Absolute Zero0 Kelvin / Quantum Stillness
Absolute Zero – 0 Kelvin / Quantum Stillness Physics T-Shirt
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Size & fitS–5XL
Unisex heavy cotton (Gildan 5000), classic fit.
| Size | Width | Length | Sleeve |
|---|---|---|---|
| S | 18 | 28 | 15.1 |
| M | 20 | 29 | 16.5 |
| L | 22 | 30 | 18 |
| XL | 24 | 31 | 19.5 |
| 2XL | 26 | 32 | 21 |
| 3XL | 28 | 33 | 22.4 |
| 4XL | 30 | 34 | 23.7 |
| 5XL | 32 | 35 | 25 |
Measurements in inches, ±1.5 in tolerance.
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∂ The physics
The floor of temperature. Nobody stands on it.
In 1848 William Thomson, later Lord Kelvin, looked for a temperature scale that belonged to no particular substance, not mercury and not air, and found one in the theory of heat engines. In the same paper he noted that the air thermometer pointed to a floor near −273 degrees, "a point which cannot be reached at any finite temperature, however low." His first scale rested on the old caloric theory. Rebuilt on energy conservation a few years later, with James Joule, it became the scale that carries his name. Its zero is absolute zero: 0 K, or −273.15 °C exactly.
Since 2019 the kelvin has been defined by fixing the Boltzmann constant at exactly \(k_B = 1.380\,649\times10^{-23}\ \text{J/K}\). Temperature is now formally tied to energy.
Two true things about the floor. First, it cannot be reached. The third law of thermodynamics says no finite sequence of cooling steps gets there. Laboratories get extraordinarily close, and that is all. Second, even at the floor nothing would be perfectly still. A quantum oscillator's lowest energy is not zero but \(\tfrac{1}{2}\hbar\omega\), because position and momentum cannot both be pinned down. Helium makes this visible. At ordinary pressure it never freezes, however close it gets to absolute zero; its zero-point motion is too large for the atoms to settle into a crystal. Solid helium takes about 25 atmospheres of pressure.
Absolute Zero is that last motion: the part that is not heat and cannot be taken away. Everything else has stopped. They have not, quite.
Equations
| Symbol | Meaning | Unit |
|---|---|---|
| \(T\) | thermodynamic temperature | \(\mathrm{K}\) |
| \(t\) | Celsius temperature | \(\mathrm{°C}\) |
| \(E_0\) | ground-state (zero-point) energy of a harmonic oscillator | \(\mathrm{J}\) |
| \(\hbar\) | reduced Planck constant | \(\mathrm{J·s}\) |
| \(\omega\) | oscillator angular frequency | \(\mathrm{rad/s}\) |
| \(S\) | entropy | \(\mathrm{J/K}\) |
| \(S_0\) | limiting entropy at 0 K | \(\mathrm{J/K}\) |
Sources
- BIPM — The International System of Units (SI Brochure) (opens in a new tab)
- NIST — Historic Vote Ties Kilogram and Other Units to Natural Constants (2018) (opens in a new tab)
- NIST CODATA 2022 — Boltzmann constant k (opens in a new tab)
- W. Thomson, On an Absolute Thermometric Scale (Phil. Mag., Oct 1848) — transcription, Le Moyne College classic-papers archive (opens in a new tab)
- Chang & Yi (2005) The Absolute and Its Measurement: William Thomson on Temperature, Annals of Science 62, 281 (opens in a new tab)
- Encyclopaedia Britannica — Third law of thermodynamics (opens in a new tab)
- Encyclopaedia Britannica — Zero-point energy (opens in a new tab)
- Encyclopaedia Britannica — Helium (opens in a new tab)
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