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FIGURE EX20.10 is a histogram showing the speeds of the molecules in a very small gas. What are (a) The most probable speed, (b) The average speed, (c) The rms speed? N In. 3- 2- -v (m/s) FIGURE... A cylinder contains gas at a pressure of 2.0 atm and a number density of 4.2 1025 m -3 . The rms speed of the atoms is 660 m/s. Identify the gas. Atoms can be cooled to incredibly low temperatures by letting them interact with a laser beam. Various novel quantum phenomena appear at these temperatures. What is the rms speed of cesium atoms that... During a physics experiment, helium gas is cooled to a temperature of 10 K at a pressure of 0.10 atm. What are (a) The mean free path in the gas, (b) The rms speed of the atoms, (c) The average... The thermal energy of 1.0 mol of a substance is increased by 1.0 J. What is the temperature change if the system is (a) A monatomic gas, (b) A diatomic gas, (c) A solid? 4.0 mol of monatomic gas A interacts with 3.0 mol of monatomic gas B. Gas A initially has 9000 J of thermal energy, but in the process of coming to thermal equilibrium it transfers 1000 J of heat... Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. After a long time has passed, you record the number of balls in each... Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H 2 ). The number density is about 1 atom/cm 3 and the temperature is about 3 K. a. Estimate the... a. Find an expression for the v rms of gas molecules in terms of p, V, and the total mass of the gas M. b. A gas cylinder has a piston at one end that is moving outward at speed v piston during an... A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? a.... An experiment youre designing needs a gas with = 1.50. You recall from your physics class that no individual gas has this value, but it occurs to you that you could produce a gas with = 1.50 by... Rank in order, from largest to smallest, the thermal efficiencies 1 to 4 of the four heat engines in FIGURE Q21.5. Explain. Hot reservoir Hot reservoir 10 J 100 J 4 J 2 40 J 6J 60 J Cold reservoir... A heat engine uses a diatomic gas in a Brayton cycle. What is the engines thermal efficiency if the gas volume is halved during the adiabatic compression? The electric output of a power plant is 750 MW. Cooling water flows through the power plant at the rate 1.0 10 8 L/h. The cooling water enters the plant at 16C and exits at 27C. What is the power... FIGURE P21.57 shows the cycle for a heat engine that uses a gas having Ï = 1.25. The initial temperature is T 1 = 300 K, and this engine operates at 20 cycles per second. a. What is the power... A heat engine with 0.20 mol of a monatomic ideal gas initially fills a 2000 cm 3 cylinder at 600 K. The gas goes through the following closed cycle: Isothermal expansion to 4000 cm 3 . Isochoric... The heat engine shown in FIGURE P21.62 uses 2.0 mol of a monatomic gas as the working substance. a. Determine T 1 , T 2 , and T 3 . b. Make a table that shows ÎE th , W s , and Q for each of... A heat engine using a diatomic ideal gas goes through the following closed cycle: Isothermal compression until the volume is halved. Isobaric expansion until the volume is restored to its initial... The rms speed of the molecules in 1.0 g of hydrogen gas is 1800 m/s. a. What is the total translational kinetic energy of the gas molecules? b. What is the thermal energy of the gas? c. 500 J of work... A gas of 1.0 10 20 atoms or molecules has 1.0 J of thermal energy. Its molar specific heat at constant pressure is 20.8 J/mol K. What is the temperature of the gas? Consider a container like that shown in Figure 20.12, with n 1 moles of a monatomic gas on one side and n 2 moles of a diatomic gas on the other. The monatomic gas has initial temperature T 1i .... A glass rod that has been charged to +12 nC touches a metal sphere. Afterward, the rods charge is +8.0 nC. a. What kind of charged particle was transferred between the rod and the sphere, and in... What is the total charge of all the electrons in 1.0 L of liquid water? Metal spheres A and B in FIGURE Q22.11 are initially neutral and are touching. A positively charged rod is brought near A, but not touching. Is A now positive, negative, or neutral? Use both charge... What are the strength and direction of an electric field that will balance the weight of a 1.0 g plastic sphere that has been charged to -3.0 nC? A Van de Graaff generator is a device that accumulates electrons on a large metal sphere until the large amount of charge causes sparks. As youll learn in Chapter 23, the electric field of a charged... What is the force F on the 1.0 nC charge at the bottom in FIGURE P22.46? Give your answer in component form. -6.0 nC 2.0 nC, 2.0 nC 5.0 cm 45 45 , 5.0 cm +, 1.0 nC FIGURE P22.46 A positive point charge Q is located at x = a and a negative point charge -Q is at x = -a. A positive charge q can be placed anywhere on the y-axis. Find an expression for (F net ) x , the x... FIGURE P22.51 shows four charges at the corners of a square of side L. What is the magnitude of the net force on q? +, FIGURE P22.51 +. -0 Two equal point charges 2.5 cm apart, both initially neutral, are being charged at the rate of 5.0 nC/s. At what rate (N/s) is the force between them increasing 1.0 s after charging begins? You have a lightweight spring whose un-stretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5.0... Two 5.0 g point charges on 1.0-m-long threads repel each other after being charged to +100 nC, as shown in FIGURE P22.62. What is the angle θ? You can assume that θ is a... An electric field E = 100,000 in N/C causes the 5.0 g point charge in FIGURE P22.67 to hang at a 20° angle. What is the charge on the ball? 120 5.0 g FIGURE P22.67 You are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem. (9.0 10 Nm/C)... The force on the -1.0 nC charge is as shown in FIGURE CP22.76. What is the magnitude of this force? -1.0 nC 60 30 +. 5.0 cm FIGURE CP22.76 10 nC An electric dipole is formed from two charges, q, spaced 1.0 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x, y) = (0 cm, 10 cm) is 360... An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0 10 -7 C m is 25... A sphere of radius R has charge Q. The electric field strength at distance r > R is E i . What is the ratio E f /E i of the final to initial electric field strengths if (a) Q is halved, (b) R is... Rank in order, from largest to smallest, the electric field strengths E 1 to E 5 at the five points in FIGURE Q23.11. Explain. 5. 2 3 FIGURE Q23.11 1 1 1 + + + + + + + + + + A small object is released at point 3 in the center of the capacitor in FIGURE Q23.11. For each situation, does the object move to the right, to the left, or remain in place? If it moves, does it... Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to -20 nC and the right ring is charged to +20 nC. a. What is the electric field E, both magnitude and... A 20 cm 20 cm horizontal metal electrode is uniformly charged to +80 nC. What is the electric field strength 2.0 mm above the center of the electrode? An electron is launched at a 45? angle and a speed of 5.0 10 6 m/s from the positive plate of the parallel-plate capacitor shown in FIGURE P23.52. The electron lands 4.0 cm away. a. What is the... The two parallel plates in FIGURE P23.53 are 2.0 cm apart and the electric field strength between them is 1.0 à 10 4 N/C. An electron is launched at a 45° angle from the positive plate.... The ozone molecule O 3 has a permanent dipole moment of 1.8 10 -30 C m. Although the molecule is very slightly bentwhich is why it has a dipole momentit can be modeled as a uniform rod of length 2.5... A thin cylindrical shell of radius R and length L, like a soda straw, is uniformly charged with surface charge density . What is the electric field strength at the center of one end of the cylinder? A proton orbits a long charged wire, making 1.0 10 6 revolutions per second. The radius of the orbit is 1.0 cm. What is the wires linear charge density? FIGURE EX24.1 shows two cross sections of two infinitely long coaxial cylinders. The inner cylinder has a positive charge, the outer cylinder has an equal negative charge. Draw this figure on your... What is the electric flux through each of the surfaces A to E in FIGURE Q24.6? Give each answer as a multiple of q/ 0 . D E A + ) 3q C -)-3 FIGURE Q24.6 A small, metal sphere hangs by an insulating thread within the larger, hollow conducting sphere of FIGURE Q24.10. A conducting wire extends from the small sphere through, but not touching, a small... A 2.0 cm 3.0 cm rectangle lies in the xy-plane. What is the magnitude of the electric flux through the rectangle if a. E = (100i - 200k) N/C? b. E = (100i- 200j) N/C? FIGURE EX24.27 shows a hollow cavity within a neutral conductor. A point charge Q is inside the cavity. What is the net electric flux through the closed surface that surrounds the conductor? Closed... A tetrahedron has an equilateral triangle base with 20-cm long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength 200... A spherically symmetric charge distribution produces the electric field E = (5000r 2 )r N/C, where r is in m. a. What is the electric field strength at r = 20 cm? b. What is the electric flux through... A hollow metal sphere has inner radius a and outer radius b.The hollow sphere has charge + 2Q. A point charge + Q sits at thecenter of the hollow sphere. a. Determine the electric fields in the three... An infinite slab of charge of thickness 2z 0 lies in the xy plane between z = -z 0 and z = +z 0 . The volume charge density (C/m 3 ) is a constant. a. Use Gausss law to find an expression for the... The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gausss law to a Gaussian surface that is entirely... An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nucleus) at the center of a sphere of radius R with uniformly... All examples of Gausss law have used highly symmetric surfaces where the flux integral is either zero or EA. Yet weve claimed that the net Φ e = Q in /Ñ 0 is independent of the... An electron moves along the trajectory of FIGURE Q25.3 from i to f. a. Does the electric potential energy increase, decrease, or stay the same? Explain.b. Is the electron??s speed at f greater than,... A sphere of radius R has total charge Q. The volume charge density (C/m 3 ) within the sphere is (r) = C/r 2 , where C is a constant to be determined. a. The charge within a small volume dV is dq = ... A proton is released from rest at the positive plate of a parallelplate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. The experiment is repeated with... FIGURE Q25.9 shows two points inside a capacitor. Let V = 0 V at the negative plate.a. What is the ratio V 2 /V 1 of the electric potentials? Explain.b. What is the ratio E 2 /E 1 of the electric... Reproduce FIGURE Q25.12 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) at which the electric potential is zero. | FIGURE Q25.12 FIGURE Q25.11 shows three points near two point charges. The charges have equal magnitudes. For each part, rank in order, from most positive to most negative, the potentials V a to V c . a. b. +, +)... What potential difference is needed to accelerate an electron from rest to a speed of 2.0 10 6 m/s? A proton with an initial speed of 800,000 m/s is brought to rest by an electric field. a. Did the proton move into a region of higher potential or lower potential? b. What was the potential... Through what potential difference must a proton be accelerated to reach the speed it would have by falling 100 m in vacuum? Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is 5.0 10 5 V/m. a. What is the voltage across the capacitor? b. An electron is... In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. a. What is the electric potential of the proton at the position of the electron? b. What is... What is the electric potential at the point indicated with the dot in FIGURE EX25.31? 1.0 nC 3.0 cm,' 3.0 cm 3.0 cm -2.0 nC -2.0 nC FIGURE EX25.31 The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot? ++++++++ FIGURE EX25.35 A proton moves along the x-axis where some arrangement of charges has produced the potential V(x) = V 0 sin(2x/, where V 0 = 5000 V and = 1.0 mm. a. What minimum speed must the proton have at x = 0... Two 2.0 g plastic buttons each with +50 nC of charge are placed on a frictionless surface 2.0 cm (measured between centers) on either side of a 5.0 g button charged to +250 nC. All three are released... What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10 nC? Three electrons form an equilateral triangle 1.0 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges? Your lab assignment for the week is to measure the amount of charge on the 6.0-cm-diameter metal sphere of a Van de Graaff generator. To do so, youre going to use a spring with spring constant 0.65... A proton is fired from far away toward the nucleus of an iron atom. Iron is element number 26, and the diameter of the nucleus is 9.0 fm. What initial speed does the proton need to just reach the... A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number 80, and the diameter of the nucleus is 14.0 fm. If the proton is fired at a speed of 4.0 10 7 m/s,... In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons,... A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. a. How... Two 10-cm-diameter electrodes 0.50 cm apart form a parallelplate capacitor. The electrodes are attached by metal wires to the terminals of a 15 V battery. After a long time, the capacitor is... Two positive point charges q are located on the y-axis at y = 1/2s. a. Find an expression for the potential along the x-axis. b. Draw a graph of V versus x for - < x < . For comparison, use a... The wire in FIGURE P25.73 has linear charge density λ. What is the electric potential at the center of the semicircle? 2R 2R FIGURE P25.73 You are given the equation(s) used to solve a problem. For each of these, a. Write a realistic problem for which this is the correct equation(s). b. Finish the solution of the problem. (1.67 X 10-27... A thin rod of length L and total charge Q has the nonuniform linear charge distribution (x) = 0 x/L, where x is measured from the rods left end. a. What is 0 in terms of Q and L? b. What is the... A 1.0-m-diameter oil droplet (density 900 kg/m 3 ) is negatively charged with the addition of 25 extra electrons. It is released from rest 2.0 mm from a very wide plane of positive charge, after... A point charge Q is distance r from a dipole consisting of charges q separated by distance s. The dipole is initially oriented so that Q is in the plane bisecting the dipole. Immediately after the... Both batteries in Figure Q27.8 are ideal and identical, and all lightbulbs are the same. Rank in order, from brightest to least bright, the brightness of bulbs a to c. Explain. 00 Q00 000 FIGURE Q27.8 The wires leading to and from a 0.12-mm-diameter lightbulb filament are 1.5 mm in diameter. The wire to the filament carries a current with a current density of 4.5 10 5 A/m 2 . What are (a) The... The current in a wire is doubled. What happens to (a) The current density, (b) The conduction-electron density, (c) The mean time between collisions, (d) The electron drift speed? Are each of these... A car battery is rated at 90 A h, meaning that it can supply a 90 A current for 1 h before being completely discharged. If you leave your headlights on until the battery is completely dead, how much... What is the mean time between collisions for electrons in (a) An aluminum wire (b) An iron wire? What is the resistance of a. A 2.0-m-long gold wire that is 0.20 mm in diameter? b. A 10-cm-long piece of carbon with a 1.0 mm 1.0 mm square cross section? The electric field inside a 30-cm-long copper wire is 5.0 mV/m. What is the potential difference between the ends of the wire? a. How long must a 0.60-mm-diameter aluminum wire be to have a 0.50 A current when connected to the terminals of a 1.5 V flashlight battery? b. What is the current if the wire is half this length? A circuit calls for a 0.50-mm-diameter copper wire to be stretched between two points. You dont have any copper wire, but you do have aluminum wire in a wide variety of diameters. What diameter... Household wiring often uses 2.0-mm-diameter copper wires. The wires can get rather long as they snake through the walls from the fuse box to the farthest corners of your house. What is the potential... The electron beam inside an old television picture tube is 0.40 mm in diameter and carries a current of 50 A . This electron beam impinges on the inside of the picture tube screen. a. How many... Energetic particles, such as protons, can be detected with a silicon detector. When a particle strikes a thin piece of silicon, it creates a large number of free electrons by ionizing silicon atoms....
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