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| 55683 | In 1993 the federal government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in Btu/h, to its electrical power requirement in watts.
(a) Convert the EER of 10.0 to dimensionless form, using the conversion 1 Btu = 1 055 J.
(b) What is the appropriate name for this dimensionless quantity?
(c) In the 1970s it was common to find room air conditioners with EERs of 5 or lower. Compare the operating costs for 10 000-Btu/h air conditioners with EERs of 5.00 and 10.0. Assume that each air conditioner operates for 1 500 h during the summer in a city where electricity costs 10.0¢ per kWh. |
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| 55684 | In 1816 Robert Stirling, a Scottish clergyman, patented the Stirling engine, which has found a wide variety of applications ever since. Fuel is burned externally to warm one of the engine’s two cylinders. A fixed quantity of inert gas moves cyclically between the cylinders, expanding in the hot one and contracting in the cold one. Figure P22.57 represents a model for its thermodynamic cycle. Consider n mol of an ideal monatomic gas being taken once through the cycle, consisting of two isothermal processes at temperatures 3Ti and Ti and two constant volume processes. Determine, in terms of n, R, and Ti,
(a) The net energy transferred by heat to the gas and
(b) The efficiency of the engine. A Stirling engine is easier to manufacture than an internal combustion engine or a turbine. It can run on burning garbage. It can run on the energy of sunlight and produce no material exhaust. |
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| 55685 | In 1801 Humphrey Davy rubbed together pieces of ice inside an ice-house. He took care that nothing in their environment was at a higher temperature than the rubbed pieces. He observed the production of drops of liquid water. Make a table listing this and other experiments or processes, to illustrate each of the following.
(a) A system can absorb energy by heat, increase in internal energy, and increase in temperature.
(b) A system can absorb energy by heat and increase in internal energy, without an increase in temperature.
(c) A system can absorb energy by heat without increasing in temperature or in internal energy.
(d) A system can increase in internal energy and in temperature, without absorbing energy by heat.
(e) A system can increase in internal energy without absorbing energy by heat or increasing in temperature.
(f) What If? If a system’s temperature increases, is it necessarily true that its internal energy increases? |
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| 55686 | In a 100-m linear accelerator, an electron is accelerated to 1.00% of the speed of light in 40.0m before it coasts for 60.0m to a target.
(a) What is the electron’s acceleration during the first 40.0 m?
(b) How long does the total flight take? |
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| 55687 | Imagine a baby alien playing with a spherical balloon the size of the Earth in the outer solar system. Helium gas inside the balloon has a uniform temperature of 50.0 K due to radiation from the Sun. The uniform pressure of the helium is equal to normal atmospheric pressure on Earth. (a) Find the mass of the gas in the balloon. (b) The baby blows an additional mass of 8.00 X 1020 kg of helium into the balloon. At the same time, she wanders closer to the Sun and the pressure in the balloon doubles. Find the new temperature inside the balloon, whose volume remains constant. |
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| 55688 | If you wish to cook a piece of meat thoroughly on an open fire, why should you not use a high flame? (Note that carbon is a good thermal insulator.) |
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| 55689 | If you toss two dice, what is the total number of ways in which you can obtain (a) a 12 and (b) a 7? |
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| 55690 | If you shake a jar full of jellybeans of different sizes, the larger beans tend to appear near the top, and the smaller ones tend to fall to the bottom. Why? Does this process violate the second law of thermodynamics? |
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| 55691 | If you hold water in a paper cup over a flame, you can bring the water to a boil without burning the cup. How is this possible? |
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| 55692 | If you can’t walk to outer space, can you at least walk halfway? Using the law of atmospheres from Problem 43, we find that the average height of a molecule in the Earth’s atmosphere is given by |
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| 55693 | If water with a mass mh at temperature Th is poured into an aluminum cup of mass mAl containing mass mc of water at Tc, where Th > Tc , what is the equilibrium temperature of the system? |
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| 55694 | If water is a poor thermal conductor, why can its temperature be raised quickly when it is placed over a flame? |
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| 55695 | If the velocity of a particle is zero, can its acceleration be nonzero? Explain. |
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| 55696 | If the velocity of a particle is nonzero, can its acceleration be zero? Explain. |
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| 55697 | If the average velocity of an object is zero in some time interval, what can you say about the displacement of the object for that interval |
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| 55698 | If a supersaturated sugar solution is allowed to evaporate slowly, sugar crystals form in the container. Hence, sugar molecules go from a disordered form (in solution) to a highly ordered crystalline form. Does this process violate the second law of thermodynamics? Explain. |
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| 55699 | If an object’s average velocity is zero over some time interval, show that its instantaneous velocity must be zero at some time during the interval. It may be useful in your proof to sketch a graph of x versus t and to note that vx(t ) is a continuous function. |
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| 55700 | If an object’s average velocity is nonzero over some time interval, does this mean that its instantaneous velocity is never zero during the interval? Explain your answer. |
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| 55701 | If it takes 35s for the 50-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest, determine the force of the rope on the tugboat. The propeller provides the propulsion force F winch gives the tugboat forward motion, whereas the barge moves freely. Also, determine F acting on the tugboat. The barge has a mass of 75 mg. |
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| 55702 | If a helium-filled balloon initially at room temperature is placed in a freezer, will its volume increase, decrease, or remain the same? |
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