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| 55803 | Consider the particles in a gas centrifuge, a device used to separate particles of different mass by whirling them in a circular path of radius r at angular speed w. The force acting toward the center of the circular path on a given particle is mw2r.
(a) Discuss how a gas centrifuge can be used to separate particles of different mass.
(b) Show that the density of the particles as a function of r is |
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| 55804 | Consider the following combinations of signs and values for velocity and acceleration of a particle with respect to a one-dimensional x axis:
Velocity Acceleration
a. Positive Positive
b. Positive Negative
c. Positive Zero
d. Negative Positive
e. Negative Negative
f. Negative Zero
g. Zero Positive
h. Zero Negative
Describe what a particle is doing in each case, and give a real life example for an automobile on an east-west one-dimensional axis, with east considered the positive direction. |
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| 55805 | Consider the cyclic process depicted in Figure P20.30. If Q is negative for the process BC and ΔEint is negative for the process CA, what are the signs of Q, W, and ΔEint that are associated with each process? |
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| 55806 | Consider an object with any one of the shapes displayed in Table 10.2. What is the percentage increase in the moment of inertia of the object when it is heated from 0°C to 100°C if it is composed of (a) copper or (b) aluminum? Assume that the average linear expansion coefficients shown in Table 19.1 do not vary between 0°C and 100°C. |
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| 55807 | Consider Joule’s apparatus described in Figure 20.1. The mass of each of the two blocks is 1.50 kg, and the insulated tank is filled with 200 g of water. What is the increase in the temperature of the water after the blocks fall through a distance of 3.00 m? |
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| 55808 | Consider 2.00 mol of an ideal diatomic gas.
(a) Find the total heat capacity of the gas at constant volume and at constant pressure assuming the molecules rotate but do not vibrate.
(b) What If? Repeat, assuming the molecules both rotate and vibrate. |
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| 55809 | A concrete walk is poured on a day when the temperature is 20.0°C in such a way that the ends are unable to move. (a) What is the stress in the cement on a hot day of 50.0°C? (b) Does the concrete fracture? Take Young’s modulus for concrete to be 7.00 X 109 N/m2 and the compressive strength to be 2.00 X 109 N/m2. |
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| 55810 | Concrete has a higher specific heat than soil. Use this fact to explain (partially) why cities have a higher average nighttime temperature than the surrounding countryside. If a city is hotter than the surrounding countryside, would you expect breezes to blow from city to country or from country to city? Explain. |
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| 55811 | A commuter train travels between two downtown stations. Because the stations are only 1.00 km apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the time interval ∆t between two stations by accelerating for a time interval ∆t1 at a rate a1 = 0.100 m/s2 and then immediately braking with acceleration a 2 = -0.500 m/s2 for a time interval ∆t 2 Find the minimum time interval of travel ∆t and the time interval ∆t1. |
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| 55812 | A combination of 0.250 kg of water at 20.0°C, 0.400 kg of aluminum at 26.0°C, and 0.100 kg of copper at 100°C is mixed in an insulated container and allowed to come to thermal equilibrium. Ignore any energy transfer to or from the container and determine the final temperature of the mixture. |
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| 55813 | Collectible coins are sometimes plated with gold to enhance their beauty and value. Consider a commemorative quarter-dollar advertised for sale at $4.98. It has a diameter of 24.1mm, a thickness of 1.78 mm, and is completely covered with a layer of pure gold 0.180 µ m thick. The volume of the plating is equal to the thickness of the layer times the area to which it is applied. The patterns on the faces of the coin and the grooves on its edge have a negligible effect on its area. Assume that the price of gold is $10.0 per gram. Find the cost of the gold added to the coin. Does the cost of the gold significantly enhance the value of the coin? |
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| 55814 | A clock with a brass pendulum has a period of 1.000 s at 20.0°C. If the temperature increases to 30.0°C, (a) By how much does the period change, and (b) How much time does the clock gain or lose in one week? |
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| 55815 | Clearly distinguish among temperature, heat, and internal energy. |
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| 55816 | A classmate tells you that it is just as likely for all the air molecules in the room you are both in to be concentrated in one corner (with the rest of the room being a vacuum) as it is for the air molecules to be distributed uniformly about the room in their current state. Is this a true statement? Why doesn’t the situation he describes actually happen? |
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| 55817 | A child throws a marble into the air with an initial speed vi. Another child drops a ball at the same instant. Compare the accelerations of the two objects while they are in flight. |
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| 55818 | A certain telescope forms an image of part of a cluster of stars on a square silicon charge-coupled detector (CCD) chip 2.00 cm on each side. A star field is focused on the CCD chip when it is first turned on and its temperature is 20.0°C. The star field contains 5 342 stars scattered uniformly. To make the detector more sensitive, it is cooled to -100°C. How many star images then fit onto the chip? The average coefficient of linear expansion of silicon is 4.68 X 10-6 (°C)-1. |
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| 55819 | A certain molecule has f degrees of freedom. Show that an ideal gas consisting of such molecules has the following properties: (1) its total internal energy is fnRT / 2; (2) its molar specific heat at constant volume is fR / 2; (3) its molar specific heat at constant pressure is (f + 2) R /2; (4) its specific heat ratio is y = CP/CV = (f + 2)/f. |
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| 55820 | Carry out the following arithmetic operations: (a) The sum of the measured values 756, 37.2, 0.83, and 2.5; (b) The product 0.003 2 X 356.3; (c) The product 5.620 X π. |
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| 55821 | A Carnot heat engine uses a steam boiler at 100°C as the high-temperature reservoir. The low-temperature reservoir is the outside environment at 20.0°C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W.
(a) Determine the useful power output of the heat engine.
(b) How much steam will it cause to condense in the high temperature reservoir in 1.00 h? |
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| 55822 | A Carnot engine has a power output of 150 kW. The engine operates between two reservoirs at 20.0°C and 500°C.
(a) How much energy does it take in per hour?
(b) How much energy is lost per hour in its exhaust? |
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