cours-thermo

Description

29Chapitre 3Bilans d’énergie : le premierprincipe de la thermodynamique3.1. Les di¤érentes formes d’énergie; la notiond’énergie interne3.1.1. Les énergies3.1.1.1. Exemple 1ressort masse enceinte calorifugée et fermée air Fig.3.1.Considérons une masse accrochée au bout d’un ressort, le tout placé dans une enceinte rem-plie d’air (voir schéma 3.1). L’enceinte est fermée (pas d’échange de matière avec l’extérieur)et isolée (pas d’échange d’énergie avec l’extérieur; la paroi de l’enceinte est donc parfaitementcalorifugée). Le système étudié est l’ensemble (ressort + masse M + air).Un mouvement initial est donné à la masse M. Son énergie cinétique au départ est Ec ,0et son énergie potentielle est Ep . L’énergie mécanique de M est dé…nie comme étant Em =0Ec+ Ep. Or, du fait de la présence de l’air, il y a une force de frottement lors du mouvementde la masse qui aura donc un mouvement amorti, jusqu’à s’immobiliser dans sa positiond’équilibre. L’énergie mécanique de la masse a diminué au cours du temps à cause de la forcede frottement qui est une force non conservative. Mais qu’est devenue l’énergie mécaniqueperdue? A-t-elle disparue ou s’est-elle seulement transformée?Une fois l’expérience terminée, la température de l’air est mesurée précisément : on re-marque qu’elle a augmenté. L’énergie mécanique perdue par M a donc été récupérée par legaz sous forme d’énergie interne. Le premier principe est tout simplement un principe deconservation de ...

Informations

• Publié par: Thion
• Nombre de lectures: 46
• Langue: Français

Extrait

/6 @e^mfqob 0 ?fi^kp a ækbodfb 7 ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb

0+.+ Ibp af æobkqbp clojbp a ækbodfb 8 i^ klqflk a ækbodfb fkqbokb 0+.+.+ Ibp ækbodfbp 0+.+.+.+ Bubjmib .

ressort   masse encei nte calori fugée et fermée air

Cfd+0+.+ @lkpfaæolkp rkb j^ppb ^‘‘ol‘eæb ^r _lrq a rk obpploq) ib qlrq mi^‘æ a^kp rkb bk‘bfkqb obj* mifb a ^fo %slfo p‘ j^ 0+.&+ I bk‘bfkqb bpq cbojæb %m^p a æ‘e^kdb ab j^qfåob ^sb‘ i buqæofbro& eæ bq fpliæb %m^p a æ‘e^kdb a ækbodfb ^sb‘ i buqæofbro 8 i^ m^olf ab i bk‘bfkqb bpq alk‘ m^oc^fqbjbkq ‘^ilofcrdæb&+ Ib pvpqåjb æqrafæ bpq i bkpbj_ib %obpploq ( j^ppb M ( ^fo&+ Rk jlrsbjbkq fkfqf^i bpq alkkæ Ý i^ j^ppb M + Plk ækbodfb ‘fkæqfnrb ^r aæm^oq bpq Ec 0 ) bq plk ækbodfb mlqbkqfbiib bpq Ep 0 + I ækbodfb jæ‘^kfnrb ab M bpq aæ kfb ‘ljjb æq^kq Em = Ec + Ep + Lo) ar c^fq ab i^ moæpbk‘b ab i ^fo) fi v ^ rkb clo‘b ab colqqbjbkq ilop ar jlrsbjbkq ab i^ j^ppb nrf ro^ alk‘ rk jlrsbjbkq ^jloqf) grpnr Ý p fjjl_fifpbo a^kp p^ mlpfqflk ^ a ænrfif_ob+ I ækbodfb jæ‘^kfnrb ab i^ j^ppb ^ afjfkræ ^r ‘lrop ar qbjmp Ý ‘^rpb ab i^ clo‘b ab colqqbjbkq nrf bpq rkb clo‘b klk ‘lkpbos^qfsb+ J^fp nr bpq absbkrb i ækbodfb jæ‘^kfnrb mboarb < >*q*biib afpm^orb lr p bpq*biib pbribjbkq qo^kpclojæb < Rkb clfp i bumæofbk‘b qbojfkæb) i^ qbjmæo^qrob ab i ^fo bpq jbproæb moæ‘fpæjbkq 7 lk ob* j^onrb nr biib ^ ^rdjbkqæ+ I ækbodfb jæ‘^kfnrb mboarb m^o M ^ alk‘ æqæ oæ‘rmæoæb m^o ib d^w plrp clojb a ækbodfb fkqbokb+ Ib mobjfbo mofk‘fmb bpq qlrq pfjmibjbkq rk mofk‘fmb ab ‘lkpbos^qflk ab i ækbodfb 7 ‘biib*‘f kb mbrq m^p afpm^o^ëqob) j^fp pbribjbkq pb qo^kpjbqqob plrp

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0- @e^mfqob 0 ?fi^kp a ækbodfb 7 ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb

afsbopbp clojbp+ A^kp ib ‘^p moæpbkq) ‘b plkq ibp ‘el‘p bkqob i^ j^ppb bk jlrsbjbkq bq ibp m^oqf‘ribp ‘lkpqf ^kq i ^fo nrf lkq qo^kpcæoæ i ækbodfb ‘fkæqfnrb a bkpbj_ib ab i^ j^ppb M bk qr ækbodfb ‘fkæqfnrb jf‘olp‘lmfnrb %ækbodfb a ^dfq^qflk qebojfnrb& abp m^oqf‘ribp+ ?fi^k abp ækbodfbp fkqbosbk^kq f‘f 7 * Ec macro ab i j ppb ^ ^ * Ep macro ækbodfb mlqbkqfbiib abp clo‘bp buqæofbrobp %ab mbp^kqbro ab i^ j^ppb& 8 * Ec micro = P ec pljjb ab i ækbodfb ‘fkæqfnrb ab ‘e^nrb m^oqf‘rib ab i ^fo 8 * Ep micro ækbodfb mlqbkqfbiib a fkqbo^‘qflk bkqob ibp m^oqf‘ribp %pf i ^fo bpq objmi^‘æ m^o rk d^w klk m oc^fq&+ ^ I ækbodfb jæ‘^kfnrb %j^‘olp‘lmfnrb& bpq 7 Em = Ec macro + Ep macro I ækbodfb afqb fkqbokb %jf‘olp‘lmfnrb& bpq 7 U = Ec micro + Ep micro  Obj^onrb 0+. Ibp ækbodfbp ‘fkæqfnrbp afqbp j^‘olp‘lmfnrbp clkq oæcæobk‘b Ý abp jlrsb* jbkqp a bkpbj_ib 7 qlrqbp ibp m^oqf‘ribp %^qljbp& ‘lkpqfqr^kq i^ j^ppb M lkq rk jçjb jlr* sbjbkq 8 fip pb aæmi^‘bkq bk _il‘ + Ibp ækbodfbp ‘fkæqfnrbp afqbp jf‘olp‘lmfnrbp clkq oæcæobk‘b Ý abp jlrsbjbkqp aæplo* alkkæp 7 ibp m^oqf‘ribp slkq a^kp qlrp ibp pbkp ) j^fp bk d^oa^kq rkb mlpfqflk jlvbkkb ‘lkpq^kqb+ Bk oæ^ifqæ) i^ j^ppb M ^rppf slfq p^ qbjmæo^qrob ^rdjbkqbo 8 ‘bi^ bpq ifæ ^r c^fq nrb ibp m^oqf‘ribp ‘lkpqfqr^kq i^ j^ppb M ) _fbk nrb uæbp mol‘eb a rkb mlpfqflk a ænrfif_ob) mbrsbkq sf_obo ^rqlro ab ‘bqqb abokfåob+ I ækbodfb ‘fkæqfnrb jf‘olp‘lmfnrb a ^dfq^qflk qebojfnrb bpq ‘bqqb ækbodfb ab sf_o^qflk ^rqlro ab i^ mlpfqflk a ænrfif_ob+ 0+.+.+/+ Bubjmib / Plfq rkb j^ppb m ab d^w p æ‘lri^kq a^kp rk qrv^r+ Ib _rq bpq a b b‘qrbo rk fi^k ab _ i ækbodfb qlq^ib ar d^w+ Ib ‘bkqob ab do^sfqæ ab i bkpbj_ib abp m^oqf‘ribp ar d^w bpq klqæ G + A rk mlfkq j^‘olp‘lmfnrb) i bkpbj_ib ar d^w p æ‘lrib Ý i^ sfqbppb v −→ G + Rkb l_pbos^qflk jf‘olp‘lmfnrb a rkb pbrib m^oqf‘rib mbojbq ‘lkpq^qbo nr bk oæ^ifqæ ib jlrsbjbkq ab ‘biib*‘f k bpq m^p rkfclojb bq æd^i Ý v −→ G ) j^fp qlrq Ý c^fq aæploalkkæ+ @ bpq pbribjbkq i^ jlvbkkb ab i^ sfqbppb ab qlrqbp ibp m^oqf‘ribp nrf alkkb i æ‘lribjbkq a bkpbj_ib v −→ G + Af æobkqbp clojbp a ækbodfb plkq ^ilop aæ kfbp 7 * Ec macro = 21 mv 2 G ækbodfb ‘fkæqfnrb ab i æ‘lribjbkq * Ep macro ækbodfb mlqbkqfbiib abp clo‘bp buqæofbrobp %mbp^kqbro& 8 * Ec micro = P ec ∗ pljjb ab i ækbodfb ‘fkæqfnrb ab ‘e^nrb m^oqf‘rib ar d^w a^kp ib oæcæobkqfbi _^ov‘bkqofnrb 8 * Ep micro ækbodfb mlqbkqfbiib a fkqbo^‘qflk bkqob ibp m^oqf‘ribp %pf ib d^w k bpq m^p m^o* c^fq&+ 0+.+.+0+ @lk‘irpflk Bk ‘lk‘irpflk) nrbi nrb plfq ib pvpqåjb æqrafæ) 1 clojbp a ækbodfb plkq afpqfkdræbp 7 * Ec macro = 1 ækbodfb ‘fkæqfnrb j^‘olp‘lmfnrb % a bkpbj ib & 8 ^sb‘ m j 2 mv 2 G _ ^ppb qlq^ib bq G ‘bkqob ab do^sfqæ * Ep macro ækbodfb mlqbkqfbiib abp clo‘bp buqæofbrobp 8 * Ec micro = P ec ∗ pljjb ab i ækbodfb ‘fkæqfnrb ab ‘e^nrb m^oqf‘rib a^kp ib oæcæobk* _ qfbi ^ov‘bkqofnrb 8 * Ep micro ækbodfb mlqbkqfbiib a fkqb ^‘qflk bkqob ibp m^oqf‘ribp+ o I ækbodfb jæ‘^kfnrb %lr j^‘olp‘lmfnrb& bpq 7 Em = Ec macro + Ep macro .5 ^sofi /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+

Pb‘qflk 0+/ Ib qo^s^fi abp clo‘bp ab mobppflk

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0+.+/+ Ibp æ‘e^kdbp a ækbodfb I ækbodfb mbrq p æ‘e^kdbo m^o afsbop jlvbkp nrb klrp ^iilkp f‘f oæprjbo 7 ib qo^s^fi abp clo‘bp bq ib qo^kpcboq ‘^ilof nrb+ 0+.+/+.+ Qo^kpcboq m^o ib qo^s^fi W a rkb clo‘b Bk jæ‘^kfnrb) klrp ^slkp sr nrb ib qo^s^fi a rkb clo‘b %klqæ W & æq^fq Ý i lofdfkb a rkb s^of^qflk a ækbodfb ‘fkæqfnrb %qeæloåjb ab i ækbodfb ‘fkæqfnrb& 7 W = Z δW = Z − F →  d −→ l  0+.+/+/+ Qo^kpcboq ‘^ilof nrb Ib qo^kpcboq ‘^ilof nrb bpq ^mmbiæ ^rppf qo^kpcboq qebojfnrb lr ‘e^ibro ) ‘b abokfbo qbojb æq^kq Ý æsfqbo+ I^ jfpb bk ‘lkq^‘q ab abru d^w ab qbjmæo^qrobp af æobkqbp jlaf b ‘bp abokfåobp grpnr Ý ‘b nr biibp absfbkkbkq æd^ibp i rkb Ý i ^rqob+ Fi v ^ alk‘ br rk qo^kpcboq ‘^ilof nrb ar mirp ‘e^ra sbop ib mirp colfa nrb i lk s^ klqbo Q m^o i^ prfqb+ Ib qo^kpcboq ‘^ilof nrb æiæjbkq^fob) ‘ bpq Ý afob ^v^kq br ifbr mbka^kq rk ‘lroq fkpq^kq dt ) bpq klqæ δQ + Obj^ nrb 0+0 Fi bpq fjmloq^kq ab afpqfkdrbo ibp klqflkp ab ‘e^ibro) qo^kpcboq ‘^ilof nrb bq o qbjmæo^qrob+ Ib qbojb ‘e ibro bk m^oqf‘rifbo bpq qoåp ^j_fdrè bq alfq çqob æsfqæ+ Bk b bq) i^ ^ klqflk ab ‘e^ibro bpq dækæo^ibjbkq obifæb Ý i^ klqflk ab qbjmæo^qrob a^kp ib i^kd^db ‘lro^kq+ Kb afq*lk m^p nrbiib ‘e^ibro ffi nr^ka i^ qbjmæo^qrob bpq æibsæb < >ilop nrb ib qbojb ‘e^ibro) bk mevpfnrb) obmoæpbkqbo^fq mirqñq rk qo^kpcboq ‘^ilof nrb) ‘ bpq Ý afob rk qo^kpcboq a ækbodfb a rk pvpqåjb sbop rk ^rqob mbka^kq i^ aroæb ab i bumæofbk‘b+ Afob nrb i^ ‘e^ibro a rk pvpqåjb s^rq qbiib s^ibro k ^ ^r‘rk pbkp) ‘lkqo^fobjbkq Ý i^ qbjmæo^qrob+ Lk afq mirqñq nrb i^ ‘e^ibro æ‘e^kdæb %‘ bpq Ý afob ib qo^kpcboq ‘^ilof nrb& ilop a rkb bumæofbk‘b bkqob rk pvpqåjb . bq rk pvpqåjb / s^rq q^kq+ Bk oæprjæ) ib qo^kpcboq ‘^ilof nrb bq i^ ‘e^ibro plkq abru qbojbp ænrfs^ibkqp bk qebojlavk^jfnrb) j^fp i rqfifp^qflk ar jlq ‘e^ibro alfq çqob æsfqæb+ Bk k) ibp klqflkp ab qo^kpcboq ‘^ilof nrb bq qbjmæo^qrobp plkq qlrq Ý c^fq af æobkqbp+ Lk mbrq ‘e^r bo rk pvpqåjb) ‘ bpq Ý afob irf ^mmloqbo ab i ækbodfb plrp clojb ‘^ilof nrb p^kp mlro ^rq^kq nrb i^ qbjmæo qrob ar pvpqåjb ^rdjbkqb+ M^o bubjmib) ib ‘e^r ^db a b^r bk æ_ri* ^ ifqflk k ^rdjbkqb m^p i^ qbjmæo^qrob) j^fp qo^kpclojb qlrq pfjmibjbkq ib ifnrfab bk s^mbro+

0+/+ Ib qo^s^fi abp clo‘bp ab mobppflk

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.5 ^sofi /--1

0/ @e^mfqob 0 ?fi^kp a ækbodfb 7 ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb 0+/+.+ Mobppflk buqæofbrob bq mobppflk a^kp rk rfab 0+/+.+.+ Bubjmib .

piston ant P ext  couliss cales air (GP)  à t=0 , les cales sont enlevées P i <P ext  

Cfd+0+/+ Plfq rk pvpqåjb ( S 0 ) ‘lkpqfqræ a ^fo bkcbojæ a^kp rk oæ‘fmfbkq %slfo p‘eæj^ 0+/&) alkq i^ m^oqfb prmæofbrob bpq cbojæb m^o rk mfpqlk ab pb‘qflk S bq ‘lrifpp^kq+ >r aæm^oq) i^ mobppflk buqæofbrob bpq P ext bq i^ mobppflk Ý i fkqæofbro ar oæ‘fmfbkq P i < P ext + Ib mfpqlk bpq _ilnræ m^o abru ‘^ibp+ > aæ_rq ab i bumæofbk‘b) ibp ‘^ibp plkq bkibsæbp+ I^ mobppflk buqæofbrob mlrppb alk‘ pro ib mfpqlk nrf abp‘bka grpnr Ý i ænrfif_ob+ @b abokfbo bpq ^qqbfkq nr^ka i^ mobppflk ar pvpqåjb %i ^fo Ý i fkqæofbro& bpq P f = P ext + roÝ P ext rb ib pvpqåjb Bkqob ibp abru æq^qp a ænrfif_ob) i ^fo buqæofbro obpqb qlrgl p ) q^kafp n %^fo fkqæofbro& s^ofb moldobppfsbjbkq ab P i Ý P f + > rk fkpq^kq nrbi‘lknrb fkqbojæaf^fob) i^ mobppflk Ý i fkqæofbro k ^ ^r‘rkb o^fplk a çqob æd^ib Ý i^ mobppflk Ý i buqæofbro+ 0+/+.+/+ Bubjmib / piston libre de coulisser  P 0   P 0   à t=0, une masse M est air (GP)  placée sur le piston  M g P i =P 0   Pf état initial (t<0) état fi nal

Cfd+0+0+ Rkb bumæofbk‘b nr^pf pfjfi^fob bpq f‘f oæ^ifpæb+ Ib mfpqlk bpq i^fppæ if_ob ab ‘lrifppbo %slfo p‘eæj^ 0+0&+ I^ mobppflk ar pvpqåjb ^r aæm^oq bpq alk‘ P i = P 0 + > t = 0 ) lk mi^‘b rkb .5 ^sofi /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+

Pb‘qflk 0+/ Ib qo^s^fi abp clo‘bp ab mobppflk

00

j^ pb M pro ib mfpqlk 7 ‘b abokfbo abp‘bka bq p fjjl_fifpb nr^ka ibp clo‘bp ^mmifnræbp pro ‘b p mfpqlk p æd^ifpbkq 7 P f = P 0 + M gS + Mbka^kq qlrqb i^ qo^kpcloj^qflk) i^ mobppflk p buboä^kq Ý i buqæofbro ar mfpqlk bpq P ext = P f ) ^ilop nrb i^ mobppflk Ý i fkqæofbro s^ofb ab P 0 ^r aæm^oq Ý P f Ý i^ k+ > rk fkpq^kq t fkqbojæaf^fob nrbi‘lknrb) i^ mobppflk ar pvpqåjb bpq fk‘lkkrb bq bk qlrq ‘^p af æobkqb ab i^ mobppflk Ý i buqæofbro) bq k bpq a ^fiibrop jçjb m^p kæ‘bpp^fobjbkq eljldåkb a^kp qlrq ib pvpqåjb ffi Bk ‘lk‘irpflk ab ‘bp abru bubjmibp) fi m^o^fq kæ‘bpp^fob ab _fbk afpqfkdrbo mobppflk ar pvpqåjb bq mobppflk buqæofbrob ) ‘bqqb abokfåob æq^kq i^ mobppflk ab ‘b nrf bkqlrob ib pvpqåjb bq mlrpp^kq pro ‘birf*‘f+ 0+/+/+ Ib qo^ ^fi æiæjbkq^fob abp clo‘bp ab mobppflk s %qo^kpcloj^qflk æiæjbkq^fob& I bubjmib / ar m^o^do^meb moæ‘æabkq bpq f‘f obmofp+ Ib pvpqåjb æqrafæ bpq i ^fo fkqæofbro ^r oæ‘fmfbkq+ Ib _rq bpq ab ‘^i‘ribo ib qo^s^fi abp clo‘bp buqæofbrobp ab mobppflk+ @bp clo‘bp p ^mmifnrbkq pro qlrqbp ibp m^olfp aæifjfq^kq ib pvpqåjb ‘elfpf+ Pbrib ib mfpqlk _lrdb) alk‘ pbribp ibp clo‘bp ab mobppflk p ^mmifnr^k ib mfpqlk qo^s^fiibkq+ q pro Bkqob abp fkpq^kqp t bq t + dt fkqbojæaf^fobp ^r ‘lrop ab i bumæofbk‘b) ib qo^s^fi æiæjbkq^fob ab i^ clo‘b ab mobppflk buqæofbrob p ^mmifnr^kq pro ib pvpqåjb bpq 7 − δW = F → ext  − d → l = ( − P ext S − u → z ) d −→ l = − P ext Sdx dx æq^kq ib aæmi^‘bjbkq æiæjbkq^fob ar mfpqlk+ Ib qo^s^fi ab i^ clo‘b ab mobppflk bpq alk‘ 7 δW = − P ext dV Fi bpq fjmloq^kq ab obj^onrbo nrb ‘ bpq i^ mobppflk buqæofbrob nrf ^mmifnrb rkb clo‘b pro ib pvpqåjb 8 ‘ bpq alk‘ P ext nrf alfq çqob mofpb bk ‘ljmqb a^kp ib ‘^i‘ri ar qo^s^fi ab i^ clo‘b ab mobppflk) bq klk i^ mobppflk ar pvpqåjb nrf) ‘ljjb klrp i ^slkp sr) mbrq çqob af æobkqb+ dV obmoæpbkqb i^ s^of^qflk ab slirjb ar pvpqåjb %ab i ^fo bkcbojæ a^kp ib oæ‘fmfbkq&+ 0+/+0+ Ib qo^s^fi ^r ‘lrop a rkb qo^kpcloj^qflk klk æiæjbkq^fob Ilop a rkb bumæofbk‘b) ib qo^s^fi æiæjbkq^fob abp clo‘bp ab mobppflk bkqob abru fkpq^kqp qoåp mol‘ebp t bq t + dt bpq δW = − P ext dV Ilop ab i bumæofbk‘b ‘ljmiåqb) fi pr§q ab pljjbo qlrp ibp qo^s^ru æiæjbkq^fobp ar aæ rq ab i bumæofbk‘b Ý i^ k ab i bumæofbk‘b 7 _ Z fi u n t δW = − Z P W = ext dV d ´ eb 0+/+1+ Ib ‘^p abp qo^kpcloj^qflkp nr^pf*pq^qfnrbp oæsbopf ibp _ Klrp ^slkp sr nrb ilop ab i bumæofbk‘b /) i^ mobppflk buqæofbrob Ý rk fkpq^kq nrbi‘lknrb bpq af æobkqb ab i^ mobppflk ar pvpqåjb+ Bk mobk^kq ‘boq^fkbp moæ‘^rqflkp) fi bpq mlppf_ib ab oæ^ifpbo abp æslirqflkp afqbp nr^pf*pq^qfnrbp ^r ‘lrop abpnrbiibp i^ mobppflk buqæofbrob obpqb qlrglrop æd^ib Ý i^ mobppflk fkqbokb+ Bubjmib 0 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+

.5 ^sofi /--1

01 @e^mfqob 0 ?fi^kp a ækbodfb 7 ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb Oæ^ifplkp i bumæofbk‘b / ab j^kfåob nr^pf*pq^qfnrb oæsbopf_ib) ‘ bpq Ý afob nr ^r ifbr ab jbqqob rkb j^ppb m pro ib mfpqlk bq ib i ‘ebo pr_fqbjbkq) klrp ^iilkp jbqqob moldobppfsbjbkq bq aæif‘^qbjbkq pro ib mfpqlk ab jfkrp‘ribp j^ppbp dm ibp rkbp ^moåp ibp ^rqobp) bk ^qqbka^kq bkqob ‘e^nrb j^ppb nrb i ænrfif_ob plfq æq^_if bkqob i buqæofbro bq ib pvpqåjb+ I bumæofbk‘b bpq ^ooçqæb nr^ka i^ pljjb ab qlrqbp ibp mbqfqbp j^ppbp dm bpq æd^ib Ý i^ j^ppb m ab i bumæofbk‘b /+ Mlro ‘e^nrb fkpq^kq fkqbojæaf^fob ab i bumæofbk‘b) fi v ^ ænrfif_ob bkqob i buqæofbro bq i fkqæofbro 7 P = P ext bk klq^kq P i^ mobppflk ar pvpqåjb+ Lk ^ ^ilop mlro rkb qo^kpcloj^qflk æiæjbkq^fob 7 δW = − P dV bq mlro i^ qo^kpcloj^qflk dil ^ib _ W = Z δW = − Z P dV P æq^kq i^ mobppflk ar pvpqåjb %‘^o ‘bqqb abokfåob bpq æd^ib Ý i^ mobppflk buqæofbrob&+ 0+/+2+ Bubjmibp ab ‘^i‘rip ab qo^s^fi ab clo‘b ab mobppflk 0+/+2+.+ Bslirqflk fpl‘elob % V = cte & Mlro rkb æslirqflk fk kfqæpfj^ib 7 δW = − P est dV = 0 ‘^o dV = 0 + Ilop a rkb æslirqflk fpl‘elob) ibp clo‘bp ab mobppflk kb qo^s^fiibkq m^p+ 0+/+2+/+ Bslirqflk ^sb‘ P ext = cte @ bpq ib ‘^p abp bubjmibp . bq /+ Mlro i bubjmib . 7 P ext = P f 8 mlro i bubjmib / 7 P ext = P 0 + mgS = P f + Ib pvpqåjb bpq ib d^w fkqæofbro ^r oæ‘fmfbkq+ Plk æq^q fkfqf^i bpq klqæ 7 P i ) V i ) T i 8 plk æq^q k^i bpq 7 P f = P ext ) V f ) T f + Ib qo^s^fi bpq) ‘ljmqb qbkr nrb P ext bpq ‘lkpq^kqb 7 W = − Z P est dV = − P ext Z dV = − P f ( V f − V i )  0+/+2+0+ Bslirqflk nr^pf*pq^qfnrb fplqebojb a rk d^w m^oc^fq Nr^pf*pq^qfnrb pfdkf b nrb i bumæofbk‘b bpq b b‘qræb pr§p^jjbkq ibkqbjbkq mlro nr fi v ^fq qlrglrop ænrfif_ob) Ý qlrq fkpq^kq fkqbojæaf^fob ab i bumæofbk‘b 7 alk‘ P ext = P + Ab mirp p fi p ^dfq a rk d^w m^oc^fq 7 P V = nRT + Bk k) i^ qo^kpcloj^qflk bpq fplqebojb 7 T = cte + Lk   mbrq alk‘ æ‘ofob 7 δW = − P ext dV = − P dV ^sb‘ nRT P = V  plfq δW = − nRT d V V nrf p fkqådob bk 7 W = − nRT ln µ V V i f ¶ = nRT ln µ P P i f ¶ ‘^o P f V f = P i V i %i^ qbjmæo^qrob bpq ‘lkpq^kqb&+ .5 ^sofi /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+

Pb‘qflk 0+0 Ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb 0+/+3+ Ib af^do^jjb ab @i^mbvolk Oæa^‘qflk riqæofbrob

02

0+0+ Ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb Ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb bpq qlrq pfjmibjbkq rk mofk‘fmb ab ‘lkpbos^* qflk ab i ækbodfb 7 ‘bqqb abokfåob kb mbrq m^p afpm^o^ëqob lr pb ‘oæbo j^fp pbribjbkq p æ‘e^kdbo+ @ljjb qlrq mofk‘fmb) fi kb pb aæjlkqob m^p j^fp obpqb mlpæ q^kq nr ^r‘rkb bumæofbk‘b kb i ^ jfpb bk aæc^rq+ 0+0+.+ Bklk‘æ I^ s^of^qflk ab i ækbodfb qlq^ib %ækbodfb jæ‘^kfnrb bq ækbodfb fkqbokb& a rk pvpqåjb qebojl* avk^jfnrb cbojæ bpq i^ pljjb abp qo^kpcboqp ‘^ilof nrbp Q bq ar qo^s^fi abp clo‘bp buqæofbrobp W ab mobppflk 7 Δ ( E m + U ) = W + Q Bk a ^rqob qbojbp) i^ s^of^qflk ab i ækbodfb a rk pvpqåjb kb mbrq çqob nrb ib oæpriq^q a rk æ‘e^kdb ^sb‘ i buqæofbro) plfq m^o qo^kpcboq ‘^ilof nrb) plfq m^o i fkqbojæaf^fob ar qo^s^fi a rkb clo‘b+ Obj^onrb 0+1 E m = Em macro + Ec macro ) ^sb‘ Ec macro = 1  2 mv 2 G ) G æq^kq ib ‘bkqob ab do^sfqæ ar pvpqåjb+ I ækbodfb ‘fkæqfnrb j^‘olp‘lmfnrb bpq ‘biib ar jlrsbjbkq a bkpbj_ib ar rfab+ I^ sfqbppb a æ‘lribjbkq bpq dækæo^ibjbkq qoåp ibkqb abs^kq i sfqbppb fkafsfarbiib abp ^ m^oqf‘ribp 8 i ækbodfb ‘fkæqfnrb j^‘olp‘lmfnrb bpq alk‘ qlrq Ý c^fq kædifdb^_ib abs^kq i ækbodfb ‘fkæqfnrb jf‘olp‘lmfnrb+ Pf i lk mbrq kædifdbo æd^ibjbkq ibp s^of^qflkp a ækbodfb mlqbkqfbiib j^‘olp‘lmfnrb) ‘b nrf bpq plrsbkq ib ‘^p) ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb mbrq pb pfjmif bo plrp i^ clojb prfs^kqb 7 Δ U = W + Q %.& M^o i^ prfqb) i^ obi^qflk pfjmif æb %.& pbo^ rqfifpæb) j^fp fi c^rq _fbk d^oabo Ý i bpmofq nrb %.& bpq rkb æd^ifqæ nrf k bpq s^i^ ib nrb nr^ka i ækbodfb jæ‘^kfnrb obpqb ‘lkpq^kqb+ _ Obj^onrb 0+2 Rk pvpqåjb ob‘bs^kq ab i ækbodfb ab i buqæofbro slfq æsfabjjbkq plk ækbodfb U ^rdjbkqbo+ Ibp ‘lksbkqflkp ab pfdkb plkq alk‘ ibp prfs^kqbp 7 W bq Q plkq positifs pf ib pvpqåjb reçoit ab i buqæofbro) bq kæd^qfcp pf ib pvpqåjb alkkb ab i ækbodfb Ý i buqæofbro+ Obj^onrb 0+3 A^kp ib ‘^p a rk pvpqåjb cbojæ bq fpliæ) fi k v ^ kf clo‘b %alk‘ m^p ab qo^s^fi&) kf qo^kpcboq ‘^ilof nrb 7 W = 0 ) Q = 0 ) bq alk‘ Δ U = 0 + Obj^onrb 0+4 Mlro rkb æslirqflk fpl‘elob 7 V = cte alk‘ W = 0 ) plfq Δ U = Q + Obj^onrb 0+5 Pf ib pvpqåjb k bpq m^p cbojæ) fi c rq glrqbo i ækbodfb abp m^oqf‘ribp bk* ^ ^ qo^kqbp a^kp ib pvpqåjb) bq bkibsbo i ækbodfb abp m^oqf‘ribp ploq^kqbp ar pvpqåjb+ J^fp ‘b ‘^p I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+ .5 ^sofi /--1

03 @e^mfqob 0 ?fi^kp a ækbodfb 7 ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb ab drob k bpq m^p ^r moldo^jjb 7 lk p ^oo^kdbo^ ^ilop qlrglrop mlro pb o^jbkbo Ý abp pvp* qåjbp cbojæp) nrfqqb Ý prfsob ib rfab p fi bpq bk jlrsbjbkq+ Ib mobjfbo mofk‘fmb %.& mbrq p æ‘ofob æd^ibjbkq mlro rkb æslirqflk æibjbkq^fob %bkqob / æq qp qoåp mol‘ebp& 7 ^ dU = δW + δQ %/& 0+0+/+ Bubjmib ab i^ aæqbkqb ab Glrib*D^v Irpp^‘ 0+0+/+.+ Mlpfqflk ar mol_iåjb

paroi retirable  robinet V 1  V 2      ou V 1  V 2       gaz vide gaz vide parois calorifugées

Cfd+0+1+ Obmoæpbkq^qflk abp abru ‘lk dro^qflkp mlppf_ibp a^kp i bumæofbk‘b ab Glrib %æq^qp fkfqf^ru abp ‘ljm oqfjbkqp& ^ I bumæofbk‘b nrf prfq) nrb i lk ^mmbiib aæqbkqb ab Glrib*D^v Irpp^‘ %lr pfjmibjbkq aæqbkqb ab Glrib&) ^ æqæ oæ^ifpæb ^r UFUfåjb pfå‘ib m^o Glrib) D^v Irpp^‘ bq Efok+ Biib ‘lkpfpqb Ý pæm^obo rkb bk‘bfkqb ‘^ilofcrdæb bk abru ‘ljm^oqfjbkqp %.& ab slirjb V 1 bq %/& ab slirjb V 2 plfq m^o rkb m^olf ^jlsf_ib) plfq m^o rk ol fkbq %slfo drob 0+1&+ _ Ib ‘ljm^oqfjbkq %.& bpq objmif ab d^w Ý i^ mobppflk P i ^ilop nrb ib ‘ljm^oqfjbkq %/& bpq fkfqf^ibjbkq sfab+ I^ pæm^o^qflk bkqob ibp abru ‘ljm^oqfjbkqp bpq bkprfqb bkibsæb %lr ib ol_fkbq lrsboq& 7 i^ af rpflk ar d^w p b b‘qrb a^kp qlrq ib slirjb ( V 1 + V 2 ) grpnr Ý i ænrfif_ob+ 0+0+/+/+ Oæplirqflk ar mol iåjb _ Ib pvpqåjb ‘lkpfaæoæ bpq ib d^w+ I^ mobppflk buqæofbrob p ^mmifn ^kq pro ‘b d^w æq^kq kri) fi sfbkq 7 W = 0 %i buqæofbro bpq r sfab&+ Ibp m^olfp plkq ^af^_^qfnrbp %‘^ilofcrdæbp& 7 ib qo^kpcboq ‘^ilof nrb bpq alk‘ kri 7 Q = 0 + Bk k Δ U = W + Q = 0 7 i ækbodfb fkqbokb ar d^w obpqb ‘lkpq^kqb ilop a rkb aæqbkqb ab Glrib*D^v Irpp^‘ + 0+0+/+0+ Aæqbkqb ab Glrib a rk d^w m^oc^fq Pf ib d^w bpq m^oc^fq) ‘ljjb i ækbodfb fkqbokb obpqb ‘lkpq^kqb) ^ilop i^ qbjmæo^qrob obpqb æd^ibjbkq ‘lkpq^kqb %.fåob ilf ab Glrib 7 U kb aæmbka nrb ab T &+ I^ aæqbkqb ab Glrib*D v ^ Irpp^‘ a rk d^w m^oc^fq bpq fplqebojb + Obj^onrb 0+6 I bumæofbk‘b ab i^ aæqbkqb ab Glrib mbojbq ab sæof bo i^ mobjfåob ab Glrib 7 .5 ^sofi /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+

Pb‘qflk 0+1 I bkqe^imfb 8 ibp ‘^m^‘fqæp qebojfnrbp %lr ‘^ilof nrbp&

04

pf i^ qbjmæo^qrob ar d^w s^ofb ilop ab ‘bqqb bumæofbk‘b) i^ mobjfåob ilf ab Glrib k bpq m^p sæof æb 7 ib d^w k bpq alk‘ m^p rk d^w m oc^fq+ ^ 0+0+/+1+ Aæqbkqb ab Glrib a rk d^w ab S^k*abo*T^^ip I ækbodfb fkqbokb a rk d^w ab S^k*abo*T^^ip bpq U = nC V m T − n V 2 a  %0& Ilop a rkb aæqbkqb ab Glrib) i ækbodfb fkqbokb obpqb ‘lkpq^kqb+ Klq^kq T i bq T f ibp qbjmæ* o^qrobp fkfqf^ibp bq k^ibp) bq V i ) V f ibp slirjbp ‘loobpmlka^kqp) i ænr^qflk %0& alkkb 7 nC V m ( T f − T i ) = n 2 a µ V 1 f − V 1 i ¶  V f > V i ) alk‘ T f < T i 7 ilop ab i^ aæqbkqb a rk d^w ab S^k*abo*T^^ip) i^ qbjmæo^qrob _^fppb+ I^ jbprob ab ‘bp qbjmæo^qrobp mbojbq a bpqfjbo bumæofjbkq^ibjbkq ib ‘lb§‘fbkq a + I fkqbomoæq^qflk mevpfnrb ab ‘b meækljåkb p bumifnrb ‘ljjb prfq 7 ib d^w l‘‘rmb rk sl* irjb mirp fjmloq^kq Ý i^ k ab i^ aæqbkqb 7 i^ afpq^k‘b fkqbo*m^oqf‘ri^fob jlvbkkb ^rdjbkqb alk‘+ I ækbodfb a fkqbo^‘qflk bkqob ibp jliæ‘ribp %kæd^qfsb mlro rk d^w ab S^k*abo*T^^ip& pb o^mmol‘eb alk‘ rk mbr mirp ab 0 + Lo i ækbodfb fkqbokb obpqb ‘lkpq^kqb 7 i ækbodfb ‘fkæqfnrb jf‘olp‘lmfnrb %bq alk‘ i^ qbjmæo^qrob& _^fppb % U = cte = Ec micro + Ep int &+ 0+0+0+ @^i‘rip ab qo^kpcboq qebojfnrb Klrp kb afpmlplkp bk‘lob a ^r‘rkb clojrib nrf mbojbqqo^fq ab ‘^i‘ribo afob‘qbjbkq Q + @b ‘^i‘ri mbrq qlrqbclfp p b b‘qrbo ab j^kfåob fkafob‘qb p^‘e^kq nrb Q = Δ U − W + Bubjmib . 7 i^ qo^kpcloj^qflk oæsbopf_ib fplqebojb a rk d^w m^oc^fq+ Δ U = 0 %‘^o T = cte & alk‘ Q = − W = nRT ln ( V f V i ) + Bubjmib / 7 i æslirqflk fpl‘elob+ @ljjb ib slirjb bpq ‘lkpq^kq) ib qo^s^fi abp clo‘bp ab mobppflk bpq kri 7 W = 0 ) alk‘ Q = Δ U = nC V m ( T f − T i )  Bubjmib 0 7 i^ ‘ljmobppflk Ý mobppflk buqæofbrob P ext ‘lkpq^kqb+ Mlro rk d^w m^oc^fq 7 dU = nC V m dT plfq Δ U = nC V m ( T f − T i ) + ab mirp W = − R P est dV = − P ext ( V f − V i ) + Cfk^ibjbkq Q = Δ U − W = nC V m ( T f − T i ) + P ext ( V f − V i ) + @bqqb abokfåob æ‘ofqrob mbrq çqob pfjmif æb 7 ‘bi^ ‘lkpqfqrb i l_gbq ab i^ m^oqfb nrf prfq+

0+1+ I bkqe^imfb 8 ibp ‘^m^‘fqæp qebojfnrbp %lr ‘^ilof nrbp&

0+1+.+ Fkqolar‘qflk ab i bkqe^imfb Ab qoåp klj_obrpbp oæ^‘qflk qebojlavk^jfnrbp p b b‘qrbkq bk ‘lkq^‘q ^sb‘ i ^qjlpmeåob) alk‘ Ý mobppflk ‘lkpq^kqb+ M^o bubjmib i^ oæ^ifp^qflk ab oæ^‘qflk ‘efjfnrb %nrf bpq rkb qo^kp* cloj^qflk qebojlavk^jfnrb& m^o jæi^kdb ab abru oæ^‘qfcp %æq^q fkfqf^i& alkq oæpriqb rk lr abp molarfq%p& %æq^q k^i& bpq coænrbjjbkq oæ^ifpæ Ý i ^fo if_ob ) ‘ bpq Ý afob nrb i^ mobppflk obpqb ‘lkpq^kqb bq æd^ib Ý i^ mobppflk ^qjlpmeæofnrb+ Ib slirjb m^o ‘lkqob mbrq s^ofbo+ I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+ .5 ^sofi /--1

05 @e^mfqob 0 ?fi^kp a ækbodfb 7 ib mobjfbo mofk‘fmb ab i^ qebojlavk^jfnrb Lk mbrq ^ilop æ‘ofob P ext = P 0 ab i ^qjlpmeåob) alk‘ δW = − P ext dV plfq W = − P 0 ( V f − V i )  Ib qo^kpcboq ‘^ilof nrb ^sb‘ i buqæofbro ilop ab i æslirqflk bpq alk‘ 7 Q = Δ U − W = U f − U i + P 0 V f − P 0 V i = ( U f + P 0 V f ) − ( U i + P 0 V i ) = Δ ( U + P V )  Ib qo^kpcboq ‘^ilof nrb Q bpq i^ s^of^qflk ab ( U + P V ) bkqob i æq^q fkfqf^i bq i æq^q k^i+ Rkb klrsbiib clk‘qflk H ^mmbiæb bkqe^imfb bpq fkqolarfqb ^sb‘ H = U + P V Lk ^ alk‘) ilop a rkb æslirqflk Ý mobppflk ‘lkpq^kqb 7 Q = Δ H bq mlro rkb æslirqflk fk kfqæpfj^ib 7 δQ = dH O^mmbi 7 Ý slirjb ‘lkpq^kq ) W = 0 alk‘ 7 Q = Δ U bq mlro rkb æslirqflk fk kfqæpfj^ib 7 δQ = dU Obj^onrb 0+.-U bpq rkb clk‘qflk a æq^q %aæmbka^kq abp m^o^jåqobp a æq^q& 8 P bq V plkq abp m^o^jåqobp a æq^q) alk‘ i bkqe^imfb H = U + P V bpq æd^ibjbkq rkb clk‘qflk a æq^q+

0+1+/+ Ibp ‘^m^‘fqæp qebojfnrbp 0+1+/+.+ I^ ‘^m^‘fqæ qebojfnrb Ý mobppflk ‘lkpq^kqb A^kp rk mobjfbo qbjmp) rk pvpqåjb bpq ‘e^r æ Ý mobppflk ‘lkpq kqb + ^ I^ ‘^m^‘fqæ qebojfnrb Ý mobppflk ‘lkpq^kqb klqæb C P bpq i ækbodfb Q Ý ^mmloqbo plrp clojb qebojfnrb mlro ^rdjbkqbo i^ qbjmæo qrob ar pvpqåjb ab 1 K 7 ^ C P = µ δ dT Q ¶ P = µ ∂ ∂ H T ¶ P ‘^o δQ = dH Ý mobppflk ‘lkpq^kqb+ C P bpq alk‘ c^‘fib Ý aæqbojfkbo bumæofjbkq^ibjbkq 7 ib pvpqåjb bpq ‘e^r æ plrp mobppflk ‘lkpq^kqb 8 ‘ bpq i ækbodfb ab ‘e^r ^db ^mmloqæb mlro l_qbkfo rkb æiæs^qflk ab qbjmæo^qrob ab 1 K + .5 ^sofi /--1 I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J^kp+

Pb‘qflk 0+1 I bkqe^imfb 8 ibp ‘^m^‘fqæp qebojfnrbp %lr ‘^ilof nrbp& 06 0+1+/+/+ I^ ‘^m^‘fqæ qebojfnrb Ý slirjb ‘lkpq^kq A^kp rk pb‘lka qbjmp) ib pvpqåjb bpq ‘e^r æ Ý slirjb ‘lkpq^kq + I^ ‘^m^‘fqæ qebojfnrb Ý slirjb ‘lkpq^kq klqæb C V bpq i ækbodfb Q Ý ^mmloqbo plrp clojb qebojfnrb mlr ^rdjbkqbo i^ qbjmæo^qrob ar pvpqåjb ab 1 K 7 o C V = µ δ dT Q ¶ V = µ ∂ ∂ T U ¶ V ‘^o δQ = dU Ý mobppflk ‘lkpq^kqb+ C V bpq alk‘ c^‘fib Ý aæqbojfkbo bumæofjbkq^ibjbkq 7 ib pvpqåjb bpq ‘e^r æ a^kp rk oæ‘fmfbkq cbojæ ab m^olfp ofdfabp ab j^kfåob Ý ‘b nrb ib slirjb obpqb ‘lkpq^kq %m^o bubjmib ^rql‘rfpbro& 8 ‘ bpq i ækbodfb ab ‘e^r ^db ^mmloqæb mlro l_qbkfo rkb æiæs^qflk ab qbjmæo^qrob ab 1 K + 0+1+/+0+ Ibp ‘^m^‘fqæp jli^fobp bq j^ppfnrbp Lk mbrq aæ kfo æd^ibjbkq 7 *i^ ‘^m^‘fqæ qebojfnrb j^ppfnrb Ý mobppflk ‘lkpq^kqb 7 c p = C P m % m j^ppb ar pvpqåjb& 8 *i^ ‘^m^‘fqæ qebojfnrb j^ppfnrb Ý slirjb ‘lkpq^kq 7 c v = C V m 8 lr bk‘lob 7 *i^ ‘^m^‘fqæ qebojfnrb jli^fob Ý mobppflk ‘lkpq^kqb 7 C pm = C P n % m nr^kqfqæ ab j^qfåob& 8 *i^ ‘^m^‘fqæ qebojfnrb jli^fob Ý slirjb ‘lkpq^kq 7 C vm = C V n + 0+1+/+1+ Bubjmib ar d^w m^ ^fq 7 i^ obi^qflk ab J^vbo oc U kb aæmbka nrb ab i^ qbjmæo^qrob) alk‘ dU GP = µ ∂ ∂ T U ¶ V V dT dT = C plfq U GP = C V T  I^ ‘lkpq^kqb a fkqædo^qflk bpq kriib) ‘^o U kb ‘lkqfbkq nrb i ækbodfb ‘fkæqfnrb mlro rk d^w m^oc^fq % Ep micro = 0 ) m^p a fkqbo^‘qflk fkqbo*jliæ‘ri^fob&) alk‘ nr^ka fi k v ^ m^p a ^dfq^qflk qebojfnrb ( T = 0) 7 U = 0 + A ^rqob m^oq 7 H = U + P V = C V T + nRT = ( C V + nR ) T  Lo C H P = µ ∂ ∂T ¶ P alk‘) mlro rk d^w m^oc^fq C P = C V + nR nrf p æ‘ofq æd^ibjbkq bk clk‘qflk abp ‘^m^‘fqæp jli^fobp 7 C pm = C vm + R @ bpq i^ obi^qflk ab J^vbo + I+ Jbkdrv) Iv‘æb Jlkqbpnrfbr Ib J ^kp+

.5 ^sofi /--1