Chapter(s) : Ch 6 Due Date : May 5 , 2011 Total Problems / Points : 8 / 45

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 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. 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 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 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
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 ?

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.