0-9-0 he First Lw of hermoynmis Effiieny When severl lterntive proesses involving het n work re ville to hnge system from n initil stte hrterize y given vlues of the mrosopi prmeters (pressure p i, temperture i, volume i ) to finl stte hrterize y vlues of the mrosopi prmeters (pressure p f, temperture f, volume f ), the mounts of het n W of work epen on the proess. But the hnge in the internl energy of the system U W How to improve effiieny How to get most of wht we wnt: Work or Het U W hs fixe vlue whih oes not epen on the proess itself. Note tht U W Close yle stem power plnt For loop, U = 0 oiler onenser turine ompressor U 0 W W 0 he effiieny of the proess is W turine W oiler ompressor oiler onenser onenser oiler oiler Si Crnot (796-8) First pge of S. Crnot s pper Niols Léonr Si Crnot (Prijs, juni 796 ugustus 8) ws een Frns wiskunige. Hij ws e zoon vn Lzre Crnot. Deze ws tijens e expeitie vn Npoleon in Egypte geweest en gf rom zijn zoon e Arishe nm Si. Si Crnot ws een vn e elngrijkste tijgenoten vn Fourier met interesse in e wrmtetheorie. Hij stierf, eveneens in Prijs, n holer. Hij is één vn e 7 Frnsen wier nmen op e Eiffeltoren stn. http://www.numm.org/numm-in/item?i=asens_87 9_0
0-9-0 he ie. In mhine, you hve some kin of yle he 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. here shoul e no unneessry losses he system shoul e reversile (if there re no losses you n go k for free) if het trnsfer: isotherml if hnging, no het trnsfer: iti he Crnot yle he Seon Lw of thermoynmis No frition et., onverting mehnil energy into het Only het trnsfer etween ojets of (nerly) the sme temperture Sty lwys lose to equilirium he Seon Lw An engine operting in yle nnot trnsform het into work without ny effet on its surrounings. Crnot s theorem he effiieny of ny engine nnot exee tht of Crnot engine; the effiieny of ny reversile engine equls tht of Crnot engine. () Isotherml expnsion t () iti expnsion to ( ) isotherml ompression t () iti ompression to An engine etter thn Crnot oes not exist Crnot engine := Reversile engine if super engine exists it n rive Crnot engine in reverse the net effet is pumping het to (the super engine hs less wste het) AND net output of work (the super engine hs less wste het, hene more work output) inreses AND work is one Both mehnil n het energy re inresing ht is impossile Hene the super engine oes not exist Crnot engine Super engine All Crnot engines hve the sme effiieny if less effiient Crnot engine exists it n e riven y Crnot engine in reverse the net effet is pumping het to (the norml engine hs less wste het) AND net output of work (the norml engine hs less wste het, hene more work output) inreses AND work is one Both mehnil n het energy re inresing ht is impossile Hene the less effiient engine oes not exist less effiient Crnot engine All reversile engines hve the sme effiieny norml Crnot engine
0-9-0 he Crnot yle he Crnot yle in - igrm 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 he Crnot yle in p- igrm Work one uring Crnot yle p F A Fx Ax E p p E p p p Work one long n isotherm Infinitesiml hnge p U p U p p n p p nr ln p nr We nee /
0-9-0 olume hnge long n it Crnot yle: reltion etween volumes n p 0 ln Rln n p nr n R p p p ln Rln p ln Rln Crnot yle p nr ln oiler onenser turine ompressor U 0 W W 0 p nr ln he effiieny of the proess is W W turine ompressor oiler onenser onenser oiler oiler oiler Effiieny of the Crnot yle Crnot yle: the entropy p p 0 p p
0-9-0 Crnot yle: the entropy Entropy Pressure For eh infinitesiml Crnot yle we hve 0 hus, for the whole yle rev 0 his implies tht the entropy hnge S rev S : p A U p n p iel gs: n nr S : n nr n nr S rev : nnot integrte epens on pth (see vs p) esy to integrte see previous sheet ΔS n nr n ln nrln olume is uniquely etermine (is pth inepenent) Entropy n proility (isotherml) Entropy n proility ΔS n ln nrln isotherml expnsion ΔS ln nr ln isotherml expnsion ΔS 0 llowe Alwys: ΔS 0 ΔS 0 unlikely, mrosopilly not llowe From lulte entropy hnge you n eie whether ertin proess is thermoynmilly llowe Ptom t l.h.s.) PN toms t l.h.s.) N P ) ln P Nln N ΔS ΔS nr k B ΔS k B ln P N hermoynmi temperture p nr ln Het pump p ln empirilly this hols for nr ny sustne 0 Δ Δ efine the thermoynmi temperture y n the triple point of wter 5
0-9-0 Het pump oiler onenser turine ompressor W 0 net U 0 W W 0 he effiieny of the proess is W : W hot turine ompressor oiler onenser onenser : ol oiler oiler oiler W 0 net Effiieny of the reverse Crnot yle: het pump p COP oeffiient of performne h.p. W h.p. p W 0 Crnot yle Effiieny of the reverse Crnot yle: het pump p p ln nr nr ln p COP oeffiient of performne h.p. W h.p. p h.p. W 0 Het pump Otto engine 6
0-9-0 Otto engine: Internl Comustion Engine he four strokes of the yle re intke, ompression, power, n exhust. Eh orrespons to one full stroke of the piston, therefore the omplete yle requires two revolutions of the rnkshft to omplete. http://www.keveney.om/otto.html Het Eletriity: Stirling Engines 5 kw 7
0-9-0 Expnsion. At this point, most of the gs in the system hs just een riven to the hot en of the yliner. he gs hets n expns riving the piston outwr. ol hot rnsfer. At this point, the gs hs expne. Most of the gs is still lote in the hot en of the yliner. Flywheel momentum rries the rnkshft the next qurter turn. he ulk of the gs is trnsferre roun the ispler to the ool en of the yliner. ol hot Contrtion. Now the mjority of the expne gs hs een shifte to the ool en. It ontrts, rwing the piston inwr. ol rnsfer. he ontrte gs is still lote ner the ool en of the yliner. Flywheel momentum rries the rnk nother qurter turn, moving the ispler n trnsferring the ulk of the gs k to the hot en of the yliner. ol hot hot NASA Stirling motor 8
0-9-0 he Stirling yle in - igrm he Stirling yle in - igrm high hot gs rives piston n is still hete high hot gs rives piston n is still hete ispler moves ispler moves removing het hene ompression removing het hene to ompression low low he Stirling yle in - igrm he Stirling yle in - igrm high hot gs rives piston n is still hete high hot gs rives piston n is still hete ispler moves ispler moves removing het hene to ompression removing het hene to ompression low low At onstnt volume (isohore) Isotherml proess high low Infinitesiml hnge U p high low high low U p U p n p p nr lrge p Rhigh ln smll 9
0-9-0 he Stirling yle in - igrm high lrge p Rhigh ln smll hot gs rives piston n is still hete high low low smll high R ln low lrge removing het ue to ompression low he Stirling yle in - igrm high lrge p Rhigh ln smll hot gs rives piston n is still hete low high high low ln smll Rlow lrge removing het ue to ompression low W W 0 R high ln R low ln smll l rge smll high low R high ln l rge W W he effiieny is given y W W high low ispler moves he Stirling yle R high ln R low ln high low R high ln R high ln R low ln high low R high ln high low high low Rln Rln high high high low he Stirling yle with regenertor he effiieny is given y W W high low ispler moves R high ln R low ln high low R high ln R high ln R low ln high low R high ln high low high low Rln high low high high Crnot Gs turine yle Cross setion of gs turine 0
0-9-0 Gs turine yle: Joule yle Worl`s lrgest n most effiient gs turine (60%) with pity of 0 megwtts hermoynmi potentils * Pressure p, temperture n volume re stte vriles. * he internl energy U is uniquely etermine for stte with ertin (p, n) * he entropy S is lso uniquely etermine for stte with ertin p, n * One n onstrut other thermoynmi potentils. For exmple U-S, U+p, U-S+p... hey re uniquely etermine for stte with p, n Enthlpy n Gi s Free Energy otl energy neee to rete system in onstnt p environment energy to rete the system + energy to move the environment H = U + p if the pressure p is onstnt, we n integrte this to H = U + p Enthlpy G = U + p - S Gi s Free Energy Summry U W U p U n S đ