Thermodynamics

434 | ThermodynamicsFor a heat engine, the exergy supplied is the decrease in the exergy of theheat transferred to the engine, which is the difference between the exergy ofthe heat supplied and the exergy of the heat rejected. (The exergy of theheat rejected at the temperature of the surroundings is zero.) The net workoutput is the recovered exergy.For a refrigerator or heat pump, the exergy supplied is the work inputsince the work supplied to a cyclic device is entirely available. The recoveredexergy is the exergy of the heat transferred to the high-temperaturemedium (which is the reversible work) for a heat pump, and the exergy ofthe heat transferred from the low-temperature medium for a refrigerator.For a heat exchanger with two unmixed fluid streams, normally theexergy supplied is the decrease in the exergy of the higher-temperature fluidstream, and the exergy recovered is the increase in the exergy of the lowertemperaturefluid stream. This is discussed further in Sec. 8–8.EXAMPLE 8–6Second-Law Efficiency of Resistance Heaters21°CResistanceheater 10°CFIGURE 8–19Schematic for Example 8–6.A dealer advertises that he has just received a shipment of electric resistanceheaters for residential buildings that have an efficiency of 100 percent(Fig. 8–19). Assuming an indoor temperature of 21°C and outdoor temperatureof 10°C, determine the second-law efficiency of these heaters.Solution Electric resistance heaters are being considered for residentialbuildings. The second-law efficiency of these heaters is to be determined.Analysis Obviously the efficiency that the dealer is referring to is the firstlawefficiency, meaning that for each unit of electric energy (work) consumed,the heater will supply the house with 1 unit of energy (heat). That is,the advertised heater has a COP of 1.At the specified conditions, a reversible heat pump would have a coefficientof the performance ofCOP HP,rev 111 T L >T H 1 1283 K2>1294 K2 26.7That is, it would supply the house with 26.7 units of heat (extracted fromthe cold outside air) for each unit of electric energy it consumes.The second-law efficiency of this resistance heater ish II COP 1.0 0.037 or 3.7%COP rev 26.7which does not look so impressive. The dealer will not be happy to see thisvalue. Considering the high price of electricity, a consumer will probably bebetter off with a “less” efficient gas heater.INTERACTIVETUTORIALSEE TUTORIAL CH. 8, SEC. 4 ON THE DVD.8–4 ■ EXERGY CHANGE OF A SYSTEMThe property exergy is the work potential of a system in a specified environmentand represents the maximum amount of useful work that can beobtained as the system is brought to equilibrium with the environment.