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## Sample Document Text

Chemistry 360
Fall 2008
Dr. Jean M. Standard
Sample Final Exam - Solutions
(150 points)
1.) (13 points) Consider an equation of state for a gas given by
P V
m
?b
( )
= RT
,
where b is a constant. Starting from the definition of work,
w = ? P
ext
dV
?
, derive an
expression for the work done in a reversible isothermal expansion from V
1
to V
2
at
temperature T for one mole of gas.
We start with the basic definition of work,
w = ? P
ext
dV
?
.
Since the process is reversible,
P = P
ext
, which gives
w = ? PdV
?
.
We now need an equation for P for the gas. Solving the equation of state for P yields,
P =
RT
V
m
?b
=
nRT
V ?nb
.
Substituting this relation for P gives the work,
w = ?
nRT
V ?nb
dV
?
.
Since the process is isothermal, T can be pulled out of the integral along with the other constants to yield
w = ?
nRT
V ?b
dV
?
= ? nRT
1
V ? nbV
1
V
2
?
dV
w = ? nRT ln
V
2
? nb
V
1
...

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