Sackur-Tetrode constant

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[(2πm_ukT₁/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.