Thermodynamics

Chapter 6 | 307That is, this Carnot heat engine converts 67.2 percent of the heat it receivesto work.(b) The amount of heat rejected Q L by this reversible heat engine is easilydetermined from Eq. 6–16 to beQ L,rev T LT HQ H,rev 130 2732 KDiscussion Note that this Carnot heat engine rejects to a low-temperaturesink 164 kJ of the 500 kJ of heat it receives during each cycle.1652 2732 K 1500 kJ2 164 kJ Low-temperature reservoirThe Quality of EnergyThe Carnot heat engine in Example 6–5 receives heat from a source at 925 Kand converts 67.2 percent of it to work while rejecting the rest (32.8 percent)to a sink at 303 K. Now let us examine how the thermal efficiency varieswith the source temperature when the sink temperature is held constant.The thermal efficiency of a Carnot heat engine that rejects heat to a sink at303 K is evaluated at various source temperatures using Eq. 6–18 and islisted in Fig. 6–49. Clearly the thermal efficiency decreases as the sourcetemperature is lowered. When heat is supplied to the heat engine at 500instead of 925 K, for example, the thermal efficiency drops from 67.2 to 39.4percent. That is, the fraction of heat that can be converted to work drops to39.4 percent when the temperature of the source drops to 500 K. When thesource temperature is 350 K, this fraction becomes a mere 13.4 percent.These efficiency values show that energy has quality as well as quantity.It is clear from the thermal efficiency values in Fig. 6–49 that more of thehigh-temperature thermal energy can be converted to work. Therefore, thehigher the temperature, the higher the quality of the energy (Fig. 6–50).Large quantities of solar energy, for example, can be stored in largebodies of water called solar ponds at about 350 K. This stored energy canthen be supplied to a heat engine to produce work (electricity). However,the efficiency of solar pond power plants is very low (under 5 percent)because of the low quality of the energy stored in the source, and the constructionand maintenance costs are relatively high. Therefore, they are notcompetitive even though the energy supply of such plants is free. The temperature(and thus the quality) of the solar energy stored could be raisedby utilizing concentrating collectors, but the equipment cost in that casebecomes very high.Work is a more valuable form of energy than heat since 100 percent ofwork can be converted to heat, but only a fraction of heat can be convertedto work. When heat is transferred from a high-temperature body to a lowertemperatureone, it is degraded since less of it now can be converted towork. For example, if 100 kJ of heat is transferred from a body at 1000 K toa body at 300 K, at the end we will have 100 kJ of thermal energy stored at300 K, which has no practical value. But if this conversion is made througha heat engine, up to 1 300/1000 70 percent of it could be converted towork, which is a more valuable form of energy. Thus 70 kJ of work potentialis wasted as a result of this heat transfer, and energy is degraded.High-temperature reservoirat T HRev. HEη that T L = 303 KT H , K925800700500350η th , %67.262.156.739.413.4FIGURE 6–49The fraction of heat that can beconverted to work as a function ofsource temperature (for T L 303 K).T, K200015001000500ThermalenergyQualityFIGURE 6–50The higher the temperature of thethermal energy, the higher its quality.