same? Explain.
How many atoms are in a 2.0 cm × 2.0 cm × 2.0 cm cube of aluminum?
A gas is in a sealed container. The gas pressure is tripled and the temperature is doubled.a. Does the number of moles of gas in the container increase, decrease, or stay the same?b. By what factor does the number density of the gas increase?
How many moles are in a 2.0 cm × 2.0 cm × 2.0 cm cube of copper?
A gas is in a sealed container. By what factor does the gas temperature change if:a. The volume is doubled and the pressure is tripled?b. The volume is halved and the pressure is tripled?
A hollow aluminum sphere with outer diameter 10.0 cm has a mass of 690 g. What is the sphere’s inner diameter?
The cylinder in FIGURE Q18.4 is divided into two compartments by a frictionless piston that can slide back and forth. If the piston is in equilibrium, is the pressure on the left side greater than, less than, or equal to the pressure on the right? Explain. Piston 20°C 80°C FIGURE Q18.4
What is the diameter of a copper sphere that has the same mass as a 10 cm × 10 cm × 10 cm cube of aluminum?
a. Is there a highest temperature at which ice can exist? If so, what is it? If not, why not?b. Is there a lowest temperature at which water vapor can exist? If so, what is it? If not, why not?
The nucleus of a uranium atom has a diameter of 1.5 × 10-14 m and a mass of 4.0 × 10-25 kg. What is the density of the nucleus?
The sample in an experiment is initially at 10°C. If the sample’s temperature is doubled, what is the new temperature in °C?
What volume of water has the same mass as 100 cm3 of gold?
Rank in order, from highest to lowest, the temperatures T1 = 0 K, T2 = 0°C, and T3 = 0°F.
The three identical loudspeakers in FIGURE P17.71 play a 170 Hz tone in a room where the speed of sound is 340 m/s. You are standing 4.0 m in front of the middle speaker. At this point, the amplitude of the wave from each speaker is a. a. What is the amplitude at this point?b. How far must speaker
A 44-cm-diameter water tank is filled with 35 cm of water. A 3.0-mm-diameter spigot at the very bottom of the tank is opened and water begins to flow out. The water falls into a 2.0-cm-diameter, 40-cm-tall glass cylinder. As the water falls and creates noise, resonance causes the column of air in
The 40-cm-long tube of FIGURE P17.54 has a 40-cm-long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. As the insert is slowly pulled out, the sound from the tuning fork creates standing waves in the tube when the total length L is 42.5 cm, 56.7 cm, and 70.9
Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the “bends” from breathing high pressure nitrogen. The helium has the side effect of making the divers’ voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold
Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = rfn for all n. In this system, the frequency doubles every 12 notes—an interval called an octave.a. What is
FIGURE EX17.27 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
In music, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. Suppose you have a guitar string playing frequency f0. To increase the frequency by an octave, to 2f0, by what factor would you have to(a) Increase the tension(b) Decrease the length?
An organ pipe is tuned to exactly 384 Hz when the room temperature is 20°C. If the room temperature later increases to 22°C, does the pipe’s frequency increase, decrease, or stay the same? Explain.
FIGURE EX17.3a is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. At what time was the snapshot graph in FIGURE EX17.3b taken? (a) (b) D (cm) at t = 0s D (cm) 1.0 m/s 1- 1- 1.0 m/s 0- 0+ x (m) 10 4 10 6. (u) x FIGURE EX17.3 -4-
FIGURE Q17.3 shows the displacement of a standing sound wave in a 32-cm-long horizontal tube of air open at both ends. a. What mode (m-value) is this?b. Are the air molecules moving horizontally or vertically? Explain.c. At what distances from the left end of the tube do the molecules oscillate
FIGURE EX17.2 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s. D (cm) at t =0s 1.0 m/s 1.0 m/s, x (m) 10 8. -1- FIGURE EX17.2 -0o 4,
If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants?
FIGURE EX17.1 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s. D (cm) at t = 0 s 1 1.0 m/s x (m) 6 8 fo -14 1.0 m/s FIGURE EX17.1 4- N.
FIGURE Q17.1 shows a standing wave oscillating on a string at frequency f0. a. What mode (m-value) is this?b. How many antinodes will there be if the frequency is doubled to 2f0? FIGURE Q17.1
A water wave is a shallow-water wave if the water depth d is less than ≈ λ/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v = √gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when
Some modern optical devices are made with glass whose index of refraction changes with distance from the front surface. FIGURE CP16.84 shows the index of refraction as a function of the distance into a slab of glass of thickness L.The index of refraction increases linearly from n1at the front $Index of refraction n П2 п Distance FIGURE CP16.84$
A communications truck with a 44-cm-diameter dish receiver on the roof starts out 10 km from its base station. It drives directly away from the base station at 50 km/h for 1.0 h, keeping the receiver pointed at the base station. The base station antenna broadcasts continuously with 2.5 kW of power,
One way to monitor global warming is to measure the average temperature of the ocean. Researchers are doing this by measuring the time it takes sound pulses to travel underwater over large distances. At a depth of 1000 m, where ocean temperatures hold steady near 4C, the average sound speed is
You have just been pulled over for running a red light, and the police officer has informed you that the fine will be $250. In desperation, you suddenly recall an idea that your physics professor recently discussed in class. In your calmest voice, you tell the officer that the laws of physics
Wavelengths of light from a distant galaxy are found to be 0.50% longer than the corresponding wavelengths measured in a terrestrial laboratory. Is the galaxy approaching or receding from the earth? At what speed?
A loudspeaker, mounted on a tall pole, is engineered to emit 75% of its sound energy into the forward hemisphere, 25% toward the back. You measure an 85 dB sound intensity level when standing 3.5 m in front of and 2.5 m below the speaker.What is the speaker’s power output?
A starship approaches its home planet at a speed of 0.10c. When it is 54 × 106 km away, it uses its green laser beam (λ = 540 nm) to signal its approach.a. How long does the signal take to travel to the home planet?b. At what wavelength is the signal detected on the home planet?
Show that the Doppler frequency f- of a receding source is f- = f0/(1 + vs /v).
A loudspeaker on a pole is radiating 100 W of sound energy in all directions. You are walking directly toward the speaker at 0.80 m/s.When you are 20 m away, what are(a) The sound intensity level and(b) The rate (dB/s) at which the sound intensity level is increasing?Use the chain rule and the
An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singer’s voice and a loudspeaker to rebroadcast the sound toward the
A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the highest and lowest frequencies heard by a student in the classroom?
The intensity of a sound source is described by an inverse square law only if the source is very small (a point source) and only if the waves can travel unimpeded in all directions. For an extended source or in a situation where obstacles absorb or reflect the waves, the intensity at distance r can
Your ears are sensitive to differences in pitch, but they are not very sensitive to differences in intensity. You are not capable of detecting a difference in sound intensity level of less than 1 dB. By what factor does the sound intensity increase if the sound intensity level increases from 60 dB
A compact sound source radiates 25 W of sound energy uniformly in all directions. What is the ratio of the sound intensity at a distance of 1.0 m to that at 5.0 m in(a) A two-dimensional universe,(b) Our normal three-dimensional universe,(c) A hypothetical four-dimensional universe?
A distant star system is discovered in which a planet with twice the radius of the earth and rotating 3.0 times as fast as the earth orbits a star with a total power output of 6.8 × 1029 W.a. If the star’s radius is 6.0 times that of the sun, what is the electromagnetic wave intensity at the
The sound intensity 50 m from a wailing tornado siren is 0.10 W/m2.a. What is the intensity at 1000 m?b. The weakest intensity likely to be heard over background noise is ≈ 1 цW/m2. Estimate the maximum distance at which the siren can be heard.
LASIK eye surgery uses pulses of laser light to shave off tissue from the cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mJ of light energy.a. What is the power of one laser pulse?b. During
An AM radio station broadcasts with a power of 25 kW at a frequency of 920 kHz. Estimate the intensity of the radio wave at a point 10 km from the broadcast antenna.
Is the displacement D(x, t) = (3.0 mm) ei(2.0x+8.0t+5.0), where x is in m, t is in s, and i = √-1, a possible traveling wave? If so, what is the wave speed? Complex exponentials are often used to represent waves in more advanced treatments.
Is the displacement D(x, t) = (0.10 - 0.10x2 + xt - 2.5t2) m, where x is in m and t is in s, a possible traveling wave? If so, what is the wave speed?
A sinusoidal wave travels along a stretched string. A particle on the string has a maximum speed of 2.0 m/s and a maximum acceleration of 200 m/s2. What are the frequency and amplitude of the wave?
FIGURE P16.46 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left.a. What is the wave speed?b. What is the phase constant of the wave?c. Write the displacement equation for this wave. D (mm) x (m) 191 14 Snapshot graph at t = 0 s FIGURE P16.46
The G string on a guitar is a 0.46-mm-diameter steel string with a linear density of 1.3 g/m. When the string is properly tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning is done by turning the tuning screw, which slowly tightens—and stretches—the string. By how many mm does a
A string that is under 50.0 N of tension has linear density 5.0 g/m. A sinusoidal wave with amplitude 3.0 cm and wavelength 2.0 m travels along the string. What is the maximum speed of a particle on the string?
The string in FIGURE P16.60 has linear density Î¼. Find an expression in terms of M, Î¼, and Î¸ for the speed of waves on the string. -Frictionless
A wire is made by welding together two metals having different densities. FIGURE P16.59 shows a 2.00-m-long section of wire centered on the junction, but the wire extends much farther in both directions. The wire is placed under 2250 N tension, then a 1500 Hz wave with an amplitude of 3.00 mm is
FIGURE P16.58 shows two masses hanging from a steel wire.The mass of the wire is 60.0 g. A wave pulse travels along the wire from point 1 to point 2 in 24.0 ms. What is mass m? 2.0 m 140° 2.0 m 4.0 m 40 1 2, т т FIGURE P16.58
FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string? D (cm) 45 m/s 2, 3 -2- 30 cm FIGURE P16.57
A wave on a string is described by D(x, t) = (2.00 cm) × sin[(12.57 rad/m)x - (638 rad/s)t], where x is in m and t in s. The linear density of the string is 5.00 g/m. What area. The string tension?b. The maximum displacement of a point on the string?c. The maximum speed of a point on the string?
A wave on a string is described by D(x, t) = (3.0 cm) × sin[2π(x/(2.4 m) + t/(0.20 s) + 1)], where x is in m and t is in s.a. In what direction is this wave traveling?b. What are the wave speed, the frequency, and the wave number?c. At t = 0.50 s, what is the displacement of the string at x =
A sound wave is described by D(y, t) = (0.0200 mm) × sin[(8.96 rad/m)y + (3140 rad/s)t + π/4 rad], where y is in m and t is in s.a. In what direction is this wave traveling?b. Along which axis is the air oscillating?c. What are the wavelength, the wave speed, and the period of oscillation?
A 20.0-cm-long, 10.0-cm-diameter cylinder with a piston at one end contains 1.34 kg of an unknown liquid. Using the piston to compress the length of the liquid by 1.00 mm increases the pressure by 41.0 atm. What is the speed of sound in the liquid?
Helium (density 0.18 kg/m3 at 0°C and 1 atm pressure) remains a gas until the extraordinarily low temperature of 4.2 K.What is the speed of sound in helium at 5 K?
Earthquakes are essentially sound waves—called seismic waves—traveling through the earth. Because the earth is solid, it can support both longitudinal and transverse seismic waves.The speed of longitudinal waves, called P waves, is 8000 m/s. Transverse waves, called S waves, travel at a slower
A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?
One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45° to

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