复旦大学《大学物理-热学》课件_第15次课.pdf

2021/9/51大学物理（热学）1)Review2)Carnots Ideas3)The Second Law4)Carnots cycle2006-12-13Q=nCvT Q=nCpTPV=CPV=C瓦特瓦特J.Watt蒸汽机用热做功存在限制否？卡卡 诺诺Sadi Carnot卡诺循环(1824)“The production of motive power isthen due in steam-engines not to an actualconsumptionofcaloric,buttoitstransportation from a warm body to a coldbody,that is,to its re-establishment ofequilibrium-an equilibrium considered asdestroyedby any cause whatever,bychemical action such as combustion,or byany other.”Carnots ideasCarnots ideasQW“According to this principle,the production of heat alone is notsufficient to give birth to theimpelling power:it is necessarythat there should also be cold;without it,the heat would beuseless.”Carnots ideas“The necessary condition of themaximum is,then,that in the bodiesemployedbyrealizethemotivepower of heat there should not occurany change of temperature whichmay not due to a change of volume.”Carnots ideasCarnots Cycle“All reversible engines operatingbetweenthesametwoconstanttemperatures THand TLhave the sameefficiency.Any irreversible engine operatingbetween the same two fixed temperatureswill have an efficiency less than this.”Carnots theoremQ1Q1Original proof of Carnots theoremWWWW(1834)(1850)Clapeyrons Graph(1834)(1850)A careful examination shows that the newmethod does not stand in contradiction to theessential principle of Carnot,but only to thesubsidiary statement that no heat is lost,sincein the production of work it may very well bethe case that at the same time a certain quantityof heat is consumed and another quantitytransferred from a hotter to a colder body,andboth quantities of heat stand in a definiterelation to the work that is done.Clausius ideasClausius ideas“All reversible engines operatingbetweenthesametwoconstanttemperatures TH and TL have the sameefficiency.Any irreversible engine operatingbetween the same two fixed temperatureswill have an efficiency less than this.”Carnots theoremW=WT1Q1 Q1在热力学第一定律的基础上：Clausuis statementNot possible在热力学第一定律的基础上：Q2+Q1e=1-TL/TH11.6 Carnot cycle Carnot heat engine0112QQ,1T)(1TUU=21VV 01W,2T034Q234QQ=VpWddone by engine0=UFor a complete cycle03412=+WQQEfficiency is12341212 QQQQW+=12341QQ+=121QQAlong isotherm,1T0=U12112121lnd21VVnRTVpWQQVV=432342lnd43 VVnRTVpQQVV=Similarly121432lnln1VVTVVT=4312 VVVV=142111132121 =VTVTVTVT2 34 1 112TT=