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
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
