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You're absolutely right that two different things are measured in degrees: temperatures and temperature differences. And they work as you said: you can add temp

You're absolutely right that two different things are measured in degrees: temperatures and temperature differences. And they work as you said: you can add temperatures differences, you can add a temperature difference to a temperature, but you can't add two temperatures. (This is like pointers and ints in C.) Mathematically temperature differences form a group under addition and temperatures (idealized to have no minimum temperature) form a torsor for the group. A good introduction to torsors is John Baez's Torsors made easy: http://math.ucr.edu/home/baez/torsors.html http://math.ucr.edu/home/baez/torsors.html

shasta 16y ago
Well, you can add temperatures. Temperature is defined to be average kinetic energy of particles, and addition of kinetic energies is well defined. The way Google does the addition is in this sense correct - there's a reason it's called absolute zero. The thing is that you usually don't want to add temperatures, for the same reason that you generally don't want to add other averages: they're usually not particularly interesting quantities. For this reason, you might encapsulate the definition of temperature and not expose the addition operation, but the dimensional analysis is fine the way Google does it.
- kd5bjo 16y ago
  Adding kinetic energies is well defined, but adding averages is not.
  - aphyr 16y ago
    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.

shasta 16y ago

Well, you can add temperatures. Temperature is defined to be average kinetic energy of particles, and addition of kinetic energies is well defined. The way Google does the addition is in this sense correct - there's a reason it's called absolute zero. The thing is that you usually don't want to add temperatures, for the same reason that you generally don't want to add other averages: they're usually not particularly interesting quantities. For this reason, you might encapsulate the definition of temperature and not expose the addition operation, but the dimensional analysis is fine the way Google does it.

kd5bjo 16y ago
Adding kinetic energies is well defined, but adding averages is not.
- aphyr 16y ago
  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.