ChE 485 STATISTICAL MECHANICS AND THERMODYNAMICS

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ChE 485
Mid
-
Term Spring 2012

Feb. 23, 2012



1.

Write your

favorite


form for the stability matrix for a binary fluid using the
potential
. Transform

to

and now write a
nother form for the stability matrix. In both cases at a limit of
stability what are the conditions on these matrices?

(20)







2.

The compressibility
and expansivity
of a pure fluid are given by the
foll
owing definitions:





Prove the following thermodynamic i
dentity
:





If you calculate the isot
hermal entropy change for a gas

as it expands from

to
using this equation and the virial equation truncated after the
B

term, what condition
must
B

have so that this entropy change is
0?

(35)




3.

What is the condition on
B

for the virial equation
,

truncated after the
B

term
,

to

ensure a stable single phase for a pure fluid? Can this same equation of state
predict a phase transition? If not, why not?

(20)


4.

If you had to get the virial coefficients

B

and
C

for a pure fluid by comparing it to
the VDW equation of state what would b
e the correspondence between the pure
component parameters in both models. [Hint: The identity

might come in useful].

(25)