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Unformatted text preview: , in the form of
what we call “heat”. Intimate mechanical contact (i.e. touching) usually works fine, but even if the objects
are separated by empty space, they can “radiate” energy to each other in the form of electromagnetic
waves. If you want to prevent two objects from coming to thermal equilibrium, you need to put some kind
of thermal insulation in between, like spun fiberglass, the double wall of a thermos bottle, or Aerogel.
Even then, they’ll eventually come to equilibrium; all you’re really doing is increasing the relaxation
The concept of relaxation time is usually clear enough in particular examples. When you pour
cold cream into hot coffee, the relaxation time for the contents of the cup is only a few seconds. However,
the relaxation time for the coffee to come to thermal equilibrium with the surrounding room is many
The cream-and-coffee example brings up another issue: Here the two substances not only end up
at the same temperature, they also end up blended with each other. The blending is not necessary for
thermal equilibrium, but constitutes a second type of equilibrium –diffusive equilibrium—in which the
molecules of each substance no longer have any tendency to move one way or another. There is also
mechanical equilibrium, when large-scale motions (such as the expansion of a balloon) can take place
but no longer do. For each type of equilibrium between two systems, there is a quantity that can be
exchanged between the systems:
Particles Type of equilibrium
Diffusive Notice that for thermal equilibrium, we’re claiming that the exchanged quantity is energy.
When two objects are able to exchange energy, and energy tends to move spontaneously from one
to the other, we say that the object that gives up energy is at a higher temperature, and the object that
absorbing energy is at a lower temperature. With this convention in mind, we can restate the theoretical
definition of temperature:
Temperature is a measure of the tendency of an object to spontaneously give up
energy to its surroundings. When two objects are in thermal contact, the one that tends
to spontaneously lose energy is at the higher temperature.
Meanwhile, we still need to make the operational definition of temperature (what you measure with a
thermometer) more precise. How do you make a properly calibrated thermometer, to get a numerical
value for temperature?
Most thermometers operate on the principle of thermal expansion: Materials tend to occupy more
volume (at a given pressure) when they’re hot. A mercury thermometer is just a convenient device for
measuring the volume of a fixed amount of mercury. To define actual units for temperature, we pick two 2 convenient temperatures, such as 0 and 100. We then mark these two points on our mercury thermometer,
measure off a hundred equally space intervals in between, and declare that this thermometer now
measures temperature on the Celsius (or centigrade) scale, by definition!
Of course it does not have to be a mercury thermometer; we could instead exploit the thermal
expansion of some other sub...
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This document was uploaded on 03/20/2014 for the course PHYS 215 at Lafayette.
- Fall '09