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free/or 0.5$ |
| 55543 | A tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.20 atm? |
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| 55544 | Systematic use of solar energy can yield a large saving in the cost of winter space heating for a typical house in the north central United States. If the house has good insulation, you may model it as losing energy by heat steadily at the rate 6 000 W on a day in April when the average exterior temperature is 4°C, and when the conventional heating system is not used at all. The passive solar energy collector can consist simply of very large windows in a room facing south. Sunlight shining in during the daytime is absorbed by the floor, interior walls, and objects in the room, raising their temperature to 38°C. As the sun goes down, insulating draperies or shutters are closed over the windows. During the period between 5:00 P.M. and 7:00 A.M. the temperature of the house will drop, and a sufficiently large “thermal mass” is required to keep it from dropping too far. The thermal mass can be a large quantity of stone (with specific heat 850 J/kg . °C) in the floor and the interior walls exposed to sunlight. What mass of stone is required if the temperature is not to drop below 18°C overnight? |
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| 55545 | A system consisting of n mol of an ideal gas undergoes two reversible processes. It starts with pressure Pi and volume Vi, expands isothermally, and then contracts adiabatically to reach a final state with pressure Pi and volume 3Vi.
(a) Find its change in entropy in the isothermal process. The entropy does not change in the adiabatic process.
(b) What If? Explain why the answer to part (a) must be the same as the answer to Problem 66. |
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| 55546 | Suppose your roommate is “Mr. Clean” and tidies up your messy room after a big party. Because your roommate is creating more order, does this represent a violation of the second law of thermodynamics? |
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| 55547 | Suppose you pour hot coffee for your guests, and one of them wants to drink it with cream, several minutes later, and then as warm as possible. In order to have the warmest coffee, should the person add the cream just after the coffee is poured or just before drinking? Explain. |
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| 55548 | Suppose you are working in a patent office, and an inventor comes to you with the claim that her heat engine, which employs water as a working substance, has a thermodynamic efficiency of 0.61. She explains that it operates between energy reservoirs at 4°C and 0°C. It is a very complicated device, with many pistons, gears, and pulleys, and the cycle involves freezing and melting. Does her claim that e = 0.61 warrant serious consideration? Explain. |
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| 55549 | Suppose a heat engine is connected to two energy reservoirs, one a pool of molten aluminum (660°C) and the other a block of solid mercury ("38.9°C). The engine runs by freezing 1.00 g of aluminum and melting 15.0 g of mercury during each cycle. The heat of fusion of aluminum is 3.97 X 105 J/kg; the heat of fusion of mercury is 1.18 X 104 J/kg. What is the efficiency of this engine? |
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| 55550 | Suppose 1.00 kg of water at 10.0°C is mixed with 1.00 kg of water at 30.0°C at constant pressure. When the mixture has reached equilibrium,
(a) What is the final temperature?
(b) Take cP = 4.19 kJ/kg K for water and show that the entropy of the system increases by |
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| 55551 | A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00 m above. The keys are caught 1.50 s later by the sister’s outstretched hand.
(a) With what initial velocity were the keys thrown?
(b) What was the velocity of the keys just before they were caught? |
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| 55552 | A student obtains the following data in a calorimetry experiment designed to measure the specific heat of aluminum: Initial temperature of
Water and calorimeter: 70°C
Mass of water: 0.400 kg
Mass of calorimeter: 0.040 kg
Specific heat of calorimeter: 0.63 kJ/kg . °C
Initial temperature of aluminum: 27°C
Mass of aluminum: 0.200 kg Final temperature of mixture: 66.3°C
Use these data to determine the specific heat of aluminum.
Your result should be within 15% of the value listed in Table 20.1. |
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| 55553 | A student measures the length of a brass rod with a steel tape at 20.0°C. The reading is 95.00 cm. What will the tape indicate for the length of the rod when the rod and the tape are at (a) - 15.0°C and (b) 55.0°C? |
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| 55554 | A student drives a moped along a straight road as described by the velocity-versus-time graph in Figure P2.54. Sketch this graph in the middle of a sheet of graph paper.
(a) Directly above your graph, sketch a graph of the position versus time, aligning the time coordinates of the two graphs.
(b) Sketch a graph of the acceleration versus time directly below the vx-t graph, again aligning the time coordinates. On each graph, show the numerical values of x and ax for all points of inflection.
(c) What is the acceleration? at t = 6 s?
(d) Find the position (relative to the starting point) at t = 6 s.
(e) What is the moped’s final position at t = 9 s? |
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| 55555 | A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed, vi. How do the final velocities of the balls compare when they reach the ground |
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| 55556 | A stone is thrown vertically upward from the roof of a building. Does the position of the stone depend on the location chosen for the origin of the coordinate system? Does the stone’s velocity depend on the choice of origin? Explain your answers. |
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| 55557 | A steel wire and a copper wire, each of diameter 2.000 mm, are joined end to end. At 40.0°C, each has an unscratched length of 2.000 m; they are connected between two fixed supports 4.000 m apart on a tabletop, so that the steel wire extends from x = -2.000 m to x = 0, the copper wire extends from x = 0 to x = 2.000 m, and the tension is negligible. The temperature is then lowered to 20.0°C. At this lower temperature, find the tension in the wire and the x coordinate of the junction between the wires. |
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| 55558 | A steel rod undergoes a stretching force of 500 N. Its cross-sectional area is 2.00 cm2. Find the change in temperature that would elongate the rod by the same amount as the 500-N force does. Tables 12.1 and 19.1 are available to you. |
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| 55559 | A steel guitar string with a diameter of 1.00 mm is stretched between supports 80.0 cm apart. The temperature is 0.0°C. (a) Find the mass per unit length of this string. (Use the value 7.86) 103 kg/m3 for the density.) (b) The fundamental frequency of transverse oscillations of the string is 200 Hz. What is the tension in the string? (c) If the temperature is raised to 30.0°C, find the resulting values of the tension and the fundamental frequency. Assume that both the Young’s modulus (Table 12.1) and the average coefficient of expansion (Table 19.1) have constant values between 0.0°C and 30.0°C. |
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| 55560 | A steam-driven turbine is one major component of an electric power plant. Why is it advantageous to have the temperature of the steam as high as possible? |
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| 55561 | Steam at 100°C is added to ice at 0°C.
(a) Find the amount of ice melted and the final temperature when the mass of steam is 1.0 g and the mass of ice is 50.0 g.
(b) What If? Repeat when the mass of steam is 1.00 g and the mass of ice is 50.0 g. |
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| 55562 | Starting with Equation 19.10, show that the total pressure P in a container filled with a mixture of several ideal gases is P = P1 + P2 + P3 + ., where P1, P2, . . . , are the pressures that each gas would exert if it alone filled the container (these individual pressures are called the partial pressures of the respective gases). This result is known as Dalton’s law of partial pressures |
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