differentielle.py

Created by alten01

Created on May 05, 2025

525 Bytes

dU=dQ-pdV
dQ=dU+pdV
dQ=TdS
TdS=dU+pdV => dS=dU/T + p/T dV

dU = (dU/dT)V dT+(dU/dV)T dV
Cv(V,T) = (dU/dT)V dT 
dU = Cv(V,T) + (dU/dV)T dV 

et en reinjectant
dS=Cv/T dV+1/T(dU/dV)T dV+p/TdV 

U et S sont des fonctions 
d’état. On peut donc écrire leurs 
différentielles totales en fonction 
de leurs variables naturelles

U = U(T,V)
dU = (dU/dT)V dT+(dU/dV)T dV
Cv(V,T) = (dU/dT)V dT 
dU = Cv(V,T) + (dU/dV)T dV 

S = S(T,V)
dS = (dS/dT)V dT+(dS/dV)T dV
l(V,T) = (dS/dT)V 
dS = l(V,T) + (dS/dV)T dV

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