Special case-reversible isothermal heattransferprocesses.S0SQAS=(SQ)intreyT.intrevT-QheattransferduringthereversibleprocessT,theconstanttemperatureofthesystemOAS(kJ/K)ToHeattransfertoasystemincreasestheentropyofasystemHeattransferfroma systemdecreasetheentropy of a system
• Special case– reversible isothermal heat transfer processes. – Q heat transfer during the reversible process – T0 the constant temperature of the system – Heat transfer to a system increases the entropy of a system – Heat transfer from a system decrease the entropy of a system 11
7-2 the increase of entropy principle (熵增原理)Process 1-2For a cycle:(reversibleorirreversibleprocess 1-2 → arbitraryProcess2-1→reversibleProcess 2-1.FromClausius inequality(intemallyreversible)801%+ [(%)E0≤0Tre2280S-S≤0-T=forreversibleprocess808Q0dsTT> For irreversible processTheentropychangeofaclosedsystem-DuringanirreversibleprocessisgreaterthantheintegralofoQ/T-Duringareversibleprocess is equaltothe integralof oQ/T
7-2 the increase of entropy principle (熵增原理) • For a cycle: – process 1-2 → arbitrary – Process 2-1→ reversible • From Clausius inequality 12 = for reversible process > For irreversible process The entropy change of a closed system –During an irreversible process is greater than the integral of δQ/T –During a reversible process is equal to the integral of δQ/T
7-2 the increase of entropy principle (熵增原理)ASsys=S2- S,Entropy change of the system:Forreversibleprocesses,theentropychangeA5m=S:-S,=4.RepresenttheentropytransferwithheatQheattransferbetweensystemandsurroundings,kJT-absolute temperature at the boundary.KForirreversibleprocesses,theentropychange:A5m-5,-AwaysgreaterthantheentropytransferSome entropy is generated or createdSuThe entropy generated during an irreversible process is called entropy generation (熵产)60+s.AS=S,-S=Entropygeneration（摘产)：Smun≥0Entropygeneration isalwaysa positive orzeroquantity Its value depends on the process, thus it is not a property of a systemIntheabsence ofany entropytransfer,theentropy change ofa systemis equal totheentropygeneration
7-2 the increase of entropy principle (熵增原理) • Entropy change of the system: – For reversible processes, the entropy change: • Represent the entropy transfer with heat • Q—heat transfer between system and surroundings, kJ • T— absolute temperature at the boundary. K – For irreversible processes, the entropy change: • Always greater than the entropy transfer • Some entropy is generated or created • The entropy generated during an irreversible process is called entropy generation (熵产) – Entropy generation (熵产)： • Entropy generation is always a positive or zero quantity. • Its value depends on the process, thus it is not a property of a system • In the absence of any entropy transfer, the entropy change of a system is equal to the entropy generation. ≥ 0 >
7-2 the increase of entropy principle (熵增原理)Inthe absenceofany entropytransfer,theentropychangeof asystemis equal to the entropy generation.ASsys=S,-S,=Foranisolatedsystem,theheattransferiszeroSgenz0AS=S-SASisoatad20or8QS2-STSuen≥0Increaseofentropyprinciple（孤立系统的炳增原理，简称熵增原理）：theentropyofanisolatedsystemduringaprocessalwaysincreaseor,inthelimitingcaseofareversibleprocessremains（孤立系统的可以增大，或保持不变，但不可能减少）constant
7-2 the increase of entropy principle (熵增原理) • In the absence of any entropy transfer, the entropy change of a system is equal to the entropy generation. • For an isolated system, the heat transfer is zero • Increase of entropy principle (孤立系统的熵增原理，简称熵增原理): the entropy of an isolated system during a process always increase or, in the limiting case of a reversible process remains constant. （孤立系统的熵可以增大，或保持不变，但不可能减少） ≥ 0 ≥ 0 or
: System + Surroundings=lsolated systemSn=ASoi=AS+AS≥0Entropy change of a closed system includesEntropytransfer（热焰流）withheattransfer60Entropygeneration（焰产）-irreversibilitiesASV=S-S,福 Entropy change of a system can be negative during aprocess;but entropy generation cannot.0IrreversibleprocessO Reversibleprocess<0Impossibleprocess
• System + Surroundings=Isolated system • Entropy change of a closed system includes – Entropy transfer (热熵流) with heat transfer – Entropy generation（熵产）-irreversibilities • Entropy change of a system can be negative during a process； but entropy generation cannot