MS 115a, Problem Set #9
assigned 11/28/11
due
12/2/11
will
not
be accepted late
1.
Show that the chemical potential of species A in an ideal solid solution is given by
A
=
A
o
+ RTln(X
i
)
where
A
o
is the chemical potential in the pure state.
2.
The enthalpy of mixing of a regular solution is given by
H
mix
=
X
A
X
B
, where
is a
constant that can be related to the energy parameter,
є
, of the quasichemical model of
solutions. Show that for
> O (clustering) the maximum temperature at which phase
separation occurs is given by T
max
=
/2R. Hints: (1) note that the maximum occurs at
X
A
= X
B
= 0.5; (2) note that phase separation occurs because
G
mix
has a double minima
shape at low temperature, thus it changes from positive curvature to negative curvature at
T
max
.
3.
The metallic elements A and D form a solid solution at room temperature. On cooling,
phase separation occurs and the critical temperature, T
max
, is 245K. What is the difference
between the energy of AD bonds and the average of the AA and DD bonds?
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 Fall '09
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 Thermodynamics, Solubility, Gibbs

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