A lonely party balloon with a volume of 2.40 L and containing 0.100 mol of air is left behind to drift in the temporarily uninhabited and depressurized International Space Station. Sunlight coming through a porthole heats and explodes the balloon, causing the air in it to undergo a free expansion into the empty station, whose total volume is 425 m3. Calculate the entropy change of the air during the expansion.
> An uncharged metal sphere hangs from a nylon thread. When a positively charged glass rod is brought close to the metal sphere, the sphere is drawn toward the rod. But if the sphere touches the rod, it suddenly flies away from the rod. Explain why the sph
> A Volkswagen Passat has a six-cylinder Otto-cycle engine with compression ratio r = 10.6. The diameter of each cylinder, called the bore of the engine, is 82.5 mm. The distance that the piston moves during the compression in Fig. 20.5, called the stroke
> A typical coal-fired power plant generates 1000 MW of usable power at an overall thermal efficiency of 40%. (a). What is the rate of heat input to the plant? (b). The plant burns anthracite coal, which has a heat of combustion of 2.65 × 107 J/kg. How m
> Negative charge -Q is distributed uniformly over the surface of a thin spherical insulating shell with radius R. Calculate the force (magnitude and direction) that the shell exerts on a positive point charge q located a distance (a). r > R from the cent
> A monatomic ideal gas is taken around the cycle shown in Fig. P20.46 in the direction shown in the figure. The path for process c→ a is a straight line in the pV-diagram. (a). Calculate Q, W, and
> A cylinder contains oxygen at a pressure of 2.00 atm. The volume is 4.00 L, and the temperature is 300 K. Assume that the oxygen may be treated as an ideal gas. The oxygen is carried through the following processes: (i). Heated at constant pressure from
> You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is 37.0°C) and the other end at the surface of your skin, at 30.0°C. (a). What is the maximum efficiency of such a heat
> An experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 270C and 60C, respectively. (a). What is the maximum theoretical efficie
> The pV-diagram in Fig. E20.5 shows a cycle of a heat engine that uses 0.250 mol of an ideal gas with γ = 1.40. Process ab is adiabatic. Fig. E20.5: (a). Find the pressure of the gas at point a. (b). How much heat enters this gas per cycle
> A gasoline engine has a power output of 180 kW (about 241 hp). Its thermal efficiency is 28.0%. (a). How much heat must be supplied to the engine per second? (b). How much heat is discarded by the engine per second?
> A Gasoline Engine. A gasoline engine takes in 1.61 × 104 J of heat and delivers 3700 J of work per cycle. The heat is obtained by burning gasoline with a heat of combustion of 4.60 × 104 J/g. (a). What is the thermal efficiency? (b). How much heat is d
> Your clothing tends to cling together after going through the dryer. Why? Would you expect more or less clinging if all your clothing were made of the same material (say, cotton) than if you dried different kinds of clothing together? Again, why? (You ma
> An aircraft engine takes in 9000 J of heat and discards 6400 J each cycle. (a). What is the mechanical work output of the engine during one cycle? (b). What is the thermal efficiency of the engine?
> If you carry out the integral of the electric field
> (a). If the potential (relative to infinity) is zero at a point, is the electric field necessarily zero at that point? (b). If the electric field is zero at a point, is the potential (relative to infinity) necessarily zero there? Prove your answers, usi
> Which way do electric field lines point, from high to low potential or from low to high? Explain.
> If E ⃗ is zero everywhere along a certain path that leads from point A to point B, what is the potential difference between those two points? Does this mean that E ⃗ is zero everywhere along any path from A to B? Explain.
> A positive point charge is placed near a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a negative point charge of equal magnitud
> When a thunderstorm is approaching, sailors at sea sometimes observe a phenomenon called “St. Elmo’s fire,” a bluish flickering light at the tips of masts. What causes this? Why does it occur at the tips of masts? Why is the effect most pronounced when t
> A high-voltage dc power line falls on a car, so the entire metal body of the car is at a potential of 10,000 V with respect to the ground. What happens to the occupants (a). when they are sitting in the car and (b). when they step out of the car? Expla
> The potential (relative to a point at infinity) midway between two charges of equal magnitude and opposite sign is zero. Is it possible to bring a test charge from infinity to this midpoint in such a way that no work is done in any part of the displaceme
> A conducting sphere is placed between two charged parallel plates such as those shown in Fig. 23.2. Does the electric field inside the sphere depend on precisely where between the plates the sphere is placed? What about the electric potential inside the
> Is it possible to have an arrangement of two point charges separated by a finite distance such that the electric potential energy of the arrangement is the same as if the two charges were infinitely far apart? Why or why not? What if there are three char
> A -3.00-nC point charge is on the x-axis at x = 1.20 m. A second point charge, Q, is on the x axis at -0.600 m. What must be the sign and magnitude of Q for the resultant electric field at the origin to be (a).45.0 N/C in the +x-direction, (b). 45.0 N/
> A conducting sphere is to be charged by bringing in positive charge a little at a time until the total charge is Q. The total work required for this process is alleged to be proportional to Q2. Is this correct? Why or why not?
> Consider the electric dipole of Example 21.14. (a). Derive an expression for the magnitude of the electric field produced by the dipole at a point on the x-axis in Fig. 21.33. What is the direction of this electric field? Fig. 21.33: (b). How does t
> The volume charge density
> Two identical spheres with mass m are hung from silk threads of length L (Fig. P21.62). The spheres have the same charge, so q1 = q2 = q. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as poin
> A charge q1 = +5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = 2.00 nC is placed on the positive x-axis at x = 4.00 cm. (a). If a third charge q3 = +6.00 nC is now placed at the point x = 4.00 cm, y = 3.00 cm, find the x- a
> The electric field is measured for points at distances
> If the power plant uses a Carnot cycle and the desired theoretical efficiency is 6.5%, from what depth must cold water be brought? (a). 100 m; (b). 400 m; (c). 800 m; (d). deeper than 1000 m.
> Consider a Diesel cycle that starts (at point a in Fig. 20.7) with air at temperature Ta. The air may be treated as an ideal gas. Fig. 20.7: (a). If the temperature at point c is Tc, derive an expression for the efficiency of the cycle in terms of th
> A very long, straight wire has charge per unit length 3.20 × 10-10 C/m. At what distance from the wire is the electric field magnitude equal to 2.50 N/C?
> A Carnot engine operates between two heat reservoirs at temperatures TH and TC. An inventor proposes to increase the efficiency by running one engine between TH and an intermediate temperature T′ and a second engine between T′ and TC, using as input the
> A nerve signal is transmitted through a neuron when an excess of Na+ ions suddenly enters the axon, a long cylindrical part of the neuron. Axons are approximately 10.0 mm in diameter, and measurements show that about 5.6 × 1011 Na+ ions per meter (each o
> We often say that if point A is at a higher potential than point B, A is at positive potential and B is at negative potential. Does it necessarily follow that a point at positive potential is positively charged, or that a point at negative potential is n
> Point charge q1 = -5.00 nC is at the origin and point charge q2 = +3.00 nC is on the x-axis at x = 3.00 cm. Point P is on the y-axis at y = 4.00 cm. (a). Calculate the electric fields
> A point charge is placed at each corner of a square with side length a. All charges have magnitude q. Two of the charges are positive and two are negative (Fig. E21.42). What is the direction of the net electric field at the center of the square due to t
> The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4 × 10-15 m. (a). What is the electric field this nucleus produces just outside i
> The cube in Fig. E22.6 has sides of length L = 10.0 cm. The electric field is uniform, has magnitude E = 4.00 × 103 N/C, and is parallel to the xy-plane at an angle of 53.1 measured from the +x-axis toward the +y-axis. Figure E22.6: (a).
> A point charge is at the origin. With this point charge as the source point, what is the unit vector
> A particle has charge -5.00 nC. (a). Find the magnitude and direction of the electric field due to this particle at a point 0.250 m directly above it. (b). At what distance from this particle does its electric field have a magnitude of 12.0 N/C?
> An average human weighs about 650 N. If each of two average humans could carry 1.0 C of excess charge, one positive and one negative, how far apart would they have to be for the electric attraction between them to equal their 650-N weight?
> Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33 × 10-21 N?
> In Example 21.4, what is the net force (magnitude and direction) on charge q1 exerted by the other two charges?
> A cube has sides of length L = 0.300 m. One corner is at the origin (Fig. E22.6). The nonuniform electric field is given by
> A uniform electric field is directed due east. Point B is 2.00 m west of point A, point C is 2.00 m east of point A, and point D is 2.00 m south of A. For each point, B, C, and D, is the potential at that point larger, smaller, or the same as at point A?
> An ideal Carnot engine operates between 5000C and 1000C with a heat input of 250 J per cycle. (a). How much heat is delivered to the cold reservoir in each cycle? (b). What minimum number of cycles is necessary for the engine to lift a 500-kg rock thro
> Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2 = -3.00 nC and is at x = +4.00 cm. Charge q1 is at x = +2.00 cm. What is q1 (magnitude and sign) if the net force on q3 is zero?
> A negative charge of -0.550 µC exerts an upward 0.600-N force on an unknown charge that is located 0.300 m directly below the first charge. What are (a). the value of the unknown charge (magnitude and sign); (b). the magnitude and direction of the forc
> A sophomore with nothing better to do adds heat to 0.350 kg of ice at 0.00C until it is all melted. (a). What is the change in entropy of the water? (b). The source of heat is a very massive body at 25.00C. What is the change in entropy of this body? (
> You design an engine that takes in 1.50 × 104 J of heat at 650 K in each cycle and rejects heat at a temperature of 290 K. The engine completes 240 cycles in 1 minute. What is the theoretical maximum power output of your engine, in horsepower?
> A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation, the heat rejected by the engine melts 0.0400 kg of ice. During this time,
> A Carnot engine whose high-temperature reservoir is at 620 K takes in 550 J of heat at this temperature in each cycle and gives up 335 J to the low-temperature reservoir. (a). How much mechanical work does the engine perform during each cycle? What is
> A Carnot engine is operated between two heat reservoirs at temperatures of 520 K and 300 K. (a). If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it discard to the reservoir at 300 K
> A conductor that carries a net charge Q has a hollow, empty cavity in its interior. Does the potential vary from point to point within the material of the conductor? What about within the cavity? How does the potential inside the cavity compare to the po
> It is easy to produce a potential difference of several thousand volts between your body and the floor by scuffing your shoes across a nylon carpet. When you touch a metal doorknob, you get a mild shock. Yet contact with a power line of comparable voltag
> The air temperature and the velocity of the air have different values at different places in the earth’s atmosphere. Is the air velocity a vector field? Why or why not? Is the air temperature a vector field? Again, why or why not?
> The electric fields at point P due to the positive charges q1 and q2 are shown in Fig. Q21.22. Does the fact that they cross each other violate the statement in Section 21.6 that electric field lines never cross? Explain. Figure Q21.22: 42
> Sufficiently strong electric fields can cause atoms to become positively ionized—that is, to lose one or more electrons. Explain how this can happen. What determines how strong the field must be to make this happen?
> Atomic nuclei are made of protons and neutrons. This shows that there must be another kind of interaction in addition to gravitational and electric forces. Explain.
> Two irregular objects A and B carry charges of opposite sign. Figure Q21.19 shows the electric field lines near each of these objects. Figure Q21.19: (a). Which object is positive, A or B? How do you know? (b). Where is the electric field stronger,
> In electronics it is customary to define the potential of ground (thinking of the earth as a large conductor) as zero. Is this consistent with the fact that the earth has a net electric charge that is not zero?
> In Example 21.1 (Section 21.3) we saw that the electric force between two
> Because electric field lines and equipotential surfaces are always perpendicular, two equipotential surfaces can never cross; if they did, the direction of
> A point charge of mass m and charge Q and another point charge of mass m but charge 2Q are released on a frictionless table. If the charge Q has an initial acceleration a0, what will be the acceleration of 2Q: a0, 2a0, 4a0, a0/2, or a0/4? Explain.
> If the electric potential at a single point is known, can
> The potential difference between the two terminals of an AA battery (used in flashlights and portable stereos) is 1.5 V. If two AA batteries are placed end to end with the positive terminal of one battery touching the negative terminal of the other, what
> You have a negatively charged object. How can you use it to place a net negative charge on an insulated metal sphere? To place a net positive charge on the sphere?
> If you walk across a nylon rug and then touch a large metal object such as a doorknob, you may get a spark and a shock. Why does this tend to happen more on dry days than on humid days? (Hint: See Fig. 21.30.) Why are you less likely to get a shock if yo
> A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each cycle. (a). How much heat must be supplied to the engine in each cycle? (b). What is the thermal efficiency of the engine?
> If E ⃗ is zero throughout a certain region of space, is the potential necessarily also zero in this region? Why or why not? If not, what can be said about the potential?
> In a conductor, one or more electrons from each atom are free to roam throughout the volume of the conductor. Does this contradict the statement that any excess charge on a solid conductor must reside on its surface? Why or why not?
> Good conductors of electricity, such as metals, are typically good conductors of heat; insulators, such as wood, are typically poor conductors of heat. Explain why there is a relationship between conduction of electricity and conduction of heat in these
> Since potential can have any value you want depending on the choice of the reference level of zero potential, how does a voltmeter know what to read when you connect it between two points?
> You find a sealed box on your doorstep. You suspect that the box contains several charged metal spheres packed in insulating material. How can you determine the total net charge inside the box without opening the box? Or isn’t this possible?
> In Fig. 22.15, suppose a third point charge were placed outside the purple Gaussian surface C. Would this affect the electric flux through any of the surfaces A, B, C, or D in the figure? Why or why not? Fig. 22.15: D.
> A certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?
> A student asked, “Since electrical potential is always proportional to potential energy, why bother with the concept of potential at all?” How would you respond?
> The electric force between two charged particles becomes weaker with increasing distance. Suppose instead that the electric force were independent of distance. In this case, would a charged comb still cause a neutral insulator to become polarized as in F
> Suppose that in Fig. 22.15 both charges were positive. What would be the fluxes through each of the four surfaces in the example? Fig. 22.15: D.
> A rubber balloon has a single point charge in its interior. Does the electric flux through the balloon depend on whether or not it is fully inflated? Explain your reasoning.
> Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities s1, s2, s3, and s4 on their surfaces (Fig. E22.30). These surface charge densities have the values s1 = -6.00 µC/m2, s2 = +5.00 µC/
> An infinitely long cylindrical conductor has radius R and uniform surface charge density
> A square insulating sheet 80.0 cm on a side is held horizontally. The sheet has 4.50 nC of charge spread uniformly over its area. (a). Calculate the electric field at a point 0.100 mm above the center of the sheet. (b). Estimate the electric field at a
> Apply Gauss’s law to the Gaussian surfaces S2 , S3 , and S4 in Fig. 22.21b to calculate the electric field between and outside the plates. Fig. 22.21b: (b) Idealized model 1 In the idealized case we ignore "fringing" at the plate
> A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area s = 5.00 × 10-6 C/m2. (a). A small sphere of mass m = 8.00 × 10-6 kg and charge q is placed 3.00 cm above the sheet of charge and then released from rest. (a). If t
> A conductor with an inner cavity, like that shown in Fig. 22.23c, carries a total charge of +5.00 nC. The charge within the cavity, insulated from the conductor, is -6.00 nC. How much charge is on Fig. 22.23c: (a). the inner surface of the conductor
> Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E = 940 N/C. What are (a).
> A solid copper sphere has a net positive charge. The charge is distributed uniformly over the surface of the sphere, and the electric field inside the sphere is zero. Then a negative point charge outside the sphere is brought close to the surface of the
> An electron is released from rest at a distance of 0.300 m from a large insulating sheet of charge that has uniform surface charge density +2.90 × 10-12 C/m2. (a). How much work is done on the electron by the electric field of the sheet as the electron
> A point charge of -3.00 µC is located in the center of a spherical cavity of radius 6.50 cm that, in turn, is at the center of an insulating charged solid sphere. The charge density in the solid is
> The electric field at a distance of 0.145 m from the surface of a solid insulating sphere with radius 0.355 m is 1750 N/C. (a). Assuming the sphere’s charge is uniformly distributed, what is the charge density inside it? (b). Calculate the electric field
> (a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N/C. What is the electric field 0.600 cm from the center of the sphere? (b) At a distance of 0.200 cm from the axis of a very lo
> A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37 × 10-6 C/m2. A charge of -0.500 µC is now introduced at the center of the cavity inside the sphere. (a). What is the
> The electric field 0.400 m from a very long uniform line of charge is 840 N/C. How much charge is contained in a 2.00-cm section of the line?
> A very long uniform line of charge has charge per unit length 4.80 µC/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.40 µC/m and is parallel to the x-axis at y = 0.400 m. What is the net electric field (ma
> Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of -3.63 × 1016 N ∙ m2/C at the planet’s surface. Calculate: (a). the total electric charge on the p
> How many excess electrons must be added to an isolated spherical conductor 26.0 cm in diameter to produce an electric field of magnitude 1150 N/C just outside the surface?
> A solid metal sphere with radius 0.450 m carries a net charge of 0.250 nC. Find the magnitude of the electric field (a). at a point 0.100 m outside the surface of the sphere and (b). at a point inside the sphere, 0.100 m below the surface.
