Thermodynamics

380 | ThermodynamicsS inMassHeatSystem∆S systemS gen ≥ 0S outMassHeatFIGURE 7–61Mechanisms of entropy transfer for ageneral system.ImmediatesurroundingsSYSTEMQT surrFIGURE 7–62Entropy generation outside systemboundaries can be accounted for bywriting an entropy balance on anextended system that includes thesystem and its immediatesurroundings.Entropy Generation, S genIrreversibilities such as friction, mixing, chemical reactions, heat transferthrough a finite temperature difference, unrestrained expansion, nonquasiequilibriumcompression, or expansion always cause the entropy of a systemto increase, and entropy generation is a measure of the entropy createdby such effects during a process.For a reversible process (a process that involves no irreversibilities), theentropy generation is zero and thus the entropy change of a system is equalto the entropy transfer. Therefore, the entropy balance relation in thereversible case becomes analogous to the energy balance relation, whichstates that energy change of a system during a process is equal to the energytransfer during that process. However, note that the energy change of a systemequals the energy transfer for any process, but the entropy change of asystem equals the entropy transfer only for a reversible process.The entropy transfer by heat Q/T is zero for adiabatic systems, and theentropy transfer by mass ms is zero for systems that involve no mass flowacross their boundary (i.e., closed systems).Entropy balance for any system undergoing any process can be expressedmore explicitly asS in S out123Net entropy transferby heat and massor, in the rate form, as S gen ¢S system 1kJ>K2S # in S # out S # gen dS system >dt1kW>K2123Rate of net entropytransfer by heatand mass123Entropygeneration123Rate of entropygeneration123Changein entropy123Rate of changein entropy(7–76)(7–77)where the rates of entropy transfer by heat transferred at a rate of Q . andmass flowing at a rate of m . are S . heat Q . /T and Ṡ mass m . s. The entropy balancecan also be expressed on a unit-mass basis as1s in s out 2 s gen ¢s system 1kJ>kg # K2(7–78)where all the quantities are expressed per unit mass of the system. Note thatfor a reversible process, the entropy generation term S gen drops out from allof the relations above.The term S gen represents the entropy generation within the system boundaryonly (Fig. 7–61), and not the entropy generation that may occur outsidethe system boundary during the process as a result of external irreversibilities.Therefore, a process for which S gen 0 is internally reversible, but notnecessarily totally reversible. The total entropy generated during a processcan be determined by applying the entropy balance to an extended systemthat includes the system itself and its immediate surroundings where externalirreversibilities might be occurring (Fig. 7–62). Also, the entropy changein this case is equal to the sum of the entropy change of the system and theentropy change of the immediate surroundings. Note that under steady conditions,the state and thus the entropy of the immediate surroundings (let uscall it the “buffer zone”) at any point does not change during the process,and the entropy change of the buffer zone is zero. The entropy change of thebuffer zone, if any, is usually small relative to the entropy change of the system,and thus it is usually disregarded.