Thirty years ago (when
some of us took physics) some physics textbooks
described temperature as a “fundamental
indefinable”: something, like length,
time or mass, which 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.
Figure
1. A screen shot from the "Harmonic OSC."
worksheet of The Relation of Temperature
to Energy Spreadsheet.
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. A description of the individual worksheets
included 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.
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.
