Beside the obvious benefit of confusing the public and colleagues in other fields, the apparent chaotic use of physical units like keV and Kevin has an addictive convenience beyond a simple matter of convention. Yes, I said “convenience”.

All roads to Rome, All quantities to Energy

In fact, mixing up the units of the physical quantities doesn’t end with energy and temperature.  If I am the one breaking this to you, then I am terribly sorry, but the plague has already spread to pretty much all the physical quantities.

Energy = Temperature = Mass = Length = Time = …

So, there you have it: Energy costs Money since Time is Money.

At the center of this pandemic, you find “energy”, which seems to be the culprit, linking all of them together. Although, once they are all linked, it doesn’t really matter. This appears a gross misuse or misunderstanding of these quantities at best. Now what drives “normal” physicists to become “keV” junkies if there is such a thing called normal physicist? Well, the answer is already in vlk’s slog about “keV vs keV”.

Ice, Water or Vapor

Do you know what it feels like at T=200 K, T=300 K or T=400 K?

Of course, it’s a matter of being frozen to death, being comfortable under the sun shine or being burnt to death.

Ok, then, now how about T=10,000 K, 10,000,000 K, or 10,000,000,000 K?

Hmm, hmm, interesting. Very hot, extremely hot, and hellish hot? I know I will be dead either way.

A shear number of zeros is already annoying and begging for another unit or a shorter form, but more importantly, it seems that we, … I mean, normal human beings don’t really have a good “physical” feel of Kelvin, Celsius or Fahrenheit at these high temperatures. Why should we? After all, we use Celsius or Fahrenheit for the daily use, and it’s not like that we need to burn and destroy T1000 to save the humanity everyday. Even so a couple of 1000 K heat might do the job.

Ok, ok, Let me think for a moment for change.  Judging from a factor of 1000 differences which is a lot more than 100, there’s got to be equally significant differences in the matter at these temperatures. Perhaps changing-their-physical-state kind of differences?

Hmm, only if we have an easy way to express the state change or a unit to convey the essence of their differences. A-ha, yes, yes, I knew it’s not our fault, our ignorance or lack of our knowledge.  It’s the useless unit here that keeps us in the dark. The unit is good at around, say, less than 1000 C.  Just like T=0 C means ice to water and T=100 C means water to vapor.  More than that, this K, C, or F is so useless.

De Nile isn’t just a river in Egypt, and it flows in our mind too, quite beautifully I suppose.

Wait a minute, there are more states than solid, liquid and gas?

1 [eV] ≡ 1.6021892 · 10^-19 [Joule] ≡ 1.6021892 · 10^-12 [erg] .

The confusion is because the same units are used to denote two separate quantities which happen to have similar magnitudes for a commonly encountered spectral model, Bremsstrahlung emission.

1. the frequency ν, or wavelength λ, of a photon: As Planck discovered, the energy of a photon is directly related to the frequency ν,
   

   E = h · ν ≡ h · c / λ ,

   where h=6.6261760 · 10^-27 [erg s] is Planck’s constant and c=2.9979246 · 10¹⁰ [cm s^-1] is the speed of light in vaccum. When λ is given in [Ångström] ≡ 10^-8 [cm], we can convert it as

   [keV] = 12.398521 / [Å] ,

   which is an extraordinarily useful thing to know in high-energy astrophysics.

2. the temperature T of a gas or plasma: Here we look to thermodynamics, which relates the kinetic energy of random motion of particles in a gas to a gross property, the temperature of the gas,
   

   E = k_B · T ,

   where k_B = 1.3806620 · 10^-16 [erg K^-1] is Boltzmann’s constant. Then, a temperature in degrees Kelvin can be written in units of keV by converting it with the formula

   [keV] = 8.6173468 · 10^-8 · [K] ≡ 0.086173468 · [MK] .

It is tempting to put the two together and interpret a temperature as a photon energy. This is possible for the aforementioned Bremsstrahlung radiation, where plasma at a temperature T produces a spectrum of photons distributed as e^{-h ν / k_B T} and it is possible to tie the temperature to the photon energy at the point where the numerator and denominator have the same numerical value. For example, a 1 keV (temperature) Bremsstrahlung spectrum extends out to 1 keV (photon energy). X-ray Astronomers use this as shorthand all the time, and it confuses the hell out of everybody else.