Thermodynamics

Chapter 8 | 431The irreversibility for this process is determined from its definition,I W rev W u 8191 0 8191 kJDiscussion Notice that the reversible work and irreversibility (the wastedwork potential) are the same for this case since the entire work potential iswasted. The source of irreversibility in this process is the heat transferthrough a finite temperature difference.EXAMPLE 8–5Heating Potential of a Hot Iron BlockThe iron block discussed in Example 8–4 is to be used to maintain a houseat 27°C when the outdoor temperature is 5°C. Determine the maximumamount of heat that can be supplied to the house as the iron cools to 27°C.Solution The iron block is now reconsidered for heating a house. The maximumamount of heating this block can provide is to be determined.Analysis Probably the first thought that comes to mind to make the mostuse of the energy stored in the iron block is to take it inside and let it coolin the house, as shown in Fig. 8–14, transferring its sensible energy asheat to the indoors air (provided that it meets the approval of the household,of course). The iron block can keep “losing” heat until its temperaturedrops to the indoor temperature of 27°C, transferring a total of38,925 kJ of heat. Since we utilized the entire energy of the iron blockavailable for heating without wasting a single kilojoule, it seems like wehave a 100-percent-efficient operation, and nothing can beat this, right?Well, not quite.In Example 8–4 we determined that this process has an irreversibility of8191 kJ, which implies that things are not as “perfect” as they seem.A “perfect” process is one that involves “zero” irreversibility. The irreversibilityin this process is associated with the heat transfer through a finite temperaturedifference that can be eliminated by running a reversible heatengine between the iron block and the indoor air. This heat engine produces(as determined in Example 8–4) 8191 kJ of work and reject the remaining38,925 8191 30,734 kJ of heat to the house. Now we managed toeliminate the irreversibility and ended up with 8191 kJ of work. What canwe do with this work? Well, at worst we can convert it to heat by running apaddle wheel, for example, creating an equal amount of irreversibility. Or wecan supply this work to a heat pump that transports heat from the outdoorsat 5°C to the indoors at 27°C. Such a heat pump, if reversible, has a coefficientof performance ofCOP HP 11 T L >T H5°C11 1278 K2>1300 K2 13.6That is, this heat pump can supply the house with 13.6 times the energy itconsumes as work. In our case, it will consume the 8191 kJ of work anddeliver 8191 13.6 111,398 kJ of heat to the house. Therefore, the hotiron block has the potential to supply130,734 111,3982 kJ 142,132 kJ 142 MJIron200°C27°CHeatFIGURE 8–14Schematic for Example 8–5.