What the what? Averages over kinetic energies are summations. Adding them is well-defined and has a straightforward interpretation as the average energy per particle.
Formally, temperature is defined as
T = 1/(\partial(S)/\partial(E)) with fixed external parameters volume, particle count, etc.
where S is the entropy of the system and E is its total energy.
Playing fast and loose with words, as you pump energy into a system, if it becomes chaotic slowly, you're at high temperature. If it becomes chaotic quickly, you're at low temperature.
Much of the difficulty involved with calculating temperatures comes from the fact that we chose the inverse of that partial to be "temperature"--which means that you cannot add temperatures for most systems together and negative absolute temperatures are "hotter" than positive ones, (yes, Cindy, you can experimentally obtain systems below absolute 0 :)).
However, it is usually possible to calculate the thermal equilibrium of the system, which would be an excellent "average" temperature.
Formally, temperature is defined as
T = 1/(\partial(S)/\partial(E)) with fixed external parameters volume, particle count, etc.
where S is the entropy of the system and E is its total energy.
Playing fast and loose with words, as you pump energy into a system, if it becomes chaotic slowly, you're at high temperature. If it becomes chaotic quickly, you're at low temperature.
Much of the difficulty involved with calculating temperatures comes from the fact that we chose the inverse of that partial to be "temperature"--which means that you cannot add temperatures for most systems together and negative absolute temperatures are "hotter" than positive ones, (yes, Cindy, you can experimentally obtain systems below absolute 0 :)).
However, it is usually possible to calculate the thermal equilibrium of the system, which would be an excellent "average" temperature.