Sackur-Tetrode constant
| Value | -1.15170754 — |
| Status | Measured: ± 5.00e-09 — (4.3e-09 relative) |
| Source | CODATA 2022 |
| Categories | ThermodynamicChemistry |
| part per trillion | -1,151,707,500,000 ppt |
| part per billion | -1,151,707,500 ppb |
| part per million | -1,151,707.5 ppm |
| per cent mille | -115,170.75 pcm |
| basis point | -11,517.075 bp |
| per mille | -1,151.7075 per mille |
| percent | -115.17075 % |
| ratio | -1.1517075 — |
Learning zone
The Sackur-Tetrode equation gives the absolute entropy of a monatomic ideal gas, and this constant is its dimensionless anchor: S₀/R = 5/2 + ln[(2πmukT₁/h²)^(3/2) kT₁/p₀]. At the reference state of 1 K and 100 kPa it equals −1.151 707 5; for 101.325 kPa the value is −1.164 870 5. Feed it a real atomic mass and temperature and it reproduces the measured entropy of argon to better than 0.1 %.
Otto Sackur and Hugo Tetrode derived it independently in 1912, and it is quietly remarkable: classical thermodynamics cannot fix the zero of entropy at all, and the only way to get an absolute value is to let Planck's constant set the size of a cell in phase space. A gas at room temperature, obeying no visibly quantum behaviour, still carries h in its entropy. The constant is not exact — it depends on the atomic mass constant, which since 2019 is measured rather than defined.