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Information • Textbooks • Media • Resources
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JCE WebWare: Web-Based Learning Aids
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The Relation of Temperature to Energy Spreadsheet
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Christopher King
Department of Chemisry, Troy State University, Troy, AL 36082
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April 2005
Vol. 82 No. 4
p. 656
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| Abstract |
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Thirty years ago (when some of us took physics) some physics textbooks described
temperature as a “fundamental indefinable”: something, like length,
time, or mass that could not be expressed in terms simpler than itself (1).
In fact, temperature can be expressed in “simpler” terms: the relation
between temperature, energy, and the properties of a material is well developed
(2). Yet, this relation is not clearly elaborated in most physical chemistry
textbooks. However, these relationships can easily be included in the early
part of a physical chemistry course on thermodynamics, and this interactive
Excel spreadsheet can help.
The spreadsheet actually contains 14 individual worksheets. Many include interactive
figures—changing the input parameters changes the respective graphs.
See Table 1 for a description of each included sheet; the first three and the “Heat
Capacity” sheet are all that are required for presenting the basic concept
of temperature. Other sheets develop additional concepts for more advanced
study.
Table 1. Decription of the Individual Worksheets in The Relation of Temperature to Energy Spreadsheet
| Sheet |
Description |
| Intro |
Provides
introductory figures and information |
| Harmonic
Osc. |
Shows
that temperature is the slope of
a plot of entropy heat transferred. |
| Same
Temp. |
Shows
that what two objects at the same
temperature have in common is the
slope of a plot of entropy vs. heat
transferred. |
| Large
Systems |
The
determination of the lowest possible
non-zero temperature for a large
system. The gamma function
and the Stirling approximation
are presented. |
| Harmonic
Osc. Ave |
Same
as the “Harmonic Osc.” sheet,
except an average is used to determine
temperatures. |
| Large
Systems, Ave. |
Same
as the “Large Systems” sheet,
except an average is used to determine
temperatures. |
| Heat
Capacity |
Compares
experimental and calculated heat
capacities of N2. Also
uses Excel’s built-in Solver
tool to find the best parameters
for the Shomate equation. |
| Einstein
Heat Cap. |
Applies
the harmonic oscillator model to
a solid. The Einstein temperature
can be varied to find the best
fit to the heat capacity of silver
metal. |
Mystery
Heat Cap. 1 and
Mystery Heat Cap. 2 |
The
user identifies a gas from its
heat capacity data by varying the
separation between energy levels. |
| Cv
Examples |
Presents
the heat capacities, Cv,
both experimental (Shomate equation)
and calculated (harmonic oscillator
model) of 17 different diatomic
molecules. The user can add data
for additional molecules. |
| 2-level |
Presents
the temperature of a two-level
system, which can be negative. |
| 2-level
large |
Extends
the “2-level” sheet
to handle systems with large numbers
of particles. |
| Appendix |
A brief
discussion about deriving temperature
as a function of internal energy. |
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Literature Cited
- Sears, F. W.; Zemansky, M. W.; Young, H. D. University
Physics, 5th ed.; Addison-Wesley: Reading, MA, 1978, p 265.
- Moore, T.
A.; Schroeder, D. V. Am. J. Phys. 1997, 65, 26–36.
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| Supplement |
The
Relation of Temperature
to Energy Spreadsheet ia available in the JCE WebWare
peer-reviewed collection of the JCE Digital
Library Only@JCEOnline.
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| More Information |
 Citation |
King, Christopher. J. Chem. Educ. 2005 82 656.
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Keywords |
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History |
Created:
Last Updated: |
March 4, 2005
March 14, 2005
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