Equilibre liquide / vapeur
Diagramme de phase
T(K) = 𝜃(°C) + 273,15
S y s t è m e thermodynamique = é c h a n t i l l o n m a c r o s c o p i q u e d e matière contenue dans une p or t i on donnée d’espace
Milieu extérieur
système + milieu extérieur = Univers
Surface S (réel le ou fictive), interface entre le système et le milieu extérieur
Système thermodynamique
Matière
Energie
Milieu extérieur
Système
Système ouvert
Matière
Energie
Milieu extérieur
Système
Système fermé
Matière
EnergieSystème
Milieu extérieur
Système isolé
Café dans une bouteille thermos
Liquide dans une bouteille fermée
Air dans un ballon
Bois qui brûle Eau qui
bout
Variable (ou paramètre) d’état
Grandeur macroscopique mesurable caractérisant l’état d’un système thermodynamique à un instant quelconque: pression, température, volume, quantité de matière,…
1 L d’eau à 20°C 1 L d’eau à 20°C
2 L d’eau à 20°C
Volume = grandeur extensive (dépendante de la taille du système et additive)
T e m p é r a t u r e = grandeur intensive (indépendante de la taille du système et non additive)
Grandeur extensive NotationGrandeur molaire
(intensive)Grandeur massique
(intensive)
X (grandeur générique)X (unité) X = n Xm X = m x
Xm (unité.mol-1) x (unité.g-1)
Volume V (m3) Vm (m3.mol-1) v (m3.kg-1)
Masse m (kg) M (kg.mol-1) 1
Quantité de matière n (mol) 1 (mol.kg-1)
Energie interne U (J) Um (J.mol-1) u (J.kg-1)
Capacité thermique C (J.K-1) Cm (J.K-1.mol-1) c (J.K-1.kg-1)
1
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Grandeur intensive Notation
Pression P (Pa)
Température T (K)
Equilibre thermodynamique
Toutes les variables d’état du système restent constantes au cours du temps. Il y a alors:
• équilibre mécanique ⇒ égalité des pressions du système et du milieu extérieur
• équilibre thermique ⇒ égalité des températures du système et du milieu extérieur
• équilibre de diffusion si le système (hétérogène) est diphasé qui impose une relation entre la température et la pression du système
La force pressante traduit à l’échelle macroscopique l’effet des chocs, à l’échelle microscopique, des particules en mouvement sur la paroi S séparant un fluide du milieu extérieur:
Fluide Milieu extérieur
Paroi S
�!F = P (M)S�!n
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�!n<latexit sha1_base64="2QT+hWw9RFMfrkvxXbPcTEZyKPc=">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</latexit><latexit sha1_base64="2QT+hWw9RFMfrkvxXbPcTEZyKPc=">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</latexit><latexit sha1_base64="2QT+hWw9RFMfrkvxXbPcTEZyKPc=">AAAC13icjVHLSsNAFD2N73fVpZtgUVyVRARdFty4VLC2YkUmcayDaSZMJmop4k7c+gNu9Y/EP9C/8M44BbWITkhy5tx7zsy9N8oSkesgeC15Q8Mjo2PjE5NT0zOzc+X5hYNcFirm9VgmUjUjlvNEpLyuhU54M1OcdaKEN6KLbRNvXHKVC5nu627GjzusnYozETNN1El5wW9JiivRPtdMKXnlE1kJqoFd/iAIHajArV1ZfkELp5CIUaADjhSacAKGnJ4jhAiQEXeMHnGKkLBxjhtMkragLE4ZjNgL+rZpd+TYlPbGM7fqmE5J6FWk9LFCGkl5irA5zbfxwjob9jfvnvU0d+vSP3JeHWI1zon9S9fP/K/O1KJxhi1bg6CaMsuY6mLnUtiumJv7X6rS5JARZ/ApxRXh2Cr7ffatJre1m94yG3+zmYY1+9jlFng3t6QBhz/HOQgO1qthUA33Niq1VTfqcSxhGWs0z03UsINd1Mn7Go94wrN36N16d979Z6pXcppFfFvewwda75bT</latexit><latexit sha1_base64="2QT+hWw9RFMfrkvxXbPcTEZyKPc=">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</latexit>
M Patm = 1,013.105 Pa = 1,013 bar
P° = 105 Pa = 1 bar
La température T (grandeur macroscopique) correspond à l’énergie cinétique des particules microscopiques en mouvement désordonné d’agitation thermique. T se mesure en kelvins avec:
Equation d’état = Relation entre les variables d’état d’un système thermodynamique à l’équilibre
Phases condensées indilatables et incompressibles
Système en phase liquide
ou solide
Volume molaire indépendant de la température
Volume molaire indépendant de la pression
On traduit l’indépendance du volume molaire de la température et de la pression par l’équation d’état
Vm(T, P ) = Vm0 = cste<latexit sha1_base64="J7OHUyShptWm3wlQ5JgHDF+YlvI=">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</latexit><latexit sha1_base64="J7OHUyShptWm3wlQ5JgHDF+YlvI=">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</latexit><latexit sha1_base64="J7OHUyShptWm3wlQ5JgHDF+YlvI=">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</latexit><latexit sha1_base64="J7OHUyShptWm3wlQ5JgHDF+YlvI=">AAAC4HicjVHLSsNAFD2N7/qKunQzWBQFKYkIuhEKblxWsLVQS0jGsYbmRTIRSunCnTtx6w+41a8R/0D/wjtjCj4QnZDkzLn3nJl7r5cEfiYt66VkjI1PTE5Nz5Rn5+YXFs2l5WYW5ykXDR4Hcdry3EwEfiQa0peBaCWpcEMvEKde71DFT69EmvlxdCL7ieiEbjfyL3zuSqIcc7XphGzzZJvVt9gBazqD0LGGhHgmhWNWrKqlF/sJ7AJUUKx6bD7jDOeIwZEjhEAESTiAi4yeNmxYSIjrYEBcSsjXcYEhyqTNKUtQhktsj75d2rULNqK98sy0mtMpAb0pKRnWSRNTXkpYncZ0PNfOiv3Ne6A91d369PcKr5BYiUti/9KNMv+rU7VIXGBf1+BTTYlmVHW8cMl1V9TN2aeqJDkkxCl8TvGUMNfKUZ+Z1mS6dtVbV8dfdaZi1Z4XuTne1C1pwPb3cf4EzZ2qbVXt491KbaMY9TRWsYZNmuceajhCHQ3yvsYDHvFkeMaNcWvcfaQapUKzgi/LuH8Hqy+X8w==</latexit>
Gaz parfait
Hypothèses du modèle:
• particules de gaz = points matériels • pas d’interaction entre les particules de gaz ⇒ Vm → ∞ ou
P → 0
Pression (Pa)
Volume (m3)
Quantité de matière (mol)
Constante des gaz parfaits (8,314 J.K-1.mol-1)
Température (K)PV = nRT
Gaz réel
Prise en compte des interactions entre les particules de gaz
Isothermes (T= cste) Diagramme d’Amagat
gaz réel
PV
P
T ↗gaz parfait
P
V
T ↗gaz parfait: hyperbole
gaz réel
Isothermes (T= cste) Diagramme de Clapeyron
Corps pur diphasé
C
Tr
P
T
613,3 Pa
0,01 °C = 273,16 K
SOLIDE
LIQUIDE
GAZ ou VAPEUR
Cas de l'eau
C
Tr
P
T
SOLIDE
LIQUIDE
GAZ ou VAPEUR
FLUIDE SUPERCRITIQUE
Cas général
Systèm
e diph
asé L/V
Systèm
e diph
asé L/V
Syst
ème
diph
asé
S/L
Système diphasé S/L
Systèm
e
diphas
é S/GSys
tème
diphas
é S/G
Tr: point triple Coexistence des trois phases: solide,
liquide et vapeur Intersection des trois courbes
d’équilibre diphasé
C: point critique Limite la courbe d’équilibre liquide/vapeur
P
vv vVvL
Point critique
Point d’ébullition
Point de rosée
Changement d’état sur le palier de saturation ER: T fixée impose la pression de vapeur saturante Psat = cste
• En E, le système est 100 % en phase liquide à la pression Psat: on parle de liquide saturant.
• En R, le système est 100 % en phase vapeur à la pression Psat: on parle de vapeur saturante sèche.
• En B, le système est 100 % en phase vapeur à une pression P < Psat: on parle de vapeur sèche.
• En M, le système est diphasé à la pression Psat: on parle de vapeur saturante.
★ Composition du système diphasé en M: la vapeur saturante est à w % en phase vapeur avec
Titre massique en vapeur
wE = 0 ≤ w ≤ wR = 1
w =mV
m=
mV
mV +mL<latexit sha1_base64="KUwj2AAzx2thwthcP2kJgLTCNao=">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</latexit><latexit sha1_base64="KUwj2AAzx2thwthcP2kJgLTCNao=">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</latexit><latexit sha1_base64="KUwj2AAzx2thwthcP2kJgLTCNao=">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</latexit><latexit sha1_base64="KUwj2AAzx2thwthcP2kJgLTCNao=">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</latexit>
M a s s e totale du système
Masse du système en phase vapeur
Masse du système en phase liquide
★ Volume massique du système diphasé en M:
v = vL + (vV � vL)w<latexit sha1_base64="nV3hyNAF+vrYbpSJVlYJbB+/5xk=">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</latexit><latexit sha1_base64="nV3hyNAF+vrYbpSJVlYJbB+/5xk=">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</latexit><latexit sha1_base64="nV3hyNAF+vrYbpSJVlYJbB+/5xk=">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</latexit><latexit sha1_base64="nV3hyNAF+vrYbpSJVlYJbB+/5xk=">AAAC2XicjVHLSsNAFD2Nr1pf9bFzM1iEilgSEXQjFN24cFHBPqCWkqTTGpomIZlUanHhTtz6A271h8Q/0L/wzpiCWkQnJDlz7j1n5t5rBa4TCV1/TWkTk1PTM+nZzNz8wuJSdnmlEvlxaPOy7bt+WLPMiLuOx8vCES6vBSE3e5bLq1b3WMarfR5Gju+di0HAGz2z4zltxzYFUc3sWp8dsn7zlG2zfL9Z2SG4ddXM5vSCrhYbB0YCckhWyc++4AIt+LARowcOD4KwCxMRPXUY0BEQ18CQuJCQo+IcN8iQNqYsThkmsV36dmhXT1iP9tIzUmqbTnHpDUnJsEkan/JCwvI0puKxcpbsb95D5SnvNqC/lXj1iBW4JPYv3SjzvzpZi0AbB6oGh2oKFCOrsxOXWHVF3px9qUqQQ0CcxC2Kh4RtpRz1mSlNpGqXvTVV/E1lSlbu7SQ3xru8JQ3Y+DnOcVDZLRh6wTjbyxWPklGnsY4N5Gme+yjiBCWUyfsaj3jCs1bXbrU77f4zVUslmlV8W9rDB4yClbQ=</latexit>
Gaz
Solide Liquide
Fusion
Solidification
Vaporisation
LiquéfactionSublimation
Condensation
Changements d’état
✓P +
a
V 2m
◆(Vm � b) = RT
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Equation d’état de Van der Waals
SYSTEME THERMODYNAMIQUE
A L’EQUILIBRE