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Chapter 8: Thermodynamics
37
8.9
Thermodynamic potential
When the number of particles within a system changes this number becomes a third quantity of state. Because
addition of matter usually takes place at constant
p
and
T
,
G
is the relevant quantity. If a system exists of more
components this becomes:
dG
=

SdT
+
Vdp
+
±
i
μ
i
dn
i
where
μ
=
²
∂
G
∂
n
i
³
p,T,n
j
is called the thermodynamic potential. This is a
partial quantity
. For
V
holds:
V
=
c
±
i
=1
n
i
²
∂
V
∂
n
i
³
n
j
,p,T
:=
c
±
i
=1
n
i
V
i
where
V
i
is the partial volume of component
i
. The following holds:
V
m
=
±
i
x
i
V
i
0=
±
i
x
i
dV
i
where
x
i
=
n
i
/n
is the molar fraction of component
i
. The molar volume of a mixture of two components
can be a concave line in a
V

x
2
diagram: the mixing contracts the volume.
The thermodynamic potentials are not independent in a multiplephase system. It can be derived that
∑
i
n
i
dμ
i
=

+
, this gives at constant
p
and
T
:
∑
i
x
i
dμ
i
=0
(GibbsDuhmen).
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 Spring '10
 Ye
 Thermodynamics

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