[ MPSI THERMODYNAMIQUE

Sommaire [ MPSI THERMODYNAMIQUE ]...1 SOMMAIRE...1 1 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...5 2 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...7 3 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... 10 4 PREMIER PRINCIPE DE LA THERMODYNAMIQUE... 11 I ENERGIE D'UN SYSTEME FERME EN THERMODYNAMIQUE... 11 II TRAVAIL DES FORCES DE PRESSION... 12 III PREMIER PRINCIPE DE LA THERMODYNAMIQUE... 12 IV CAPACITE THERMIQUE A PRESSION CONSTANTE... 13 V APPLICATION A LA CALORIMETRIE... 13 5 PROPRIETES ENERGETIQUES DES GAZ PARFAITS... 15 I LOIS DE JOULE... 15 II RELATION DE MAYER POUR LES GP... 15 III TRANSFORMATION ISOTHERME REVERSIBLE D'UN GP... 15 IV TRANSFORMATION ADIABATIQUE REVERSIBLE D'UN GP (ISENTROPIQUE)... 15 V CYCLE DE CARNOT D'UN GAZ PARFAIT... 16 IV DETENTE DE JOULE GAY LUSSAC : ISOENERGETIQUE... 16 VII DETENTE DE JOULE THOMPSON (OU JOULE KELVIN) : ISOENTHALPIQUE... 16 VIII METHODOLOGIE... 17 6 SECOND PRINCIPE DE LA THERMODYNAMIQUE ; ENTROPIE... 18 I NECESSITE D'UN SECOND PRINCIPE... 18 II ENONCE NON MATHEMATIQUE DU 2 E PRINCIPE... 18 III ENONCE MATHEMATIQUE DU 2 E PRINCIPE... 18 IV PROCESSUS REVERSIBLES ET PROCESSUS IRREVERSIBLES... 18 V CYCLES DITHERMES... 19 VI INEGALITE DE CLAUSIUS... 19 VII ENTROPIE... 20 VIII BILANS D'ENTROPIE... 20

7 MACHINES THERMIQUES... 22 I MACHINES MONOTHERMES... 22 II MACHINES DITHERMES... 22 8 CHANGEMENTS D'ETAT DES CORPS PURS... 23 I EQUILIBRE LIQUIDE-GAZ... 23 II EQUILIBRES SOLIDE-LIQUIDE ET SOLIDE-GAZ... 24 9 THERMOCHIMIE... 26 I CHALEURS DE REACTION... 26 II RELATION ENTRE R H ET R U... 26 III VARIATION DES CHALEURS DE REACTION AVEC LA TEMPERATURE... 26 IV CALCUL D'UNE ENTHALPIE DE REACTION... 26 V ENERGIE DE LIAISON COVALENTE... 27 VI TEMPERATURE DE FLAMME (OU T DE COMBUSTION ADIABATIQUE ISOBARE/ISOCHORE)... 27!

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# 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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ravail 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, =(!

" * 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 ';*2*(*$2)+12(9+-* ';*2*(*$2)+12(9+-* 2)';*2*(+12(9+-*-&+&+(*$2EK1,(%2;$2/(*$2)1'((3=(2,*53=-&*.'2W/$.. 2)'-2)-,)+(&2,;$&.(*$2 EA,%&%2/:/+)(&2,;$&.(*$2 ),(%2)*;;'&2(*++($(+ $*(%2(&2,;$&.(*$2.$2$4&2 E "$&,)1%2(&2,;$&.(*$2.$2$4&3+(&2,;&((9&.*0%&^%-&%2,:,(<.;&.',('+6,5&*(*$2) +12(9+-*,$%52(+/,2/9*.*,),(&2,;$&.(*$2,*,$/9$&,2 E!-/*('(9&.*0%6-&,,*$2/$2,(2( -/*('(9&.*0%6-&,,*$2/$2,(2( -% 2-$, -E 7/-/*('(9&.*0%)%,:,(<.6-&,,*$2/$2,(2( $%&%2/$&-,9$.$<23$2)';*2*(+,5&*4+,*2(2,*5,7 / -E -F.7/-/*('(9&.*0%.,,*0%6-&,,*$2/$2,(2( -3.E -F27/-/*('(9&.*0%.$+*&6-&,,*$2/$2,(2( #$ 2)'-2)0%)EK2%,,* $%&%23E#2F!EM2F! -EM2F!/ -EMF! -3.EMF! % +21:-,)&',%+(('2'&+/$2/&22(J$; %!" 2'2'&+$2-%(2'+*&)+-9,/$2)2,')52(3/&,$25$+%.,(,,G;*4+ 1,(-$%&0%$*$2/$2,*)<&,$%52( E ( -E 5 V Application 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 #

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