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[ MPSI - THERMODYNAMIQUE ]........................................................................................................................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 2E PRINCIPE.....................................................................................................18

III ENONCE MATHEMATIQUE DU 2E 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 DRH ET DRU.............................................................................................................................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

/)&)+(9&.$):2.*0%,((*,(*0%

I Divers états de la matière

&/('&*,(*0% $+*)/&*,(++*2 $+*).$&-9 &$-&*'(',./&$,/$-*0%, ",,$+*),/$2,*)'&',,&$2(*2)';$&.4+, &/('&*,(*0% "*0%*),

7*2/$.-&,,*4+,D.*,)*+((*$25/+(.-'&(%&2'+*4+>.,,,5$+%.*0%,&2), AAA

B.#-$%&+1%( #@AAB.#-$%&+.&/%&

';'&2/7%2,*('7)Er+*0%*)Fr% G 3#B.#-$%&+1*&

II Pression dans un fluide en équilibre

C+%*)2'0%*+*4&

.$%5.2(,*2/,,2(,()',$&)$22', ';*2*(*$2)+-&,,*$2';*2*(*$2)+-&,,*$2';*2*(*$2)+-&,,*$2';*2*(*$2)+-&,,*$2 ;+%*)%4&:/2(&)+1'+'.2(),%&;/

21:-,)1'+'.2(),%&;/*..&'2*('7 E .I

;7 "$*;$2).2(+)+,((*0%),;+%*), )2,+&';'&2(*+(&&,(&,%--+*+'27Er

2,%2&';'&2(*+2$2+*+'23++)5*2(7Er

&<26+,%&;/,(-&($%(+.H.'+6(.

ErGK/(,*G,()*&*'5&,+4,

EAKrG,*)-+%,3$2/9$*,*(GEA6+,%&;/+*4&

"$*;$2).2(+)+19:)&$,((*0%

7JEr9((2(*$239,(-$,*(*;

2,+/,-&(*/%+*&$8G5&*(&<,-%D ).$2-%(/$2,*)'&&0%rE/(

P®

Er;+%*)5,$+*)

&*2/*-)%4&$.<(& )$22+-&,,*$2(.$,-9'&*0%7AEr 9 2*(',

7 (.E 3A # AME 3A #4&E?@A..> ..E ##

&*2/*-)%.2$.<(&)*;;'&2(*+

GEA±r9±,%*52(+,%&;/+*4&+-+%,9%(

III Description d"un système par des variables d"état

E($%(/0%*,(6+1=('&*%&)/((,%&;/

-,).(*<&N,:,(<.$%5&(30%*'/92($%( +;%(4*2)'/&*&+,,:,(<.,0%+1$2/$2,*)<&!AAA --+',5&*4+,)1'(( ,%;;*,2(/&E;3 &*4+)1'((=(2,*5 =75$+%.3.,,32$.4&).$+,3/9&'+/(&*0% &*4+)1'((*2(2,*5

IV Equilibre d"un système

2,:,(<.,(2'0%*+*4&(9&.$):2.*0%

(9&.$):2.*0%0%1*+20%*((&-,,-$2(2'.2(

V Transformation d"un système

$(*$2)(&$(*$2)(&$(*$2)(&$(*$2)(&2,;$&.(*$22,;$&.(*$22,;$&.(*$22,;$&.(*$2 &2,;$&.(*$2

E-,,)1%2'(()1'0%*+*4&(9&.$):2.*0%6%2%(&

&2,;$&.(*$20%,*,((*0% ($%(*2,(2( &*2,),4+6,,%&;/ &2,;$&.(*$2&'5&,*4+ *25&, &2,;$&.(*$2*&&'5&,*4+ =7C*+.'(++*0%,%&+0%+$2=&/%2(2,*$2).2*<&0%,*,((*0% (.-,7(&2,;$&.(*$2&'5&,*4+ (.-,7(&2,;$&.(*$2*&&'5&,*4+(0%,*,((*0%

VI Equation d"état

0%(*$2)1'((E'0%(*$20%*&+*+,5&*4+,)1'((

33CEA7/1,(%2'0%(*$2)1'(()%,:,(<.

®!5&*4+,)1'((*2)'-2)2(,

VII Coefficients thermoélastiques (ou de réponse) d"un fluide aE bE c E

2)-+%,aEb c).$

"R I Propriétés thermoélastiques des gaz réels aux faibles pressions '0%*+*4&(9&.*0%2(&%= (.-'&(%&2%++6++/;$2)2(() AA6+(.-'&(%&)1'4%+*(*$2)+1%®'/9++/2(',*.+*,+,

2G,(2;&.')2,%2&',&5$*&&)%'

30%*,(&$%5)2,%24*2)(.-'&(%&)'(&.*2'$%

*&..)+-:&$2

72;$2/(*$2)6(.-'&(%&/$2,(2(7*,$(9&.

*&..)1.(

5&,%25+%&*2)'-2)2()%G®)';*2*(*$2)+(.-'&(%&7 F E!!F!

"&';'&2/,(/9$*,*)(++,$&(0%+1'/&()(.-'&(%&2(&+(.-'&(%&)++/;$2)2()1 (.( /++)+1%4$%*++2(,$%, (.,$*() AAQ

®QEqUK!?#3 M

+(.-'&(%&)%-$*2((&*-+)+1%

3$8/$=*,(2(+,#'((,)+1%E@AA>

E!?#3 @QEA3A U

II Définition du gaz parfait

"$*)J$:+"$*)J$:+"$*)J$:+"$*)J$:+&*$((7E/&*$((7E/&*$((7E/&*$((7E/((((6)$22'6)$22'6)$22'6)$22'

2--++G-&;*(,,$/*'6%2G&'+%2G*)'+(+0%7

· +,.$+'/%+,,$2(+,.H.,0%/++,)%G&'+

· +1*,$(9&.)2,+)*&..)1.(,(%2)&$*(9$&*G$2(+

"$*)J$:+&*$((

7$%&)$22'3E/(-$%&+G-&;*(,,$/*'

&)';)3$2%&%2&+(*$2)%(:-E&

!!!!"$*)15$)&$ V 75$+%..$+*&"$*)15$)&$ V 75$+%..$+*&"$*)15$)&$ V 75$+%..$+*&"$*)15$)&$ V 75$+%..$+*&

E2

7/$2,(2(%2*5&,++3L/$2,(2(.$+*&),G-&;*(,L

2-%(/+/%+&,5+%&)2,+,7

EAAF2AEV3# W.$+ Q

K2G,(-&;*(ÛE2

(2)'-2)0%) III Applications de l"équation d"état du gaz parfait $;;*/*2(,(9&.$'+,(*0%,$;;*/*2(,(9&.$'+,(*0%,$;;*/*2(,(9&.$'+,(*0%,$;;*/*2(,(9&.$'+,(*0%, aEbE FcE F24*2aEb c ".'+2),G-&;*(, 3 3 32 (!!3!3!32!,()*(*)'+,1*+,(,,*.*+4+6%2G-&;*(3

332(+0%2E2 K2!",.$+'/%+,),)*;;'&2(,G)1%2.'+2*)'+)G-&;*(,21*2(&*,,2(-,

2FES**F*

&,,*$2-&(*++)%G*)2,+.'+2

6+(.-'&(%&)%.'+27-*E2*

F "R ?"$*)+($2 7ES-*

C&/(*$2.$+*&)%G*

7=E2*F2E-*F

,,.$+*&.$:22 )%.'+27ES2**FS2* +/%+)-$%&+1*&7E!X.$+ rEF

ErAFAAF

$%&+1*&)2,+,7rAE 3!XB.# 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%),;+%*),®EAGF

EAGF9$89E

FEVB.r*&ErAGF9

*GTT93r*&ErA GF9ErA&/(<&*2/$.-&,,*4+)+1*&-$%&G(&<,;*4+ EA GF9EArAG7+$*;$2).2(+)+19:)&$,((*0%-$%&%2;+%*)*2/$.-&,,*4+ #R C V)*

I Modèle du GPM

· ",.$+'/%+,)%,$2(,%--$,',-$2/(%++,5$+%.$//%-'-&+,.$+'/%+,2'+*+4+-&&--$&(%

5$+%.%G

· ",.$+'/%+,,$2(,2,*2(&/(*$2

· ++,,$2(2*.',).$%5.2(,*2/,,2(,()',$&)$22',30%*/$2,(*(%2(+1*((*$2(9&.*0% · ++,;;/(%2(),/$++*,*$2,2(&++,(5/+,-&$*,)%&'/*-*2(0%*/$2(*2(+G · 2(&!/9$/,,%//,,*;,3$2/$2,*)<&+%&.$%5.2(&/(*+*2(%2*;$&. =.-+)7G-&;*(,,,$/*',%=G2$4+,

II Valeurs moyennes

2,*('.$+'/%+*&2,*('.$+'/%+*&2,*('.$+'/%+*&2,*('.$+'/%+*& "5$+%.)%G,("2$.4&).$+'/%+,)2,,( $%)2,*('5$+%.*0%).$+'/%+,2,(2YE)F)t2.# -,)52()&*,$2,),1//%.%+&2%2-$*2(0%12%2%(& )Ej5=35:35G3=3:3G)5=)5:)5G

7")*,(&*4%(*$2),5*(,,,)2,+,(9$.$<27

)Ej5=35:35G)5=)5:)5G "1*,$(&$-*,(+14,2/))*&/(*$2-&*5*+'*' )Ej )5=)5:)5G®-$+:/$--$%&(&$%5&j=/(.2(

TZE FBS*

",$..-%(-$&(&,%&($%(,+,.$+'/%+,+$&,BE

2.$2(&2-9:,*0%,((*,(*0%0%+&',%+((,(+.H.

$%&%22'0%*+*4&,((*,(*0%3TZE*,$(&$-* "5*(,,0%)&(*0%.$:22 %,()';*2*-&%EÖT5IZ T5IZE FS5*IE FS[5[I2&&$%-2(+,.$+'/%+,:2(+,.H.,2$&.,)5*(,,, III Pression d"un gaz parfait en équilibre statistique ,%--$,'/$..%26($%(,+,.$+'/%+, +/%+)Q $2/E.5=I=FE-= #R C $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 '0%(*$2)1'(()%'(4+*6-&(*&),+$*,)+.'/2*0% -E2 '0%(*$2)1'(($4(2%+$&,)+1'(%)./&$,/$-*0% %E

T5IZE#

(E%I $*(BE

FE 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

E# 2

VI Généralisation

G-&;*(-$+:($.*0%G-&;*(-$+:($.*0%G-&;*(-$+:($.*0%G-&;*(-$+:($.*0%

ESQ*.*/&$,/$-*0%9'$&<.)Q$2*7QEQYK\. K.!5I).$

Q*E\.5*IKQ*Y®E#2

F!KSQ*Y

$%&%2-$+:($.*0%3Z#2 F! $%&%2)*($.*0%3EM2

F!/$2,*)'&(*$2,)))+

%)+63E;$8;ZM2

F!"1'2&**2(&2)1%22)'-2)0%)

$*(%2;+%*)&'+2'0%*+*4&./&$,/$-*0% '2&*)/$9',*$2)%2$:%K;$&.,0%[1$%4+*

2&*EK/($8EQ.*/&$,/$-*0%K.$+'/%+*&

$2/-$%&%2;+%*)&'+3,(;$2/(*$2)() &$-&*'(',)7 · "$&,)1%2(&2,;$&.(*$23! 2)'-2)-,0%+1'(()1'0%*+*4&*2*(*+()+1'(()1'0%*+*4&;*2++2 )'-2)-,)+2(%&)+(&2,;$&.(*$20%*-&.()-,,&)+1'(( 6+1'((! · $%&%2/:/+)(&2,;$&.(*$2&($%&6+1'((*2*(*+-&<,%2,'&*)(&2,;$&.(*$2,3DEA #R C A· ),(%2)*;;'&2(*++($(+ ,$*2(!,:,(<.,*)2(*0%, (!30%+1$2&'%2*(232-+%,)*2( K*2(!+1*2(&/(*$2),.$+'/%+,) *2(&2)%,:,(<./$..%2&2)%&=(2,*5

VII Capacité thermique à volume constant

';*2*(*$2';*2*(*$2';*2*(*$2';*2*(*$2

7/-/*('(9&.*0%)%,:,(<.65$+%./$2,(2(

5)'-2))()1,(%25&*4+=(2,*5/$..32WQ

/-/*('(9&.*0%.,,*0%65$+%./$2,(2(

7/5E5F.3$8.,(+.,,)%,:,(<./5,(2WQ B 3

/-/*('(9&.*0%.$+*&65$+%./$2,(2(

753.E5F2WQ .$+

$%&%23E#2

F!5E#2

F!53.E#

F!E !3MWQ .$+ /5E#

F! !!!!,),G&'+,,),G&'+,,),G&'+,,),G&'+, "1'0%(*$2)1'((),G)2,+.$)<+)2)&]+,,(7

K2IFI24E2

2-%(2/$&'/&*&7E2

F242IFI

24,(--+'+/$5$+%.

2,(+/$5$+%..$+*&

2IFI,(--+'-&,,*$2*2(&2

2&**2(&2)%G)2)&]+,

7E2IF

®)E5)K2I)FI%2)®¥3®(G&'+®

I Energie d©un système fermé en thermodynamique

"1'2&*.'/2*0%21,(-,%2&2)%&/$2,&5(*5"1'2&*.'/2*0%21,(-,%2&2)%&/$2,&5(*5"1'2&*.'/2*0%21,(-,%2&2)%&/$2,&5(*5"1'2&*.'/2*0%21,(-,%2&2)%&/$2,&5(*5

.'/EQK$8Q,(+1'2&*/*2'(*0%./&$,/$-*0% '0%*+*4&./&$,/$-*0%DE\BI .'/2*0%21,(-,%2&2)%&/$2,&5(*5

2/$2,((0%;T**&,$%,;*4+-&,,*$2%.2(,*%.2(

2&*($(+)1%2,:,(<.;&.'7EQK=(K

$87'2&**2(&2)%,:,(<.EQ.*/&$K*2( )12,.4+./&$,/$-*0%)%,:,(<. .7.'/EQ./&$K=(K*2( &-&*2/*- -$%&%2,:,(<.;&.'(*,$+'7DEA /92,)1'2&*/92,)1'2&*/92,)1'2&*/92,)1'2&* *'/9ZA3%.2(7+,:,(<.;;/(*5.2(&^%)+1'2&* · 2/*2(0%*/$..%2*0%5/+.*+*%=('&*%&-&%2&4&($%&22(6+5*(,,2%+*&w d]EG)aEGw)(

2(&+,)(,( ((!3+,:,(<.&^$*(+(&5*+]E( (!Gw)(E'/9ED

· :+*2)&6-&$*,)*4(*0%,5/%2-*,($2)*4(*0%2)'-+/+-*,($2).2*<&6/0%+5$+%.

2;*(3'/9E]-&,,*$2

· *-_+'+/(&$/*2'(*0%*2)';$&.4+2(&+,)(,( ((!3+,:,(<.&^$*(]E%J*J)( !,#;$&.,)(&2,;&('2&'(*0%,$2(--+',(&5*+quotesdbs_dbs11.pdfusesText_17

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