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I call attention (again) to the nifty paper:
Thomas A. Moore and Daniel V. Schroeder,
"A different approach to introducing statistical mechanics"
http://ajp.aapt.org/resource/1/ajpias/v65/i1/p26_s1
http://physics.weber.edu/schroeder/statmech.pdf
... especially figure 3 therein. It is a more-or-less unforgettable
way to visualize the idea that when two subsystems have reached
equilibrium by exchanging energy, they must be at the same temperature.
This follows immediately from the definition of temperature, the
definition of equilibrium, and conservation of energy.
I liked the figure so much that I made 14 more figures of the same
type, showing what happens when you change the amount of energy in
the system ... and what happens if the two subsystems are made of
different stuff, so that they have a different amount of entropy
per unit energy.
I also added some reference lines, to "guide the eye" to some of
the especially-important features on the diagrams.
My diagrams and discussion can be found at:
http://www.av8n.com/physics/ds-de-temperature.htm
There's also a brief discussion of why constants drop out. In
particular, altitude i.e. gravitational potential energy drops
out of the definition of temperature for a parcel of gas, and
drops out of the criterion for equilibrium. So yet again we
conclude that in thermal equilibrium, a tall column of gas
must be isothermal.
http://www.av8n.com/physics/ds-de-temperature.htm#sec-constants
The spreadsheet I used to create the diagrams is available.
./ds-de-temperature.gnumeric (my version)
./ds-de-temperature.xls (should work, but may require fiddling,
depending on your system details)
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