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Chapter 4: 4.7 (page 129)
Why must you put an air conditioner in the window of a building, rather than in the middle of a room?
We must put t an air conditioner in the window to cool the room effectively.
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Table 4.5 gives experimental values of the molar enthalpy of nitrogen at 1 bar and 100 bars. Use this data to answer the following questions about a nitrogen throttling process operating between these two pressures.
(a) If the initial temperature is , what is the final temperature? (Hint: You'll have to do an interpolation between the tabulated values.)
(b) If the initial temperature is , what is the final temperature?
(c) If the initial temperature is , what is the final temperature? What fraction of the nitrogen ends up as a liquid in this case?
(d) What is the highest initial temperature at which some liquefaction takes place?
(e) What would happen if the initial temperature were ? Explain.
It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is at the ocean surface and at the ocean floor.
(a) What is the maximum possible efficiency of an engine operating between these two temperatures?
(b) If the engine is to produce of electrical power, what minimum volume of water must be processed (to suck out the heat) in every second?
Prove that if you had a heat engine whose efficiency was better than the ideal value (4.5), you could hook it up to an ordinary Carnot refrigerator to make a refrigerator that requires no work input.
A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it's the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both). Let us define the following standard symbols, all taken to be positive by convention:
(a) Explain why the "coefficient of performance" (COP) for a heat pump should be defined as Qh / W.
(b) What relation among Qh , Qc, and W is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1 ?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Tc alone.
(d) Explain why a heat pump is better than an electric furnace, which simply converts electrical work directly into heat. (Include some numerical estimates.)
In an absorption refrigerator, the energy driving the process is supplied not as work, but as heat from a gas flame. (Such refrigerators commonly use propane as fuel, and are used in locations where electricity is unavailable.* ) Let us define the following symbols, all taken to be positive by definition:
Qf= heat input from flame
Qc= heat extracted from inside refrigerator
Qr= waste heat expelled to room
Tf= temperature of flame
Tc= temperature inside refrigerator
Tr= room temperature
(a) Explain why the "coefficient of performance" (COP) for an absorption refrigerator should be defined as Qc / Qf.
(b) What relation among Qf, Qc, and Qr is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1 ?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Tf, Tc, and Tr alone.
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