Summary Thermodynamics 2

Summary Thermodynamics 2
Formulae

PV =nRT =NkT perfect gas

3 3
U = nRT = PV perfect atomic gas
2 2


dU =dQ+dW First Law for reversible and irreversible processes

dW =−Pext dV +dW ' W ' is non-volume work
dU =TdS−PdV only volume work




πT =( ∂∂VU ) T
internal pressure


1 ∂V
α= (
V ∂T )
expansion coefficient
P


−1 ∂ V
V ( ∂T )
κ =
T isothermal compressibility
P




CV= ( ∂Q
∂T )V
=(
∂U
∂T ) V
heat capacity at constant volume


3
C V = nR perfect gas
2

CP= ( ∂∂TQ ) =( ∂∂HT ) = 52 nR
P P
heat capacity at constant pressure


5
C P = nR perfect gas
2


dQrev
dS= Entropy
T
d S tot =dS +d S sur ≥0 Second Law for spontaneous processes in closed systems

dQ
dS ≥ Clausius inequality (T b is boundary temperature)
Tb

S ( T =0 ) =0 Third Law




1

, H=U + PV Enthalpy

dH =TdS+VdP
A=U−TS Helmholtz free energy

dA=−PdV −SdT
G=H −TS Gibbs free energy

dG=VdP−SdT




W max =(∆ A ¿T )

W ' max =(∆ G ¿ P ,T )


∆ H fus=T fus ∆ S fus equilibrium at melting point

∆ H vap=T vap ∆ Svap equilibrium at boiling point




dU =( ∂∂UV ) dV +( ∂∂TU ) dT
T V


∂U ∂U
dU =( ) dS+ (
∂V )
dV
∂S V S




( ∂∂ gy ) =( ∂∂ hx )
x y
Maxwell relation for df =gdx+hdy



( ∂∂TV ) =−( ∂∂ PS )
S V
Maxwell relation for U




F=C−P+2 Gibbs phase rule




( ∂∂Tμ ) =−S
P
m




( ∂∂ μP ) =V
T
m




V m(l ) ∆ P
p= p ¿ ∙ exp ⁡( ) effect of applied pressure ∆ P on vapour pressure p
RT

2