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Cengel & Boles: Ch 6:
6.79 - Effect of Source and Sink Temperatures on HE Efficiency - 6 pts
6.85 - Thermal Efficiency of a Geothermal Power Plant - 3 pts
6.107 - Carnot HE Used to Drive a Carnot Refrigerator - 6 pts
6.110 - Actual and Maximum COP of an Air-Conditioner - 8 pts
6.134 - Thermal Efficiency of Heat Engines in Series - 4 pts
WB-1 |
"Show That" Problem Using the K-P Statement of the 2nd Law - 6 pts |
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Problem Statement : |
Using the Kelvin-Planck Statement of the Second Law of Thermodynamics, demonstrate the following corollaries.
a.) The COP of an irreversible heat pump cycle is always less than the COP of a reversible heat pump cycle when both cycles exchange heat with the same two reservoirs.
b.) All reversible heat pump cycles operating between the same two reservoirs have the same COP. |
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Hints : |
a.) Use a reversible and an irreversible heat pump cycle that absorb the same amount of heat from a cold reservoir.
b.) Reverse the reversible heat pump cycle that you used in part (a) and make it a reversible heat engine. |
WB-2 |
Reversible, Irreversible and Impossible Power Cycles - 6 pts |
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Problem
Statement : |
A refrigeration cycle operating between two reservoirs receives QC from a cold reservoir at TC = 250 K and rejects QH to a hot reservoir at TH = 300 K. For each of the following cases, determine whether the cycle is reversible, irreversible or impossible.
a.) QC = 1000 kJ and Wcycle = 400 kJ
b.) QH = 1800 kJ and QC = 1500 kJ
c.) QH = 1500 kJ and Wcycle = 200 kJ
a.) COPR = 4 |
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Hints : |
The keys to this problem are the two Carnot Principles and the Kelvin Principle. |
WB-3 |
A Reversible HE Used to Drive a Reversible Heat Pump - 6 pts |
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Problem
Statement : |
A reversible power cycle receives QH from a reservoir at TH and rejects QC to a reservoir at TC. The work developed by the power cycle is used to drive a reversible heat pump that removes Q'C from a reservoir at T'C and rejects Q'H to a reservoir at T'H.
a.) Develop an expression for the ratio Q'H / QH in terms of the temperatures of the four reservoirs.
b.) What must be the relationship of the temperatures TH, TC, T'C and T'H for Q'H / QH to exceed a value of 1.0 ? |
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Hints : |
This problem involves the careful application of the 1st Law to both the HE and the HP. |
The keys is that all of the work produced by the HE is used to drive the HP and that the Kelvin Principle applies because both cycles are completely reversible. |
After that, the solution is just algebra with the goal of eliminating QC and Q'C from the two 1st law Equations. |
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