Thermodynamics

390 | Thermodynamicsat 100°C while the outer surface is at 25°C since two bodies in physical contactmust have the same temperature at the point of contact. Considering thatentropy transfer with heat transfer Q through a surface at constant temperatureT is Q/T, the entropy transfer from the water into the wall is Q/T sys 1.61kJ/K. Likewise, entropy transfer from the outer surface of the wall into thesurrounding air is Q/T surr 2.01 kJ/K. Obviously, entropy in the amount of2.01 1.61 0.4 kJ/K is generated in the wall, as illustrated in Fig. 7–70b.Identifying the location of entropy generation enables us to determinewhether a process is internally reversible. A process is internally reversibleif no entropy is generated within the system boundaries. Therefore, the heattransfer process discussed in Example 7–21 is internally reversible if theinner surface of the wall is taken as the system boundary, and thus the systemexcludes the container wall. If the system boundary is taken to be theouter surface of the container wall, then the process is no longer internallyreversible since the wall, which is the site of entropy generation, is now partof the system.For thin walls, it is very tempting to ignore the mass of the wall and toregard the wall as the boundary between the system and the surroundings.This seemingly harmless choice hides the site of the entropy generationfrom view and is a source of confusion. The temperature in this case dropssuddenly from T sys to T surr at the boundary surface, and confusion arises asto which temperature to use in the relation Q/T for entropy transfer at theboundary.Note that if the system and the surrounding air are not isothermal as aresult of insufficient mixing, then part of the entropy generation will occurin both the system and the surrounding air in the vicinity of the wall, asshown in Fig. 7–70c.SYSTEMT sysSURROUNDINGT sysWallT sysWallBoundaryT surrT surrHeattransferQQT surrQ QLocation ofQ Qentropy generationEntropytransferQT sysS genQT surrQT sysQT surrQT sysQT surr(a) The wall is ignored (b) The wall is considered (c) The wall as well as the variations oftemperature in the system and thesurroundings are consideredFIGURE 7–70Graphical representation of entropy generation during a heat transfer process through a finite temperature difference.