Thermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam

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1 April 08 Therml energy Soures of het Trnsport of het How to use het The First Lw of Thermoynmis U W Or, if we wnt to otin externl work: U W 009 vrije Universiteit msterm Close yle stem power plnt The trik of using stem high p Turine W om W t Conenser W F s pa s p lose yle: p ompression p expnsion meium with lrge wter Boiler Compressor Si Crnot (796-8) For loop, U = 0 oiler onenser turine ompressor U 0 W W 0 The effiieny of the proess is Niols Léonr Si Crnot (Prijs, juni 796 ugustus 8) ws Frenh mthemtiin. He ws sun of Lzre Crnot, who ws in Egypt uring Nploleon s expeition. Therefore he gve his sun the Ari nme Si. Si Crnot ws n importnt ontemporry of Fourier n ws, like Fourier, intereste in the theory of het. He ie from the holer in Pris. He is one of the 7 Frenhmen who s nme is engrve on the Eifel tower. W turine W oiler ompressor oiler onenser oiler onenser oiler 5 6

2 April 08 The ie. In mhine, you hve some kin of yle The reversile proess No frition et., onverting mehnil energy into het Only het trnsfer etween ojets of (nerly) the sme temperture Sty lwys lose to equilirium. There shoul e no unneessry losses The system shoul e reversile (if there re no losses you n go k for free) if het trnsfer: isotherml if hnging T, no het trnsfer: iti 7 8 Crnot yle The Seon Lw of thermoynmis The Seon Lw An operting in yle nnot trnsform het into work without ny effet on its surrounings. Crnot s theorem The effiieny of ny nnot exee tht of Crnot ; the effiieny of ny reversile equls tht of Crnot. 9 0 An etter thn Crnot oes not exist Crnot An etter thn Crnot oes not exist Crnot := Reversile T T Crnot Crnot T T

3 April 08 An etter thn Crnot oes not exist Crnot := Reversile if super exists it n rive Crnot in reverse the net effet is pumping het to T (the super hs less wste het) AND net output of work (the super hs less wste het, hene more work output) T inreses AND work is one Both mehnil n het energy re inresing Tht is impossile Hene the super oes not exist Crnot T T Super All Crnot s hve the sme effiieny if less effiient Crnot exists it n e riven y Crnot in reverse the net effet is pumping het to T (the norml hs less wste het) AND net output of work (the norml hs less wste het, hene more work output) T inreses AND work is one Both mehnil n het energy re inresing Tht is impossile Hene the less effiient oes not exist less effiient Crnot All reversile s hve the sme effiieny T T norml Crnot The Crnot yle Sine the Crnot effiieny is generl property it nnot epen on the mteril it epens only on the tempertures in the yle to lulte the effiieny, we n tke ny system: we use n iel gs The Crnot yle No frition et., onverting mehnil energy into het Only het trnsfer etween ojets of (nerly) the sme temperture Sty lwys lose to equilirium T T 5 () Isotherml expnsion t T () iti expnsion to T ( ) isotherml ompression t T () iti ompression to T 6 The Crnot yle in -T igrm The Crnot yle in p- igrm T T p T T T p T 7 8

4 April 08 Work one uring Crnot yle W p = Nottion Infinitesiml hnge U p p T Therml energy sore infinitesiml hnge integrl not well efine infinitesiml hnge Distintion is not very importnt p Therml energy relese T Differene = work one (U unhnge) NB. U U00.00 K U K ΔU U00 K U00 K 0 Work one long n isotherm p p T Infinitesiml hnge U p U p n T p [ W ] ( isotherm) p nrt olume hnge long n it p n T p 0 T ln Rln T n T p nrt n T T R T ln nrt nrt p We nee / Crnot yle: reltion etween volumes Crnot yle p p nrt ln T ln Rln T p T R ln ln T p nrt ln T T T

5 April 08 Effiieny of the Crnot yle T T T p oiler onenser turine ompressor U 0 W W 0 The effiieny of the proess is W W turine ompressor oiler onenser onenser oiler oiler oiler p T T Crnot effiieny 5 6 Het pump Het pump 7 oiler onenser turine ompressor W 0 net U 0 W W 0 The effiieny of the proess is W : W hot turine ompressor oiler onenser onenser : ol oiler oiler oiler W 0 net 8 Effiieny of the reverse Crnot yle: het pump p COP oeffiient of performne h.p. W W 0 h.p. p Crnot yle ln nrt T T T p p ln nrt T T 9 0 5

6 April 08 Effiieny of the reverse Crnot yle: het pump p COP oeffiient of performne h.p. W W 0 Het pump h.p. p T T h.p. T T 6 h.p. Het Eletriity: Stirling Engines Stirling 5 kw Stirling 5 Stirling The Stirling yle in T- igrm hot gs rives piston n is still hete ispler moves removing het ue to ompression 0 6

7 April 08 The Stirling yle in T- igrm The Stirling yle in T- igrm hot gs rives piston n is still hete hot gs rives piston n is still hete ispler moves ispler moves removing het ue to ompression removing het ue to ompression The Stirling yle in T- igrm At onstnt volume (isohore) hot gs rives piston n is still hete Infinitesiml hnge U p n T ispler moves removing het ue to ompression n T n T T high low 5 Isotherml proess U p U p n T p p nrt lrge nrthigh nrthigh ln smll W The Stirling yle in T- igrm lrge p nrthigh ln smll high low n Tlow Thigh n T T hot gs rives piston n is still hete removing het ue to ompression nrt ln smll low lrge W W 6 7 7

8 April 08 The effiieny is given y W W W ispler moves The Stirling yle nr ln nr ln n nr ln 8 The effiieny is given y W W W ispler moves The Stirling yle R ln R ln R ln R ln R ln R ln Rln Rln T low 9 The Stirling yle with regenertor The effiieny is given y W W W ispler moves R ln R ln R ln R ln R ln R ln Rln Gs turine yle Crnot 50 5 Cross setion of gs turine Wigoqio II ol-fire stem turine power plnt y Siemens in Shnghi.8 GW 5 5 8

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