Absurd Traditional Considerations of Temperature
Consider the measurement of the temperature of a gas, wherein a thermometer is placed into the gas. Obviously, thermal energy is transferred between the thermometer and the volume of gas, via a combination of:
1) The gas molecules physically exchanging their kinetic energy with the molecules within the thermometer through collisions with the thermometer; and
2) Thermal energy being absorbed from, and emitted into, the surrounding freespace, resulting in the exchange of thermal energy between the system and thermometer.
The net result is that the molecules within the thermometer attain thermal equilibrium with the system. Again, thermal equilibrium occurs when both the thermometer and gaseous system have an equal influx and efflux of thermal energy. Strangely, traditional thermodynamics only considers temperature in terms of a system’s kinematics. Can the above described thermal radiation [2)] simply be ignored when contemplating temperature?
Consider a vacuum. The traditional interpretation is that a matter-less vacuum possesses no molecular motion, and hence has no temperature. Strangely however, if a thermometer is placed into such a vacuum containing thermal radiation, then the thermometer obtains a temperature reading due to the exchange of thermal radiation. The molecules within the thermometer will eventually attain thermal equilibrium with the surrounding thermal radiation, although no kinetic energy exists within the vacuum.
We enter the metaphysical argument. Traditionalists argue that by putting a thermometer into the vacuum, there is a temperature associated with the thermometer but not with the surrounding vacuum. This sounds reasonable, until one realizes that the thermometer may actually be measuring the temperature of the vacuum. As an example, consider that the thermometer is put into an immense vacuum filled with thermal radiation. Although the energy associated with thermal radiation is often minute when compared to that of molecular kinematics, the fact that the vacuum’s volume is immense means the eventual thermometer’s temperature reading will be that associated with the vacuum. Furthermore, because the speed of light is so vast a significant quantity of heat can be exchanged within a vacuum even if the thermal radiation density in that vacuum remains diminutive.
Consider that the dark side of the moon being much colder than the bright side! It seems farcical that the word “cold” is used if it no longer relates to temperature. Certainly, the moon is matter hence it involves kinematics. What about a few millimeters above the moon’s surface? Does the term temperature not apply? Are we to believe that there is no thermal equilibrium between the matter on the moon and the space that surrounds it?
Clarity voids such metaphysical arguments, by saying: If a thermometer makes a measurement in a system, then that system has a temperature!
We realize that at a given temperature, systems containing matter:
1) Will tend to exchange thermal energy faster than vacuums; and
2) Will have more thermal energy than in freespace i.e. matter tends to concentrate thermal energy and hence increase the thermal energy density within a given volume.
Accordingly, for a gas the energy density of blackbody radiation tends to be significantly less than the energy density of the gas molecules, which they surround. So much so, that when calculating the total energy within a gaseous system, the energy associated with the radiation can often be approximated as being zero. Therefore, the total energy contained within a volume of gas can generally be calculated solely in terms of the gas’s molecular energies, i.e. their translational, vibrational and rotational energies. Hence we can appreciate the traditional thermodynamic approach, although we have stated that disregarding the existence of blackbody radiation will led to misunderstandings.
Copyright Kent W. Mayhew