类卡诺热机最大功率对应的效率问题

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1、中国物理学会2011年秋季学术会议——2011.9.15-18浙江大学类卡诺热机最大功率对应的效率问题的几个最新研究进展涂展春北京师范大学物理学系Email:tuzc@bnu.edu.cnHomepage:www.tuzc.org2011.9.17supportedbyNSFC(NO.11075015)Outline●Introduction●Recentadvances–EMP(最大功率对应的效率)ofstochasticheatengine–EMPofFeynman'sratchet*–Universality

2、inEMPproblems–BoundsofEMPforlow-dissipationCarnotengines–EMPproblemsviewedfrommin{ΔSir}*●ProspectsIntroduction●CarnotefficiencyIdealCarnotheatengineEnginesworkingbetween2reservoirsEfficiency:=∣W∣/Q1CIsothermalexpansion(absorb)Adiabaticcomp.However,theengine

3、sattheCarnotefficiencycannotproduceapoweroutputbecausetheCarnotcycleAdiabaticexpansion(release)requiresaninfinitelyslowprocessIsothermalcompressionToobtainfinitepoweroutput,T2Carnotefficiency:=1−heatenginesneedspeedingupCT1Question:Ifwetrytoachievethemaximump

4、oweroutputofaheatengine,whatisthecorrespondingefficiency?●MacroscopicCarnot-likeheatengine(1975)22T2=1−=1−1−CACT1!有限时间热力学[Remark:Novikov(1957)andChambadal(1957)foratomicpowerstations]Endoreversibleassumption11wQQ(4)(1)⇒1=2T1T1wT2w(2)T(3)1w22wT2wT2Totaltime

5、assumption:ttotal=t1t2=>Poweroutput:P=Q1−Q2/t1t2Assumptiononheatexchanges:(1):isothermalexpansionAbsorbHeat:Q1=T1−T1wt1(3):isothermalcompressionReleaseHeat:Q2=T2w−T2t2∂P∂PT2wT2max{P}:==0⇒=∂T1w∂T2wT1wT1Q−QTT122w2Efficiencyatmaximumpower:CA==1−

6、=1−Q1T1wT1我国学者严子俊、陈丽璇、陈金灿、陈林根等的研究也极大地推动了有限时间热力学的发展−1−1AbsorbHeat:Q=T−Tt11w11C1==CYCY−1−12−CYC1/ReleaseHeat:Q=T−Tt222w2dependonαandβ2CInparticular,whenα=β,CY=4−CRecentadvances●EMPofstochasticheatengine2C=SS4−C2txVx,t=2T1(high)(1)Iso

7、thermaltransitionattemperatureTduringtimeinterval0

8、ofFeynman'sratchetUratchet23φU=UMtotratchetφMφφQuestion:CanthesmallloadbeliftedifT=T=T?12Answer:Ataglance,itisquitepossible.However,the2ndLawofThermodynamics(Heatcannotbeconv