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0 degrees celsius + 0 degrees celsius -

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Re: 0 degrees celsius + 0 degrees celsius -

#72
post #62

Earlier quoted context omitted.

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 mi…

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…

Adding kinetic energies is well defined, but adding averages is not.

Re: 0 degrees celsius + 0 degrees celsius -

#73
post #72
post #62

Earlier quoted context omitted.

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…

Adding kinetic energies is well defined, but adding averages is not.

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.

Re: 0 degrees celsius + 0 degrees celsius -

#76

It looks like it must be using kelvin as its canonical units: 0C + 0C = 273.15 K + 273.15 K = 546.3 K = 273.15 C The weirdness is that conversions like that don't work for units that have different zero points. Perhaps addition of temperatures isn't really well defined? If 273.15 K + 273.15 K does not equal 0 C + 0 C, despite 273.15 K = 0 C, it's not clear what addition "means" in this context. One restricted form of…

The second result on Google for the search is now Hacker News. http://www.google.com/search?hl=en&client=firefox-a&...

I was curious about how this could happen so quickly, so I looked up the PageRank for ycombinator.com, and it's a 7 out of 10. That's a good amount of Google juice, which explains how they can so quickly rank on a keyword (and it's a very obscure keyword, so not much competition up-top).

Re: 0 degrees celsius + 0 degrees celsius -

#79
post #63

Earlier quoted context omitted.

> But then addition isn't commutative. "30 C warmer than 5 C" = 5 C + 30 C = 278.15 K + 30 K = 308.15 K = 35 C Am I missing something?

Am I missing something? Yes = 5 C + 30 C = 278.15 K + 30 K 30 C != 30 K

Exactly. The same as the OP. I'm still not catching non-commutative qualities.

Re: 0 degrees celsius + 0 degrees celsius -

#80

It looks like it must be using kelvin as its canonical units: 0C + 0C = 273.15 K + 273.15 K = 546.3 K = 273.15 C The weirdness is that conversions like that don't work for units that have different zero points. Perhaps addition of temperatures isn't really well defined? If 273.15 K + 273.15 K does not equal 0 C + 0 C, despite 273.15 K = 0 C, it's not clear what addition "means" in this context. One restricted form of…

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