Thermodynamics

When evaluating the entropy transfer between an extended system and thesurroundings, the boundary temperature of the extended system is simplytaken to be the environment temperature.Chapter 7 | 381Closed SystemsA closed system involves no mass flow across its boundaries, and itsentropy change is simply the difference between the initial and finalentropies of the system. The entropy change of a closed system is due to theentropy transfer accompanying heat transfer and the entropy generationwithin the system boundaries. Taking the positive direction of heat transferto be to the system, the general entropy balance relation (Eq. 7–76) can beexpressed for a closed system asQ kClosed system: a S gen ¢S system S 2 S 1 1kJ>K2 (7–79)T kThe entropy balance relation above can be stated as:The entropy change of a closed system during a process is equal to the sumof the net entropy transferred through the system boundary by heat transferand the entropy generated within the system boundaries.For an adiabatic process (Q 0), the entropy transfer term in the aboverelation drops out and the entropy change of the closed system becomesequal to the entropy generation within the system boundaries. That is,Adiabatic closed system: S gen ¢S adiabatic system(7–80)Noting that any closed system and its surroundings can be treated as an adiabaticsystem and the total entropy change of a system is equal to the sumof the entropy changes of its parts, the entropy balance for a closed systemand its surroundings can be written asSystem Surroundings: S gen a ¢S ¢S system ¢S surroundings (7–81)where S system m(s 2 s 1 ) and the entropy change of the surroundings canbe determined from S surr Q surr /T surr if its temperature is constant. At initialstages of studying entropy and entropy transfer, it is more instructive tostart with the general form of the entropy balance (Eq. 7–76) and to simplifyit for the problem under consideration. The specific relations above areconvenient to use after a certain degree of intuitive understanding of thematerial is achieved.Control VolumesThe entropy balance relations for control volumes differ from those forclosed systems in that they involve one more mechanism of entropyexchange: mass flow across the boundaries. As mentioned earlier, mass possessesentropy as well as energy, and the amounts of these two extensiveproperties are proportional to the amount of mass (Fig. 7–63).Taking the positive direction of heat transfer to be to the system, the generalentropy balance relations (Eqs. 7–76 and 7–77) can be expressed forcontrol volumes asaQ kT k a m i s i a m e s e S gen 1S 2 S 1 2 CV 1kJ>K2(7–82)m is iSurroundingsEntropytransferby heatControlvolumeEntropytransferby massm es e∆S CV = Q T + m i s i – m e s e + S gen{T{FIGURE 7–63The entropy of a control volumechanges as a result of mass flow aswell as heat transfer.Q