[ MPSI THERMODYNAMIQUE

Transcription

1 Sommaire [ MPSI THERMODYNAMIQUE ]...1 SOMMAIRE INTRODUCTION A LA THERMODYNAMIQUE...3 I DIVERS ETATS DE LA MATIERE...3 II PRESSION DANS UN FLUIDE EN EQUILIBRE...3 III DESCRIPTION D'UN SYSTEME PAR DES VARIABLES D'ETAT...4 IV EQUILIBRE D'UN SYSTEME...4 V TRANSFORMATION D'UN SYSTEME...4 VI EQUATION D'ETAT...5 VII COEFFICIENTS THERMOELASTIQUES (OU DE REPONSE) D'UN FLUIDE PROPRIETES THERMOELASTIQUES DES GAZ...6 I PROPRIETES THERMOELASTIQUES DES GAZ REELS AUX FAIBLES PRESSIONS...6 II DEFINITION DU GAZ PARFAIT...6 III APPLICATIONS DE L'EQUATION D'ETAT DU GAZ PARFAIT...6 IV EQUILIBRE DE L'ATMOSPHERE TERRESTRE SUPPOSEE ISOTHERME ETUDE CINETIQUE DES GAZ PARFAITS...8 I MODELE DU GPM...8 II VALEURS MOYENNES...8 III PRESSION D'UN GAZ PARFAIT EN EQUILIBRE STATISTIQUE...8 IV EQUATION D'ETAT DU GP...9 V ENERGIE D'UN GPM...9 VI GENERALISATION...9 VII CAPACITE THERMIQUE A VOLUME CONSTANT PREMIER PRINCIPE DE LA THERMODYNAMIQUE I ENERGIE D'UN SYSTEME FERME EN THERMODYNAMIQUE II TRAVAIL DES FORCES DE PRESSION III PREMIER PRINCIPE DE LA THERMODYNAMIQUE IV CAPACITE THERMIQUE A PRESSION CONSTANTE V APPLICATION A LA CALORIMETRIE PROPRIETES ENERGETIQUES DES GAZ PARFAITS I LOIS DE JOULE II RELATION DE MAYER POUR LES GP III TRANSFORMATION ISOTHERME REVERSIBLE D'UN GP IV TRANSFORMATION ADIABATIQUE REVERSIBLE D'UN GP (ISENTROPIQUE) V CYCLE DE CARNOT D'UN GAZ PARFAIT IV DETENTE DE JOULE GAY LUSSAC : ISOENERGETIQUE VII DETENTE DE JOULE THOMPSON (OU JOULE KELVIN) : ISOENTHALPIQUE VIII METHODOLOGIE SECOND PRINCIPE DE LA THERMODYNAMIQUE ; ENTROPIE I NECESSITE D'UN SECOND PRINCIPE II ENONCE NON MATHEMATIQUE DU 2 E PRINCIPE III ENONCE MATHEMATIQUE DU 2 E PRINCIPE IV PROCESSUS REVERSIBLES ET PROCESSUS IRREVERSIBLES V CYCLES DITHERMES VI INEGALITE DE CLAUSIUS VII ENTROPIE VIII BILANS D'ENTROPIE... 20

2 7 MACHINES THERMIQUES I MACHINES MONOTHERMES II MACHINES DITHERMES CHANGEMENTS D'ETAT DES CORPS PURS I EQUILIBRE LIQUIDE-GAZ II EQUILIBRES SOLIDE-LIQUIDE ET SOLIDE-GAZ THERMOCHIMIE I CHALEURS DE REACTION II RELATION ENTRE R H ET R U III VARIATION DES CHALEURS DE REACTION AVEC LA TEMPERATURE IV CALCUL D'UNE ENTHALPIE DE REACTION V ENERGIE DE LIAISON COVALENTE VI TEMPERATURE DE FLAMME (OU T DE COMBUSTION ADIABATIQUE ISOBARE/ISOCHORE)... 27!

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4 E AKρG,*)-+%,3$2/9$*,*(GEA6+,%&;/+*4& "$*;$2).2(+)+19:)&$,((*0%7 JEρ9 (2(*$239,(-$,*(*;!#$" " 2,+/,-&(*/%+*&$8G5&*(&<,-%D ).$2-%(/$2,*)'&&0%ρE/ ( Eρ G2,+/,)1%2G2;&.')2,%2&'/*-*2()5$+%.&')%*(3$2-%(2'+*&+0%2(*('ρ G -&&--$&(6 A/& G(ρ,$2(-(*(, $2/$2,*)<&0%+-&,,*$2,(%2*;$&. %&' & L"&',%+(2(),;$&/,)-&,,*$20%*,1=&/2(,%&%2/$&-,*..&')2,%2$%-+%,*%&,;+%*),2'0%*+*4&, -&&--$&(6+&&,(+1$--$,')%-$*),);+%*))'-+/'L "&',%+(2(),;$&/,)-&,,*$2,(--+'-$%,,')1&/9*.<)Π Π Eρ ;+%*)5,$+*) #,%&,)-&,,*$2>%2*(',,%&,)-&,,*$2>%2*(', &*2/*-)%4&$.<(&=-'&*2/)$&&*/ +*7$2&25&,)2,%2/%56.&/%&%2/$+$22).&/%&",%&;/+*4&)%.&/%&)2,+/$+$22%2+(*(%),%-'&*%&6+,%&;/+*4&)+/%5")*;;'&2/393 )$22+-&,,*$2(.$,-9'&*0%7 AEρ 9 2*(',7 (.E 3A # A M E 3A #4&E?@A..>..E ## &*2/*-)%.2$.<(&)*;;'&2(*+7%2(%42,(&+*')1%2-&(%G)$2($25%(.,%&&+-&,,*$23( )1%(&-&(6+1*&")*;;'&2/92(&+,+(*(%),),,)%=,%&;/,+*4&,)$22+-&,,*$2)%G7 GE A±ρ9 ±,%*52(+,%&;/+*4&+-+%,9%( III Description d'un système par des variables d'état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quilibre d'un système 2,:,(<.,(2'0%*+*4&(9&.$):2.*0%,*($%(,,,5&*4+,)1'((21'5$+%2(-, ()2,//,3+,5&*4+, *2(2,*5,,$2(%2*;$&.,;%=-$%&%2,$+*)9'('&$<2 2'0%*+*4&)$22',(/&/('&*,'-&+,5+%&,),5&*4+,)1'(( =7$*2(2.$+,)1%2G2;&.')2,%2/:+*2)&;&.'-&%2-*,($2).,,.(),%&;/-$%52( /$%+*,,&,2,;&$(.2(,"-&$*,()*(9&.E)*(9&.+E-&;*(.2(-&.'4+6+/9+%&"G,(2 '0%*+*4&(9&.$):2.*0%733E/ ( ",:,(<.21,(-,*,$+' *+,(2'0%*+*4&5/+.*+*%=('&*%& "-*,($2,(2'0%*+*4&/&,*2$2 / (.K G A GEAE AK.F *%2,:,(<.,(,$%.*,6),/$2)*(*$2,=('&*%&,%2*;$&.,(/$2,(2(,3*+'5$+%5&,%2'(()1'0%*+*4& (9&.$):2.*0%0%1*+20%* (&-,,-$2(2'.2( V Transformation d'un système $(*$2)(& $(*$2)(&2,;$&.(*$2 2,;$&.(*$2 &2,;$&.(*$2E-,,)1%2'(()1'0%*+*4&(9&.$):2.*0%6%2%(&

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quation d'état 0%(*$2)1'((E'0%(*$20%*&+*+,5&*4+,)1'(( =7-$%&%2;*+'+,(*0%3+1=-.$2(&0%1*+=*,(%2&+(*$2;33CEA7/1,(%2'0%(*$2)1'(()%,:,(<.!5&*4+,)1'((*2)'-2)2(, VII Coefficients thermoélastiques (ou de réponse) d'un fluide "1'(()2.$+,);+%*),(4*2)'/&*(-&+)$22'),5&*4+,)1'((333&+*',-&+1'0%(*$2;33EA αe P /$;;*/*2())*+((*$2*,$4&Q βe P /$;;*/*2()1%.2((*$2)-&,,*$265$+%./$2,(2(Q χ E /$;;*/*2()/$.-&,,*4*+*('*,$(9&.32 P α3β3χ,$2(),5&*4+,-$,*(*5,0%*)'-2)2()33,$2(),5&*4+,)1'(( 2)-+%, αeβ χ ).$ M

6 ! " R (%% %#$ I Propriétés thermoélastiques des gaz réels aux faibles pressions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θUK!?#3 M "(.-'&(%&);%,*$2)++/)'-2)2()+-&,,*$23+2,&-,/9$*,*/$..&';'&2/7$2/9$*,*( +(.-'&(%&)%-$*2((&*-+)+1%3$8/$=*,(2(+,#'((,)+1%E@AA> U II Définition du gaz parfait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pplications de l'équation d'état du gaz parfait $;;*/*2(,(9&.$'+,(*0%, $;;*/*2(,(9&.$'+,(*0%, αeβe F χ E F 24*2αEβ χ!'+2*)'+)g-&;*(, '+2*)'+)G-&;*(, ".'+2),G-&;*(, (!!3!3!32!,()*(*)'+,1*+,(,,*.*+4+6%2G-&;*(3 332(+0%2E2 K2!",.$+'/%+,),)*;;'&2(,G)1%2.'+2*)'+)G-&;*(,21*2(&*,,2(-, 2FEΣ * *F * &,,*$2-&(* +)%G*)2,+.'+2E-&,,*$20%1=&/&*(+G*,1*+$//%-*(,%++5$+%.)%.'+2 6+(.-'&(%&)%.'+27- *E2

7 "$*)+($27EΣ- * C&/(*$2.$+*&)%G*7=E2 *F2E- *F,,.$+*&.$:22)%.'+27EΣ2 * *FΣ2 * +/%+)-$%&+1*&7E!X.$+ #,,5$+%.*0%()2,*('),G,,5$+%.*0%()2,*('),G ρefeρ AF A AF $%&+1*&)2,+,7ρ AE 3!XB. # 2,*(')1%2G7)Eρ G3Fρ *&3E GF *&E GF!X! " R (2(*$23&+(*$22$29$.$<2 IV Equilibre de l'atmosphère terrestre supposée isotherme 25%(=-&*.&2;$2/(*$2)G:-$(9<,,7 "1*&,(,,*.*+'6%2G-&;*( "(.-'&(%&,(%2*;$&.)2,+1(.$,-9<&)*,/%(4+/&@U).$*2,/90%B. ".$)<+,(/$2524+(2(0%G&,((&<,-(*( "$*;$2).2(+)+,((*0%),;+%*), E A GF E A GF9 $89EFEVB.ρ *&Eρ A GF9 *GTT93 ρ *&Eρ A GF9Eρ A&/(<&*2/$.-&,,*4+)+1*&-$%&G(&<,;*4+ E A GF9E Aρ AG7+$*;$2).2(+)+19:)&$,((*0%-$%&%2;+%*)*2/$.-&,,*4+?

8 # RC )*%#$ J%(76-&(*)1%2.$)<+.*/&$,/$-*0%)%G-&;*(.$2$($.*0%3$25,,:&)&(&$%5&+1'0%(*$2 )1'((),G-&;*(,3'(4+*).2*<&./&$,/$-*0%(=-'&*.2(+.2( I Modèle du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aleurs moyennes 2,*('.$+'/%+*& 2,*('.$+'/%+*& "5$+%.)%G,("2$.4&).$+'/%+,)2,,( $*(%2-$*2()2,()τ%25$+%.'+'.2(*&0%*+12($%&+/$2(*2().$+'/%+,")2,*('.$+'/%+*&3 $%)2,*('5$+%.*0%).$+'/%+,2,(2YE)F)τ2. # *2Y,(*2)'-2)2()3+)*,(&*4%(*$2).$+'/%+,,()*(9$.$<23(2YEF :- 72,%--$,0%+)*,(&*4%(*$2),.$+'/%+,)1%2,(9$.$<27)1-&<,+.$)<+3+,.$+'/%+,21$2( -,)52()&*,$2,),1//%.%+&2%2-$*2(0%12%2%(&!*,(&*4%(*$2),5*(,,, *,(&*4%(*$2),5*(,,, 2-,,)2,+1,-/),5*(,,,3$8/90%.$+'/%+,(&-'&'-&%2-$*2()/$$&)$22',5 =35 :35 G$*(%2 -&+'+'-*-<)'+'.2(*&)$2(+,;/,$2(-$%&/$$&)$22',5 =35 =K)=35 :35 :K):35 G35 GK)G2/9&/9 6=-&*.&+-&$44*+*('0%1+-$*2(&-&',2((*;)1%2.$+'/%+),(&$%5&)2,+-&+'+'-*-<)7 )Eϕ5 =35 :35 G3=3:3G)5 =)5 :)5 G 2)*&0%+)*,(&*4%(*$2),5*(,,,,(9$.$<2,*ϕ,(*2)'-2)2()=3:3G :-!7")*,(&*4%(*$2),5*(,,,)2,+,(9$.$<27 )Eϕ5 =35 :35 G)5 =)5 :)5 G #,$(&$-*)+)*,(&*4%(*$2),$(&$-*)+)*,(&*4%(*$2),5*(,,,,5*(,,, "1*,$(&$-*,(+14,2/))*&/(*$2-&*5*+'*' :-#7")*,(&*4%(*$2),5*(,,,)2,+,(*,$(&$-ϕ2)'-2))$2/0%)+2$&.) )Eϕ)5 =)5 :)5 G -$+:/$--$%&(&$%5&ϕ=/(.2( *(,,,.$:22, *(,,,.$:22, T ZE FBΣ * ",$..-%(-$&(&,%&($%(,+,.$+'/%+,+$&,BE +-%(-$&(&,%&($%(,+,5+%&,-&*,,-&+5/(%&5*(,,)1%2.$+'/%+%/$%&,)%(.-, 2.$2(&2-9:,*0%,((*,(*0%0%+&',%+((,(+.H. $%&%22'0%*+*4&,((*,(*0%3T ZE*,$(&$-* "5*(,,0%)&(*0%.$:22%,()';*2*-&%E T5IZ T5IZE FΣ5 *IE FΣ [5 [I 2&&$%-2(+,.$+'/%+,:2(+,.H.,2$&.,)5*(,,, III Pression d'un gaz parfait en équilibre statistique ";$&/G -&$*,(E GF (E!Q.5 = =3$8.,(+.,,)1%2.$+'/%+3(+-&$* =Q,(+ 2$.4&)/9$/,-&,/$2),%&+,%&;/3(5 =,(+5+%&4,$+%)+/$.-$,2(,%& =)+5*(,,3,%--$,'/$..%26($%(,+,.$+'/%+, +/%+)Q7QE2$.4&)-&(*/%+2(&&*52(2(&(((K)(F)(E\2Y5 = ).$/:+*2)&(5 :* $2/E.5 =I =FE- = V

9 +&*,,.2(6($%,+,5 =-$,,*4+, -E.$+'/%+..$+'/%+T5IZF# $8 -,(+-&,,*$2=&/'-&+G,%&+-&$*.$+'/%+,(+2$.4&).$+'/%+,/$2(2%,)2,+5$+%...$+'/%+,(+.,,)1%2.$+'/%+)%G T5IZ,(+5*(,,0%)&(*0%.$:22),.$+'/%+, IV Equation d'état du GP -E..$+'/%+.$+'/%+%I # # RC '0%(*$2)1'(()%'(4+*6-&(*&),+$*,)+.'/2*0% -E2 '0%(*$2)1'(($4(2%+$&,)+1'(%)./&$,/$-*0% 22)')%*(+1*2(&-&'((*$2/*2'(*0%)+(.-'&(%&7 %E T5IZE # ( E%I # -$%&%2G)$22'3+5*(,,0%)&(*0%.$:222)'-2)0%) $*(BEF E 3#VA@ A!# WQ /$2,(2()J$+(G.2 2%IE#BF. # Q.$:22)1%2.$+'/%+E! B \.%I %E 3#B., -$%& V Energie d'un GPM $*(%22'0%*+*4&./&$,/$-*0%$*(,$21'2&**2(&2",.$+'/%+,,$2(,2,*2(&/(*$2-, )1'2&*-$(2(*++)1*2(&/(*$2 ++,,$2(-$2/(%++,'2&*/*2'(*0%)(&2,+(*$2%2*0%.2( E #! 2,(--+''2&**2(&2)% ++2)'-2)0%)-$%&%21,(%2;$2/(*$2)1'(( VI Généralisation G-&;*(-$+:($.*0% G-&;*(-$+:($.*0% $)<+7.$+'/%+,2$2-$2/(%++,>-,)1*2(&/(*$22(&+,.$+'/%+, %.$%5.2()%/2(&)1*2&(*)/90%.$+'/%+,1[$%(2(+,.$%5.2(,)&$((*$2()5*4&(*$2%($%& )//2(&,.$%5.2(,-&(%&42(-%+.$%5.2()(&2,+(*$22-%(/$2,*)'&&0%+1=-&,,*$2)+ -&,,*$2/*2'(*0%&,(+.H.(0%1$2($%[$%&,%IE#BF.(E.%IF# $2($%[$%&,E2 /*,(/$2;$&.%=&',%+((,=-'&*.2(%=,%&+,G&'+,+$&,0% A EΣ Q*.*/&$,/$-*0% 9'$&<.)Q$2*7 QE QYK\. K.!5 I).$ Q*E\.5 *IK Q*Y E#2F!KΣ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

10 # RC ),(%2)*;;'&2(*++($(+ 2($%(&*%%&3+1'2&**2(&221,(-,=(2,*56/%,)+1'2&*-$(2(*++)1*2(&/(*$2.$+'/%+*&7,$*2(!,:,(<.,*)2(*0%, (!30%+1$2&'%2*(232-+%,) *2( K *2(!+1*2(&/(*$2),.$+'/%+,) ()!3.*,*+,1*()1%2*2(&/(*$26(&<,/$%&()*,(2/30%*2/$2/&20%1%22$.4&(&<,-(*().$+'/%+, 22'+*+,/$2,(&*4%(*$2,6+1'2&*-$(2(*++)1*2(&/(*$2.$+'/%+*&3,*4*20%+1$2/$2,*)<&&+1'2&* *2(&2)%,:,(<./$..%2&2)%&=(2,*5 VII Capacité thermique à volume constant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

11 " + I Energie d'un système fermé en thermodynamique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ω $*(Γ+.$.2()%/$%-+=&/',%&+1&4&2)2()(3+1&4&+,:,(<.&^$*(+(&5*+'+'.2(*& δ]eγ)αeγω)( 2(&+,)(,( ((!3+,:,(<.&^$*(+(&5*+]E ( (!Γω)(E '/9E *]ZA3+,:,(<.&^$*(;;/(*5.2()%(&5*+(,$2'2&*%.2( :+*2)&6-&$*,)*4(*0%,5/%2-*,($2)*4(*0%2)'-+/+-*,($2).2*<&6/0%+5$+%. )%G)*.*2%2/$2,((0% ;Z *:,(<.E2.$+,) E E '/9 A 2;*(3 '/9E] -&,,*$2 *-_+'+/(&$/*2'(*0%*2)';$&.4+ 2(&+,)(,( ((!3+,:,(<.&^$*(]E% J* J)(

12 ",#;$&.,)(&2,;&('2&'(*0%,$2(--+',(&5*+ ++,/$&&,-$2)2(6%2)'-+/.2(./&$,/$-*0%.,%&4+2-%(+,/+/%+&2/+/%+2(+(&5*+)1%2;$&.$('] $*(.$+)2;&.')2,%2&'/*-*2(*2)';$&.4+)-&$*)*(9&..'(+ ((*2*(*+7+G,(2 '0%*+*4&5/%2(9&.$,((6 E!?#Q2-+$2+&'/*-*2()2,%2(9&.$,((6!E#?#Q+1'0%*+*4& ;*2+3+(.-'&(%&)%G,(!E#?#Q"1'2&**2(&2)%5&*' E!?W E E '/9",:,(<.21-,&^%)(&5*++&^%)+1'2&*,$%,;$&.)(&2,;&((9&.*0%$% /9+%&32$(' 2(&-&'((*$2.*/&$,/$-*0%7+1*((*$2(9&.*0%3-+%,&2))2,+(9&.$,((6#?#Q,/$..%2*0%) -&$/92-&$/9-&/9$/,%=.$+'/%+,)%G+2&',%+(%2;+%=)1'2&*5&,+1*2('&*%&)%,:,(<.30%*2,1&&H(0%+$&,0%1*+:'0%*+*4&,((*,(*0% J$2/$2)%/(%&,)%(&2,;&(7.'(%= %5*,/$2)%/(%&,74$*,3-$+:,(:(<23G,$+2(75*) II Travail des forces de pression 2(9&.$):2.*0%3+(&5*+&^%-&%2;+%*),(+-+%-&()%(.-,)%(&5*+),;$&/,)-&,,*$2 &5*+'+'.2(*&),;$&/,)-&,,*$2 &5*+'+'.2(*&),;$&/,)-&,,*$2 :+*2)&O-*,($2+1=('&*%&&<2+-&,,*$2 =(3%2*;$&.$*(+,%&;/)%-*,($2 :,(<.7`G3-*,($2a+&^$*(+(&5*+'+'.2(*&δ] -&,,*$2E =() ) ((2(*$23/-&&-9,%--$,0%+,,%+,;$&/,0%*,1=&/2(,%&+G,$2(+,;$&/,)-&,,*$2!&5*+'+'. &5*+'+'.2(*&&^%-&+;+%*) 2(*&&^%-&+;+%*) $*(δ] -&,,*$2+(&5*+'+'.2(*&),;$&/,)-&,,*$2&^%-&+;+%*)+$&,)%)'-+/.2('+'.2(*&)= = )%-*,($2C$&/,=&/',,%&+-*,($27 3-$*),3&'/(*$22$&.+3;$&/)-&,,*$2=&/'-&+G,%&+ -*,($23;$&/,);&$((.2(9/-*,($2 δ] -&,,*$2E =()) QKδ] ;&$(( ) QEA (&2,;$&.(*$20%,*,((*0% δ] ;&$((EA() QEA (&2,;$&.(*$20%,*,((*0%.'/2*0%.2(&'5&,*4+); δ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remier principe de la thermodynamique $*(%2,:,(<.;&.''5$+%2(2(&%2'((*2*(*+(%2'((;*2+C2&/52(+'4&*0%.2(+(&5*+](+ (&2,;&((9&.*0% QK =(K E]K.*.-$&(2(7)2,]3$22)$*(-,;*&2(&&+(&5*+),;$&/,=('&*%&,0%*)'&*52()1%2 3/&*+,( -&',2()2, =(!

13 " * QEA( =(EA3 E]K3()2,//,3-$%&),'((,(C)'(&.*2',3,()'(&.*2';$2/(*$2 )1'(((*2)-)+(&2,;$]K%,,*&/$2(&3](-&*,,'-&'.2()'-2)2()+2(%&)+ (&2,;$&.(*$2 =-&,,*$2)*;;'&2(*++)% & -&*2/*-7)QK) =(K)Eδ]Kδ IV Capacité thermique à pression constante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pplication à la calorimétrie '2'&+*(', '2'&+*(', $*(%2(&2,;$&.(*$2*,$/9$&0%,*,((*0%;*,2(5&*&+(.-'&(%&)%,:,(<.)) 2δE 5) 5,()$2/+(&2,;&((9&.*0%2'/,,*&-$%&'+5&).2*<&0%,*,((*0%(65$+%./$2,(2(+ (.-'&(%&)1%2,:,(<.;&.') Q $*(%2(&2,;$&.(*$2*,$4&.'/2*0%.2(&'5&,*4+;*,2(5&*&+(.-'&(%&)%,:,(<.))7 δe -) -,(+(&2,;&((9&.*0%2'/,,*&-$%&'+5&).2*<&*,$4&.'/2*0%.2(&'5&,*4++ (.-'&(%&)1%2,:,(<.;&.') Q +$&*.'(&*E2,.4+),(/92*0%,).,%&),(&2,;&(,(9&.*0%, ++,-&.((2()1//')&%=5+%&, ) -() 5!'(9$)),.'+2, '(9$)),.'+2, 2/9&/96)'(&.*2& --$%&%2.'(+).,,. +$&*.<(&)J&(9+$(E2/*2(*,$+2((9&.*0%>5,.'(++*0%>*((%&>(9&.$.<(&>%.,, "5,3+,//,,$*&,(+1%,$2(*2*(*+.2(2'0%*+*4&(9&.*0%6+(.-'&(%& ".'(+,(*2*(*+.2(2'0%*+*4&(9&.*0%6+(.-'&(%&!Z #

14 " 2-+$2&-*).2(+.'(+)2,+1%3$2*(($2((*2(,,G&-*).2(%2'(()1'0%*+*4&(9&.*0%6+ (.-'&(%& C 3! $*(Γ+/-/*('(9&.*0%6-&,,*$2/$2,(2()%5,(),//,,$*&, %&2%)%/+$&*.<(&+.,,µ)1%0%*%&*(+.H./-/*('(9&.*0%0%+5,(+, //,,$*&,$*(/ +/-/*('(9&.*0%.,,*0%)+1%6-&,,*$2/$2,(2(2ΓEµ/ :-7$2,%--$,0%+,5&*(*$2,)(.-'&(%&,$2(,%;;*,..2(;*4+,-$%&-$%5$*&/$2,*)'&&/ -(/ /$.. /$2,(2(, :,(<.E`/+$&*.<(&>.,,)1%>.,,.).'(+a "(&2,;$&.(*$2,(.$2$4& E&+,:,(<.,(*,$+'(9&.*0%.2(EA $*2( E`/+$&*.<(&>.,,)1%a(!E`.,,.).'(+a E K! K!EA )1$8 / Kµ C K./ - C!EA )22)')%*(/ -.,7 2-&(*0%3*+:),-&(, 2$22-$%&&)'(&.*2&/ -5/-&'/*,*$2 /+$&*E3 VW%2*('9$&,O+O+$* / %E3 VBWQ B 6 MU,$%, (. "/-/*('(9&.*0%%.2(5/ #'(9$)'+/(&*0% '(9$)'+/(&*0% 2;*(-,,&%2/$%&2()1*2(2,*('*/$2,(2(-2)2(+)%&' ()2,+/$2)%/(%&$9.*0%)&',*,(2/ 2)2( (3*+&^$*(+(&5*+]E*I (++(&2,;$&.2/9+%&-&;;([$%+3(,*+(.-'&(%&)%5,3), //,,$*&,()+1%5&*) 3$23/$.. EA3 Kµ/ *I (EA

15 M RC.%%%#%#$ $%(//*2/$2/&20%+,2,($%,+,b,%;+)&2*&3$2/$2,*)<& QE =(EA E]K I Lois de Joule 2G$4'*(6+ +$*)W$%+,*,$2'2&**2(&22)'-2)0%) 2G$4'*(6+! +$*)W$%+,*,$22(9+-*2)'-2)0%) ",$4'*,,2(%=!+$*,)W$%+ II Relation de Mayer pour les GP - 5E2 /0%**.-+*0% -Z 5 D).$ %(&,;$&.%+(*$2, E / -/ 5E 2-$,γE - Z E -Eγ γ γ. +/%+) ( -$%&(&2,;$&.(*$20%+/$20%7 E 2 γ,*5e/( E γ 2 γ,*-e/( III Transformation isotherme réversible d'un GP ",:,(<.,(/$2,(*(%'-&2.$+,)+,(2;&.')2,%2/:+*2)&;&.'-&%2-*,($2",-&$*,,$2( )*(9&.,"12,.4+,(-+$2')2,%2(9&.$,(()(.-'&(%& 2;*(5&*&+5$+%.)%G=(&H..2(+2(.2().2*<&6/0%+(.-'&(%&)%G&,(/ ( ('+6 +(.-'&(%&)%(9&.$,(( +/%+)%(&5*+&^%+$&,)1%2(&2,;$&.(*$2*,$(9&.&'5&,* !3!3 ]E2+2 F! /&δ]e) 2-$,E F!7&--$&(5$+%.'(&*0% *Z 7 Z!7/$.-&,,*$2]ZA"G&^$*(;;/(*5.2()%(&5*+ *T 7 T!7)'(2(]TA",:,(<.;$%&2*()%(&5*+%.*+*%=('&*%& %(&=-&,,*$2)]7 ]E2+2!F $*(+(&2,;&((9&.*0%&^%-&+,:,(<.)2,+(&2,;$&.(*$22]E) -$%&%2/$.-&,,*$23]ZATA7+,:,(<./<))+/9+%&%(9&.$,(( IV Transformation adiabatique réversible d'un GP (isentropique) "$*)"-+/ "$*)"-+/ "$&,)1%2(&2,;$&.(*$2)*4(*0%3+,:,(<.2&^$*(%/%2(&2,;&((9&.*0%)+1=('&*%& :,(<.7`2.$+,)a2;&.')2,%2/:+*2)&;&.'-&%2-*,($2.$4*+,2,;&$((.2(,",-&$*,,$2( ($%(,)*4(*0%,((2(*$23-&$*)*4(*0%21*.-+*0%-,(&2,;$&.(*$2)*4(*0% 225*,%2(&2,;$&.(*$2)*4(*0%&'5&,*4+ 2 γ)fk)fea "$*)"-+/7 γ E/ ( -$%&%2(&2,;$&.(*$2)*4(*0%&'5&,*4+)1%2)γ/$2,(2(*)'+ %(&,;$&.%+(*$2,)++$*)"-+/7 γ E/ ( > γ γ E/ ( "$&,)1%2/$.-&,,*$2)*4(*0%&'5&,*4+)1%2*)'+333 "$&,)1%2)'(2()*4(*0%&'5&,*4+)1%2*)'+333.&0%7 ++,(%,,*5+*),1*+:'/$%+.2(!-&',2((*$2)2,+)*&..)+-:&$2 -&',2((*$2)2,+)*&..)+-:&$2 2,+)*&..)+-:&$23+1'0%(*$2)1%2)*4(*0%J,(E/ ( F γ 225*,%2(&2,;$&.(*$2*,$(9&.&'5&,*4+ 5E5 )*4(*0% 27 EγZ +1)*4(*0%,(-+%,L-2(%L0%+1*,$(9&. 5E5 *,$(9&. M

16 #+/%+)%(&5*+&^%-&+G +/%+)%(&5*+&^%-&+G ]E2 Fγ ).$ -&*2/*-K).$*2(&)*(/+/%+, M RC V Cycle de Carnot d'un gaz parfait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γE/ ( $%(,+,/$%&4,($%&22(+%& /$2/5*('5&,+9%(/*3]TA.$(%&!&5*+((&2,;&(&^%,%&%2/:/+)&2$( &5*+((&2,;&(&^%,%&%2/:/+)&2$( :,(<.E`2.$+,)*)'+a $*(]+(&5*+&^%,%&%2/:/+ $*( +(&2,;&((9&.*0%&^%-&+,:,(<.+$&,)%/$2(/(5/+,$%&/6+(.-'&(%& *,$(9&.J $*(!+(&2,;&((9&.*0%&^%-&+,:,(<.+$&,)%/$2(/(5/+,$%&/6+(.-'&(%&!*,$(9&. %&%2/:/+3 EAE]K K!/&,%&J(3+,:,(<.2&^$*(-,)/9+%& γ J γ E γ γ! ( γ γ E γ γ! JF E F K! EA &+(*$2)+%,*%,-$%&%2*)'+! 2).2()%.$(%&)&2$(-$%&%27 ;$2/(*$222.2(7]TA3+,:,(<.;$%&2*()%(&5*+%.*+*%=('&*%& JT ZA",:,(<.&^$*(;;/(*5.2()+/9+%&)+,$%&//9%) T!TA",:,(<./<))+/9+%&6+,$%&/;&$*) 2-$,&E(&5*+;$%&2*%.*+*%=('&*%&F(&2,;&((9&.*0%&^%6+,$%&//9%) 2 &E]F E K!F E!F 2(&-&'((*$27 EP]PKP!P7(&2,;$&. 2](2!.7*+/:/+'(*()'/&*(2,2,*25&,,2,(&*$2$.'(&*0%3+,/+/%+,,&*2(+,.H.,2%&*( ]1E]31 E 31!E!C&*$ IV Détente de Joule Gay Lussac : isoénergétique '(2()W$%+:"%,,/E)'(2()*4(*0%*&&'5&,*4+)2,+5*) :,(<.E`G35*)3&$4*2(a EAE G$22'+*0%+0%,;/(%&, */1,(%23$2)-+%, EA ',%+((,=-'&*.2(%=7-$%&-&,0%($%,+,G3$2$4,&5 TA=-+*0%'-&+.$)<+)2)&]+, *,-$%&(!3 ZA-,=-+*0%' VII Détente de Joule Thompson (ou Joule Kelvin) : isoenthalpique '(2()W$%+9$.-,$2E)'(2()*4(*0%*&&'5&,*4+)1%2G6(&5&,%2-&$*-$&%, 2;$&/+G6(&5&,&%2.*+*%-$&%=$%%2'(&2+.2( =-7+-&,,*$2)*.*2%+$&,)+(&5&,') +1$4,(/+:,(<.E,:,(<.;&.'`.,,.)Ga ] E ZA7(&5*+)-$%,,' E5$+%.42)$22'-&+G

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