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Chemistry 452
July 24, 2009
Enter answers in a Blue Book
Midterm Examination Key
Useful Constants:
•
1 Newton=1 N= 1 kg m s
2
•
1 Joule=1J=1 N m=1 kgm
2
/s
2
•
1 Pascal=1Pa=1N m
2
•
1atm=101325 Pa
•
Universal Gas Constant R=8.31 J K
1
mol
1
=0.0821L atm K
1
mol
1
•
Avagadro’s Number N
A
=6.024x10
23
mol
1
All answers must be in MKS units (i.e. units of meters, seconds, kilograms, Joules,
Pascals etc.)
Part 1 (18 points) Answer THREE out of the following SIX questions. Limit
definitions to less than 200 words. Use equations where helpful or required, but
detailed calculations are not necessary.
Question 1.1
. Define Euler’s Criterion for Exactness. Explain how this rule is relevant to
the field of thermodynamics.
A differential,
()
,,
M xyd
x N xyd
y
+
is exact if there exist a function Z(x,y) such that
y
x
ZZ
dZ
dx
dy
M x y dx
N x y dy
xy
⎛⎞
∂∂
=+=
+
⎜⎟
⎝⎠
. The criterion for exactness is
therefore
2
M
NZ
yx
x
y
∂∂∂
==
∂
∂
. The path integrals of exact differentials are dependent only
on the initial and final states of the path, not on the details of the path itself. Differentials
of state functions are exact so when integrated over specific paths, the state function
change is dependent only on the definitions of the initial and final states. (74 words)
Question 1.2
. The entropy has been defined as “time’s arrow”. Explain this definition
using thermodynamic reasoning. Utilize in your argument the statistical interpretation of
entropy.
The equations of mechanics (F=Ma) are time reversible. This means they are as valid
going forward in time as going backwards. In contrast, the entropy of an isolated system
increases from initial to final state, or remains the same. The final state is understood to
be reach later in time, so moving toward the final state is marked by increased entropy.
The reversal of mechanics in an isolated system , which in turn would decrease the
entropy is not impossible, but is nevertheless a
highly improbable event. (87 words)
Question 1.3
What is the Law of Dulong and Petit for an atomic crystal? Explain this law
in terms of the mechanical motions of the atoms in the crystal.
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View Full Document The heat capacity of an atomic crystal approached 3R as the temperature increase. This
behavior results because at high temperature a atomic crystal obeys the equipartition
theorem, which distributes energy equally among mechanical degrees of freedom. Each
atom is a three dimensional oscillator, with two degrees of freedom per dimension, or six
in all. The heat capacity is thus expected to be: 6x3R/2=3R, as stated by the DulongPetit
Law. (69 words)
Question 1.4
Explain the concept of reversibility as it applies to thermodynamic
pathways.
A system is displaced from its initial state by application of an infinitesimal force. The
system is allowed to reequilibrate before further application of the force. Thus the
system’s path consists of a sequence of equilibrium states separated by these small
displacements and any step can be reversed by application of an infinitesimal force.
The
equation of state is valid along a reversible path. (64 words).
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This note was uploaded on 10/26/2010 for the course CHEM 452 taught by Professor Khalil during the Summer '08 term at University of Washington.
 Summer '08
 KHALIL
 Chemistry

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