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 the initial state (state 1) to state 2, which has T = 450 K. (ii). Cooled at constant volume to 250 K (state 3). (iii). Compressed at constant temperature to a volume of 4.00 L (state 4). (iv). Heated at constant volume to 300 K, which takes the system back to state 1. (a). Show these four processes in a pV-diagram, giving the numerical values of p and V in each of the four states. (b). Calculate Q and W for each of the four processes. (c). Calculate the net work done by the oxygen in the complete cycle. (d). What is the efficiency of this device as a heat engine? How does this compare to the efficiency of a Carnot-cycle engine operating between the same minimum and maximum temperatures of 250 K and 450 K?
> Suppose that the charge shown in Fig. 21.28a is fixed in position. A small, positively charged particle is then placed at some location and released. Will the trajectory of the particle follow an electric field line? Why or why not? Suppose instead that
> Repeat Problem 21.88 for the case where sheet B is positive. Problem 21.88: Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -8.80 µC/m2, and sheet B, which is to the right of A, carries a uniform ch
> Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -8.80 µC/m2, and sheet B, which is to the right of A, carries a uniform charge density of -11.6 µC/m2. Assume that the sheets are large enough to be tre
> Two 1.20-m nonconducting rods meet at a right angle. One rod carries +2.50 µC of charge distributed uniformly along its length, and the other carries -2.50 µC distributed uniformly along it (Fig. P21.87). Fig. P21.87: (a). F
> A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge -Q is distributed uniformly around the righ
> Negative charge -Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. Find the x- and y-components of the net electric field at the origin.
> A small sphere with mass m carries a positive charge q and is attached to one end of a silk fiber of length L. The other end of the fiber is attached to a large vertical insulating sheet that has a positive surface charge density s. Show that when the sp
> A uniformly charged disk like the disk in Fig. 21.25 has radius 2.50 cm and carries a total charge of 7.0 × 10-12 C. Fig. 21.25: (a). Find the electric field (magnitude and direction) on the x-axis at x = 20.0 cm. (b). Show that for x &
> Positive charge Q is distributed uniformly along the positive y-axis between y = 0 and y = a. A negative point charge -q lies on the positive x-axis, a distance x from the origin (Fig. P21.82). Fig. P21.82: (a). Calculate the x- and y-components of t
> A negative point charge q1 = -4.00 nC is on the x-axis at x = 0.60 m. A second point charge q2 is on the x-axis at x = -1.20 m. What must the sign and magnitude of q2 be for the net electric field at the origin to be (a). 50.0 N/C in the +x-direction an
> In a region where there is a uniform electric field that is upward and has magnitude 3.60 × 104 N/C, a small object is projected upward with an initial speed of 1.92 m/s. The object travels upward a distance of 6.98 cm in 0.200 s. What is the object’s ch
> If the electric field of a point charge were proportional to 1/r3 instead of 1/r2, would Gauss’s law still be valid? Explain your reasoning. (Hint: Consider a spherical Gaussian surface centered on a single point charge.)
> Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. A positive point charge q is located on the positive x-axis at x = a + r, a distance r to the right of the end of Q (Fig. P21.79). Fig. P21.79: (a). Calculate the x- and
> A small object with mass m, charge q, and initial speed v0 = 5.00 × 103 m/s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm (Fig. P21.78). The electric field between the plates is directed downw
> A proton is projected into a uniform electric field that points vertically upward and has magnitude E. The initial velocity of the proton has a magnitude v0 and is directed at an angle
> The earth has a downward-directed electric field near its surface of about 150 N/C. If a raindrop with a diameter of 0.020 mm is suspended, motionless, in this field, how many excess electrons must it have on its surface?
> Consider a model of a hydrogen atom in which an electron is in a circular orbit of radius r = 5.29 × 10-11 m around a stationary proton. What is the speed of the electron in its orbit?
> Two tiny spheres of mass 6.80 mg carry charges of equal magnitude, 72.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field E that is directed to the left is turned on
> Imagine two 1.0-g bags of protons, one at the earth’s north pole and the other at the south pole. (a). How many protons are in each bag? (b). Calculate the gravitational attraction and the electric repulsion that each bag exerts on the other. (c). Are
> Two point charges q1 and q2 are held in place 4.50 cm apart. Another point charge Q = -1.75 µC, of mass 5.00 g, is initially located 3.00 cm from both of these charges (Fig. P21.72) and released from rest. You observe that the initial accele
> Three identical point charges q are placed at each of three corners of a square of side L. Find the magnitude and direction of the net force on a point charge -3q placed (a). at the center of the square and (b). at the vacant corner of the square. In e
> A charge of -3.00 nC is placed at the origin of an xy-coordinate system, and a charge of 2.00 nC is placed on the y-axis at y = 4.00 cm. (a). If a third charge, of 5.00 nC, is now placed at the point x = 3.00 cm, y = 4.00 cm, find the x- and y-component
> Figure Q21.7 shows some of the electric field lines due to three point charges arranged along the vertical axis. All three charges have the same magnitude. Figure Q21.7: (a). What are the signs of the three charges? Explain your reasoning. (b). At wh
> A charge +Q is located at the origin, and a charge +4Q is at distance d away on the x-axis. Where should a third charge, q, be placed, and what should be its sign and magnitude, so that all three charges will be in equilibrium?
> In a region of space there is an electric field
> If the proposed plant is built and produces 10 MW but the rate at which waste heat is exhausted to the cold water is 165 MW, what is the plant’s actual efficiency? (a). 5.7%; (b). 6.1%; (c). 6.5%; (d). 16.5%.
> Which statement is true about
> What is the direction of
> What is the magnitude of
> Suppose that to repel electrons in the radiation from a solar flare, each sphere must produce an electric field
> A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density
> Compare the entropy change of the warmer water to that of the colder water during one cycle of the heat engine, assuming an ideal Carnot cycle. (a). The entropy does not change during one cycle in either case. (b). The entropy of both increases, but th
> What is the change in entropy of the ammonia vaporized per second in the 10-MW power plant, assuming an ideal Carnot efficiency of 6.5%? (a) +6 × 106 J/K per second; (b). +5 × 105 J/K per second; (c). +1 × 105 J/K per second; (d) 0.
> Estimate how many electrons there are in your body. Make any assumptions you feel are necessary, but clearly state what they are. (Hint: Most of the atoms in your body have equal numbers of electrons, protons, and neutrons.) What is the combined charge o
> Four identical charges Q are placed at the corners of a square of side L. (a). In a free-body diagram, show all of the forces that act on one of the charges. (b). Find the magnitude and direction of the total force exerted on one charge by the other th
> A very long, solid insulating cylinder has radius R; bored along its entire length is a cylindrical hole with radius a. The axis of the hole is a distance b from the axis of the cylinder, where a < b < R (Fig. P22.58). The solid material of the cylinder
> You are conducting experiments to study prototype heat engines. In one test, 4.00 mol of argon gas are taken around the cycle shown in Fig. P20.57. The pressure is low enough for the gas to be treated as ideal. You measure the gas temperature in states a
> For a refrigerator or air conditioner, the coefficient of performance K (often denoted as COP) is, as in Eq. (20.9), the ratio of cooling output |QC| to the required electrical energy input 0W0 , both in joules. The coefficient of performance is also exp
> In your summer job with a venture capital firm, you are given funding requests from four inventors of heat engines. The inventors claim the following data for their operating prototypes: (a). Based on the TC and TH values for each prototype, find the m
> To heat 1 cup of water (250 cm3) to make coffee, you place an electric heating element in the cup. As the water temperature increases from 200C to 780C, the temperature of the heating element remains at a constant 1200C. Calculate the change in entropy o
> An object of mass m1, specific heat c1, and temperature T1 is placed in contact with a second object of mass m2, specific heat c2, and temperature T2 > T1. As a result, the temperature of the first object increases to T and the temperature of the seco
> A person with skin of surface area 1.85 m2 and temperature 30.0°C is resting in an insulated room where the ambient air temperature is 20.0°C. In this state, a person gets rid of excess heat by radiation. By how much does the person change the entropy of
> The pV-diagram in Fig. P20.51 shows the cycle for a refrigerator operating on 0.850 mol of H2. Assume that the gas can be treated as ideal. Process ab is isothermal. Find the coefficient of performance of this refrigerator. Fig. P20.51: p (atm) a 0
> An air conditioner operates on 800 W of power and has a performance coefficient of 2.80 with a room temperature of 21.00C and an outside temperature of 35.00C. (a). Calculate the rate of heat removal for this unit. (b). Calculate the rate at which heat
> 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
> 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 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, causin
> 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
