In 2019 humanity stopped measuring k_B and fixed its value ── measure temperature in energy and k_B disappears
We treat "temperature" as if it were a property of a thing ── this iron is hot, that water is cold. In physics it is not a property of the thing. More than that: the quantity called temperature is surplus. Measure in energy instead. The conversion factor for doing so is \(k_B\), and since the 2019 revision of the International System of Units, \(k_B\) is no longer something we measure but something we decide ── its value is fixed by definition at exactly \(1.380649\times10^{-23}\ \mathrm{J/K}\). Bonus ② of the sister series "Cosmology That Clicks" asked "why did we fix the speed of light?"; this is the temperature version. And once temperature is converted to energy, an astonishing amount becomes visible through a single number ── at room temperature \(k_BT\approx\) 25 meV. Use 25 meV as your ruler and why ice melts but diamond doesn't, why semiconductors work, and why life is possible at room temperature all line up on one diagram.
Measure length in metres, time in seconds ── and temperature in kelvin. That is how we learn it. But temperature and length differ in one decisive way.
Temperature can simply be measured in energy. The mean kinetic energy of a gas molecule is \(\frac32 k_BT\). So the thing we call "temperature" is effectively energy. We just call it by a different unit.
This is not "a measurement of something in nature." It is the exchange rate for converting kelvin into joules ── the same kind of number as the "150" in 1 dollar = 150 yen. Which is why theoretical physics routinely sets \(k_B=1\) in the first line and writes temperature directly as an energy ── and then \(k_B\) never appears again.
On 20 May 2019 the SI was revised: the kelvin abandoned its material-based definition (1/273.16 of the triple point of water) and is now defined by fixing the value of \(k_B\). We stopped measuring and started deciding ── precisely the manoeuvre performed on the speed of light in 1983.
Look at any formula where temperature appears. If a state has energy \(E\), the probability of finding it is
The exponent contains nothing but the dimensionless ratio \(E/k_BT\). A dimensionful \(E\) or \(T\) never shows up alone. Therefore ──
"High temperature" has no absolute meaning. There is only whether \(k_BT\) is large or small compared with the energy you care about.
10,000 K is fairly hot as seen by a chemical bond (a few eV) and indistinguishable from absolute zero as seen by a nucleus (MeV). Conversely 1 K is bitterly cold to us but plenty hot for a superconducting gap (below a meV). Temperature means nothing until you name what you are comparing it with.
Put in \(T=300\ \mathrm{K}\) (about 27 °C):
$$k_BT=(1.381\times10^{-23})(300)=4.14\times10^{-21}\ \mathrm{J}$$Convert to eV (\(1\ \mathrm{eV}=1.602\times10^{-19}\ \mathrm{J}\)):
$$k_BT=\frac{4.14\times10^{-21}}{1.602\times10^{-19}}=0.0259\ \mathrm{eV}\approx \frac{1}{40}\ \mathrm{eV}=25\ \mathrm{meV}$$Memorise "room temperature = one fortieth of an eV" and everything else is mental arithmetic: \(k_BT\) at temperature \(T\) is \((T/300)\times25\ \mathrm{meV}\). When a physicist says "room temperature," the number 25 meV is what is moving in their head.
Line up the energies around you against that ruler.
| Thing | Energy | × room-temperature k_BT | At room temperature |
|---|---|---|---|
| A cosmic microwave background photon | ≈ 0.6 meV | 0.02 | lukewarm ── the universe is at 2.7 K |
| room-temperature k_BT | 25 meV | 1 | the ruler |
| a hydrogen bond (between water molecules) | ≈ 0.2 eV | 8 | breaking and re-forming ── which is why water is liquid |
| the band gap of silicon | 1.1 eV | 44 | nearly insulating, but slightly excited ── which is why semiconductors exist |
| a visible photon | 2–3 eV | 80–120 | heat will never produce one ── which is why room-temperature things don't glow |
| a C–C covalent bond | ≈ 3.6 eV | 140 | utterly unmoved ── which is why organic molecules survive |
| nuclear binding | ≈ 8 MeV | 300 million | completely frozen |
That table is the main thing this episode wants to say. One number ── "room temperature" ── and the ratio to the energy of interest is enough to decide, roughly, whether something happens. Hydrogen bonds sit at 8, so water is "almost but not quite breaking" = liquid. Covalent bonds sit at 140, so you do not decompose at room temperature. Life works at room temperature because biological interactions are arranged in exactly the sweet spot between 8 and 140.
The figure below lays various things out on a logarithmic energy axis. Move the temperature slider and the vertical \(k_BT\) line moves.
Reading it is simple ── things to the left of the line (smaller than \(k_BT\)) get broken or shaken by heat; things to the right (larger) are frozen solid. Set it to 300 K and the hydrogen bond sits just to the right of the line while the covalent bond is far away. Push to the solar surface (5800 K) and molecules start coming apart; past \(10^4\) K atoms ionise; at \(10^{10}\) K nuclei break ── which is the history of the universe played backwards.
If \(k_B\) is merely a conversion factor, all that is left is "energy." But energy alone is not temperature ── the same 1 J stored in a battery is not the same as 1 J held by a glass of water. What differs?
Temperature is not the amount of energy. It is how that energy is shared out among many degrees of freedom ── the slope of the sharing.
Nor is it "energy per particle" (a bigger system has more total energy at the same temperature). It is something more like "the eagerness to share" ── and next time we will make it stand up in front of you by tossing counters around at random. That will show at once why the form is \(e^{-E/k_BT}\), and why the real quantity is not \(T\) but \(1/k_BT\).
Established: that the 2019 SI revision defines the kelvin through the fixed value \(k_B=1.380649\times10^{-23}\ \mathrm{J/K}\); that unit systems with \(k_B=1\) (temperature expressed as energy) are widely used in theory; that the exponent of the Boltzmann factor \(e^{-E/k_BT}\) is the dimensionless ratio \(E/k_BT\); that \(k_BT(300\,\mathrm{K})=0.0259\) eV; and the energy values in the table (hydrogen bonds, silicon's 1.12 eV band gap, visible photons at 1.6–3.1 eV, C–C bond energies, ≈8 MeV binding per nucleon, typical CMB photon energies) ── all standard values.
Don't overstate it: (1) "\(k_B\) is not a constant of nature" means it is a coefficient linking dimensions, not that \(k_B\) is meaningless. Given that the kelvin is historically entrenched as an independent unit, the number is needed in practice. (2) "Anything bigger than \(k_BT\) is frozen" is a rule of thumb, not a threshold. The Boltzmann factor \(e^{-E/k_BT}\) falls off smoothly, so even at \(E/k_BT=44\) (silicon), with \(10^{22}\) particles around the number excited is far from negligible ── which is exactly why semiconductors work. The "at room temperature" column is a qualitative reading. (3) "Temperature is not a property of matter" means temperature is a state variable of a system, not a constant intrinsic to a substance. Of course "the temperature of this object" is well defined as a state. The final form of this claim ── that temperature depends on the observer's state of motion ── is Episode 7.
\(k_B\) is not a number obtained by measuring nature; it is the conversion factor from kelvin to joules, made a defined value in the 2019 SI revision ── we stopped measuring and decided. Which is why theory sets \(k_B=1\), writes temperature as an energy, and never sees \(k_B\) again.
Temperature only ever acts on physics through the dimensionless ratio \(E/k_BT\). So "high temperature" has no absolute meaning; you need something to compare with. There is one number to memorise ── room-temperature \(k_BT\approx\) 25 meV = 1/40 eV. Apply that ruler and the world lines up on one diagram: hydrogen bonds at 8× (almost but not quite breaking = liquid), silicon's band gap at 44× (nearly insulating but slightly excited = a semiconductor), covalent bonds at 140× (unmoved = biomolecules survive).
Print / make a PDF: ⌘+P (Ctrl+P on Windows). On screen, the temperature slider moves the k_BT line so you can read what breaks and what freezes. Buttons jump to representative temperatures. "See the answer" opens each solution.