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=">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</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

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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

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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:

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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