Seeing as how both Celsius and Fahrenheit used silly points to calibrate their temperature-scale to, we thought we could do better. How about a scale that goes from absolute zero to absolute maximum temperature. We already know the absolute zero, this totally awesome dude named Kelvin calculated it once while high. Now how to calculate the absolute maximum?
We first took the scenic route. We all know the temperature of a particle is directly related to its velocity, and since velocity is limited by the speed of light, we can use the formulas available to calculate the temperature at the maximum velocity, namely the speed of light. The formula to calculate the kinetic energy of a particle with velocity V is as follows: K = m * c * c * ((1 / (sqrt(1-(V/c)*(V/c)) - 1). Notice how we divide V by the speed of light. If we swap V with c, we get the following: K = m * c * c * ((1 / (sqrt(1-1*1) -1) Or, in summary, we divide by zero and K reaches infinity.
What does this mean? It means while Einstein was kickin' it when he gave us a limit on speed, he also mentioned in passing that when a particle approaches light-speed, its mass becomes infinite. That's what's happening here.
That's bad. It's totally not cool to have no limit on maximum temperature. It's impractical for our scale as well. So, what to do? Well, let's try a differint approach.
Let's say we use all the energy in the universe, put it in one particle, measure its temperature and use that as the maximum temperature of our scale. It's probably good enough since it's impossible to go beyond that temperature in our universe. It's an absolute max.
Ok, so we need to calculate the amount of energy in the universe. We know the mass of the universe is 3x10^52kg, and using Einstein's famous formula E = MC^2, we calculate that there is about 3e52 * (299 792 458^2) = 2.69626554e69 joules of energy in the universe.
Good, we're that far. Now we use the following formula from kinetic theory: K = 3/2kT with k being Boltzmann constant (= 1.38066e-23 J/K) or like this: T = 2/3 * K/k so we get: (2 / 3) * (2.69626554e69 / 1.38066e-23) = 1.30192108e92 degrees Kelvin as the absolute maximum temperature in our universe.
Now we just scale 1.30192108e92° Kelvin to 100° Astix and we get our scale. Pretty cool uh?
Relix (David Verhasselt) & Astrum
19/02/07
references:
http://www.newton.dep.anl.gov/askasci/phy00/phy00054.htm Temperature Limit
http://curious.astro.cornell.edu/question.php?number=342 What is the mass of the universe?
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html Kinetic Temperature
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html#c1 Ideal Gas Law