Thermodynamics

Q1kJ2 Exergy transfer by heat: X heat a 1 T 0T(8–24)T 0Chapter 8 | 441Heat is a form of disorganized energy, and thus only a portion of it canbe converted to work, which is a form of organized energy (the secondlaw). We can always produce work from heat at a temperature above theenvironment temperature by transferring it to a heat engine that rejects theHEAT SOURCEwaste heat to the environment. Therefore, heat transfer is always accom-Temperature: Tpanied by exergy transfer. Heat transfer Q at a location at thermodynamicEnergy transferred: Etemperature T is always accompanied by exergy transfer X heat in theamount ofExergy = ( 1 – T0 ETThis relation gives the exergy transfer accompanying heat transfer Qwhether T is greater than or less than T 0 . When T T 0 , heat transfer to asystem increases the exergy of that system and heat transfer from a systemdecreases it. But the opposite is true when T T 0 . In this case, theheat transfer Q is the heat rejected to the cold medium (the waste heat),and it should not be confused with the heat supplied by the environmentat T 0 . The exergy transferred with heat is zero when T T 0 at the pointof transfer.Perhaps you are wondering what happens when T T 0 . That is, what ifwe have a medium that is at a lower temperature than the environment? Inthis case it is conceivable that we can run a heat engine between the environmentand the “cold” medium, and thus a cold medium offers us an opportunityto produce work. However, this time the environment serves as the heatsource and the cold medium as the heat sink. In this case, the relation abovegives the negative of the exergy transfer associated with the heat Q transferredto the cold medium. For example, for T 100 K and a heat transferof Q 1 kJ to the medium, Eq. 8–24 gives X heat (1 300/100)(1 kJ)2 kJ, which means that the exergy of the cold medium decreases by2 kJ. It also means that this exergy can be recovered, and the coldmedium–environment combination has the potential to produce 2 units ofwork for each unit of heat rejected to the cold medium at 100 K. That is,a Carnot heat engine operating between T 0 300 K and T 100 K produces2 units of work while rejecting 1 unit of heat for each 3 units ofheat it receives from the environment.When T T 0 , the exergy and heat transfer are in the same direction.That is, both the exergy and energy content of the medium to which heat istransferred increase. When T T 0 (cold medium), however, the exergy andheat transfer are in opposite directions. That is, the energy of the coldmedium increases as a result of heat transfer, but its exergy decreases. Theexergy of the cold medium eventually becomes zero when its temperaturereaches T 0 . Equation 8–24 can also be viewed as the exergy associated withthermal energy Q at temperature T.When the temperature T at the location where heat transfer is taking placeis not constant, the exergy transfer accompanying heat transfer is determinedby integration to beFIGURE 8–26The Carnot efficiency h c 1 T 0 /Trepresents the fraction of the energytransferred from a heat source attemperature T that can be convertedto work in an environment attemperature T 0 .(X heat a 1 T 0T b dQ(8–25)