Lab 9: Entropy
Performed On:
03/09/2012
Due On:
03/30/2012
Names:
Brian Wilhelm
Andy Gutting
Weston Wands
Brian Cosey
David Bonsaver
Contributions:
See Appendix B
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In this lab analysis was applied to the results of a chance situation involving 18 two
sided, wiggleeyes which had a total of 19 possible macrostates and 262,144 microstates.
The dispersal of microstates in a metaanalysis of data from six experiments was
observed to show that the most likely macrostate was the one with the highest number of
possible microstates (and highest entropy); this was determined to be the macrostate with
9 “up” wiggly eyes and 9 “down” wiggly eyes.
ΔE was determined to be 2.384x10
22
,
which is negligibly close to zero and demonstrates a solid and accurate representation of
actual statistical probability and entropy by the experiments completed.
Introduction:
There are two methods through which one can approach entropy: the thermodynamic
definition and the statistical definition.
In this case the statistical definition was used to
evaluate the entropy of the experimental system.
Basic information that was necessary to
begin this analysis included finding the number of macrostates and microstates.
Although wiggly eyes were used in this lab, each was essentially equivalent to a coin flip
(two sides and two possible outcomes).
Determining macrostates can then be done using
the following equation:
(1)
Here
N
is the number of wiggly eyes present.
Determining microstates also involves
N
as
well as the number of possible states for each wiggly eye.
Since there are two possible
states for each wiggly eye (up or down), the total number of microstates will be
determined by:
(2)
If we let
n
equal the number of wiggly eyes that are facing up in a particular macrostate
(and therefore
Nn
will be the number of wiggly eyes facing down), we can arrive at the
probability of that particular macrostate:
(3)
Here
u
is the simply the probability of a wiggly eye being face up and
d
the probability of
a wiggly eye being face down.
Thermodynamics states that the probability of each
microstate is technically equal.
However, the energy of that microstate can vary and this
energy determines the actual probability of the occurrence of that microstate.
22
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 Spring '08
 Treacy
 Statistics, Entropy, wiggly eyes

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