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Chapter 4: 4.11 (page 129)
What is the maximum possible COP for a cyclic refrigerator operating between a high-temperature reservoir at 1K and a low-temperature reservoir at 0.01 K ?
COP=0.01
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Consider a household refrigerator that uses HFC-134a as the refrigerant, operating between the pressures of and .
(a) The compression stage of the cycle begins with saturated vapor at 1 bar and ends at 10 bars. Assuming that the entropy is constant during compression, find the approximate temperature of the vapor after it is compressed. (You'll have to do an interpolation between the values given in Table 4.4.)
(b) Determine the enthalpy at each of the points 1,2,3 and 4 , and calculate the coefficient of performance. Compare to the COP of a Carnot refrigerator operating between the same extreme temperatures. Does this temperature range seem reasonable for a household refrigerator? Explain briefly.
(c) What fraction of the liquid vaporizes during the throttling step?
Estimate the maximum possible COP of a household air conditioner. Use any reasonable values for the reservoir temperatures.
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?
Suppose you are told to design a household air conditioner using
HFC-134a as its working substance. Over what range of pressures would you have it operate? Explain your reasoning. Calculate the COP for your design, and compare to the COP of an ideal Carnot refrigerator operating between the same extreme temperatures.
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