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| 55523 | The dimensions of a room are 4.20 m X 3.00 m X 2.50 m.
(a) Find the number of molecules of air in the room at atmospheric pressure and 20.0°C. (b) Find the mass of this air, assuming that the air consists of diatomic molecules with molar mass 28.9 g/mol.
(c) Find the average kinetic energy of one molecule.
(d) Find the root-mean-square molecular speed.
(e) On the assumption that the molar specific heat is a constant independent of temperature, we have Eint = 5nRT/2. Find the internal energy in the air.
(f) What If? Find the internal energy of the air in the room at 25.0°C. |
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| 55524 | The device shown in Figure Q22.11, called a thermoelectric converter, uses a series of semiconductor cells to convert internal energy to electric potential energy, which we will study in Chapter 25. In the photograph at the left, both legs of the device are at the same temperature, and no electric potential energy is produced. However, when one leg is at a higher temperature than the other, as in the photograph on the right, electric potential energy is produced as the device extracts energy from the hot reservoir and drives a small electric motor.
(a) Why does the temperature differential produce electric potential energy in this demonstration?
(b) In what sense does this intriguing experiment demonstrate the second law of thermodynamics? |
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| 55525 | The density of gasoline is 730 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 X 10-4 /°C. If 1.00 gal of gasoline occupies 0.003 80 m3, how many extra kilograms of gasoline would you get if you bought 10.0 gal of gasoline at 0°C rather than at 20.0°C from a pump that is not temperature compensated? |
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| 55526 | The data in the following table represent measurements of the masses and dimensions of solid cylinders of aluminum, copper, brass, tin, and iron. Use these data to calculate the densities of these substances. Compare your results for aluminum, copper, and iron with those given in Table 1.5. |
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| 55527 | The concrete sections of a certain superhighway are designed to have a length of 25.0 m. The sections are poured and cured at 10.0°C. What minimum spacing should the engineer leave between the sections to eliminate buckling if the concrete is to reach a temperature of 50.0°C? |
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| 55528 | The compression ratio of an Otto cycle, as shown in Figure 22.13, is VA/VB = 8.00. At the beginning A of the compression process, 500 cm3 of gas is at 100 kPa and 20.0°C. At the beginning of the adiabatic expansion the temperature is TC = 750°C. Model the working fluid as an ideal gas with Eint = nCVT = 2.50nRT and y = 1.40.
(a) Fill in the table below to follow the states of the gas: |
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| 55529 | The compressibility / of a substance is defined as the fractional change in volume of that substance for a given change in pressure: |
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| 55530 | The average velocity of a particle moving in one dimension has a positive value. Is it possible for the instantaneous velocity to have been negative at any time in the interval? Suppose the particle started at the origin x ! 0. If its average velocity is positive, could the particle ever have been in the #x region of the axis? |
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| 55531 | The average thermal conductivity of the walls (including the windows) and roof of the house depicted in Figure P20.67 is 0.480 W/m °C, and their average thickness is 21.0 cm. The house is heated with natural gas having a heat of combustion (that is, the energy provided per cubic meter of gas burned) of 9 300 kcal/m3. How many cubic meters of gas must be burned each day to maintain an inside temperature of 25.0°C if the outside temperature is 0.0°C? Disregard radiation and the energy lost by heat through the ground. |
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| 55532 | The average coefficient of volume expansion for carbon tetrachloride is 5.81 X 10-4 (°C)-1. If a 50.0-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 30.0°C? |
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| 55533 | The air temperature above coastal areas is profoundly influenced by the large specific heat of water. One reason is that the energy released when 1 m3 of water cools by 1°C will raise the temperature of a much larger volume of air by 1°C. Find this volume of air. The specific heat of air is approximately 1 kJ/kg$ °C. Take the density of air to be 1.3 kg/m3 |
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| 55534 | The active element of a certain laser is made of a glass rod 30.0 cm long by 1.50 cm in diameter. If the temperature of the rod increases by 65.0°C, what is the increase in (a) Its length, (b) Its diameter, and (c) Its volume? Assume that the average coefficient of linear expansion of the glass is 9.00 X 10-6 (°C)-1. |
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| 55535 | The Acela is the Porsche of American trains. Shown in Figure P2.59a, the electric train whose name is pronounced ah-SELL-ah is in service on the Washington-New York- Boston run. With two power cars and six coaches, it can carry 304 passengers at 170 mi/h. The carriages tilt as much as 6- from the vertical to prevent passengers from feeling pushed to the side as they go around curves. Its braking mechanism uses electric generators to recover its energy of motion. A velocity-time graph for the Acela is shown in Figure P2.59b.
(a) Describe the motion of the train in each successive time interval.
(b) Find the peak positive acceleration of the train in the motion graphed.
(c) Find the train’s displacement in miles between t = 0 and t = 200 s.
(a) The Acela—1 171 000 lb of cold steel thundering along at 150 mi/h.
(b) Velocity-versus-time graph for the Acela. |
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| 55536 | The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared, and is given (in SI units) by a = -3.00v 2 for v > 0. If the marble enters this fluid with a speed of 1.50 m/s, how long will it take before the marble’s speed is reduced to half of its initial value? |
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| 55537 | The 5.5-Mg humpback whale is stuck on the there due to changes in the tide. In an effort to rescue a whale, 12-Mg tugboat is used to pull it fee using an inextensible rope tied to its tail. To overcome the frictional force of the sand on the whale, the tug backs up so that the rope becomes slack and then the tug proceeds forward at 3 m/s. If the tug then turns the engines off, determine the average frictional force F on the whale if hiding occurs for 1.5 s before the tug stops after the rope becomes taut. Also, what is the average force on the rope during the tow? |
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| 55538 | The 5-kg block is moving downward at v1= 2 m/s when it is 8 m from the sandy surface. Determine the impulse of the sand on the block necessary to stop its motion. Neglect the distance the block dents into the sand and assume the block does not rebound. Neglect the weight of the block during the impact with the sand. |
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| 55539 | The 5-kg block is falling downward at v1 2 m/s when it is 8 m from the sandy surface, Determine the average impulsive force acting on the block by the sand if the motion of the block is stopped in 0.9 s once the block strikes the sand. Neglect the distance the block dents into the sand and assume the block does not rebound. Neglect the weight of the block during the impact with the sand. |
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| 55540 | The 4-lb cabinet is subjected to the force F =12(t + 1)^2 lb where t is in seconds. If the cabinet is initially moving up the plane with a velocity of 10 ft/s, determine how long it will take before the cabinet comes to a stop. F always acts parallel to the plane. Neglect the size of the rollers. |
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| 55541 | The 180-lb iron worker is secured by a fall-arrest system consisting of a harness and lanyard AB, which is fixed to the beam. If the lanyard has slack of 4 ft determine the average impulsive force developed in the lanyard if he happens to fall 4 feet. Neglect his size in the calculation and assume the impulse takes place in 0.6 seconds. |
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| 55542 | A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 80.0 m/s at ground level. Its engines then fire and it accelerates upward at 4.00 m/s2 until it reaches an altitude of 1 000 m. At that point its engines fail and the rocket goes into free fall, with an acceleration of - 9.80 m/s2.
(a) How long is the rocket in motion above the ground?
(b) What is its maximum altitude?
(c) What is its velocity just before it collides with the Earth? (You will need to consider the motion while the engine is operating separate from the free-fall motion.) |
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