Chemistry 350 .
.. Winter 2011
Problem Set
#
1
R.J. Le Roy
Due: Monday, January 24
Submit STAPLED Solutions in Class
or
to my oﬃce (ESC332) by 5:00 PM
1. Evaluate the ﬁrst derivative with respect to
x
of each of the functions:
a)
sin(3
x
)
e
2
x
2
b)
cos
(3
x
)
e
2
x

e

2
x
c)
(7
x
2
+ 3
/x
)
π
d) [ sin(3
x
) ]
2
x
2. We will see later in the course that the
equation of state
of a substance (the expression which
interrelates allowed values of the macroscopic variables
P
,
V
,
T
and
N
) and the thermodynamic
internal energy
U
are related to the “total system partition function”
Q
by the expressions:
P
=
k
B
T
±
∂
ln
Q
∂V
²
N,T
and
U
=
k
B
T
2
±
∂
ln
Q
∂T
²
N,V
where
k
B
is Boltzmann’s constant. Assuming the following expression for the total partition
function for an
N
particle sample of a gas of atoms of mass
m
at temperature
T
and volume
V
:
Q
(
N,V,T
) =
1
N
!
±
2
π mk
B
T
h
2
²
3
N/
2
[
V

Nb
]
N
e
aN
2
/V k
B
T
in which
a
and
b
are constants characterizing the gas and
h
is Planck’s constant.
(a) Using the above equation for
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This note was uploaded on 09/28/2011 for the course CHEM 350 taught by Professor Prof.djasd during the Winter '10 term at Waterloo.
 Winter '10
 Prof.Djasd
 Chemistry

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