A 1913 Physics Idea Finally Explains Why Industry's Fluid Equations Work

Engineers designing distillation columns, refrigeration systems and natural-gas plants rely on equations of state — mathematical tools that predict how a fluid's volume changes with temperature and pressure. Since the 1970s, widely used versions such as the Soave-Redlich-Kwong and Peng-Robinson equations have improved accuracy using a mathematical structure developed largely through trial and error, without a clear physical explanation for why it worked so well.

Dr. Jai-Yeop Lee of the Korea Institute of Civil Engineering and Building Technology (KICT) has now traced that structure to a little-known 1913 idea by Dutch physicist Hugo Tetrode, who described fluids as collections of vibrating oscillators rather than freely moving particles. By adding a new parameter based on Tetrode's vibrational correction, Lee showed the familiar structure is not arbitrary — it is the minimal form that reduces correctly to the ideal-gas law at low density, stays solvable as a simple cubic equation, and stays flexible enough to reproduce each substance's real behavior near its critical point. The work is published in the journal Chemical Engineering Science.

The new equation was tested against high-accuracy reference data for 76 fluids, from simple gases like argon and methane to strongly interacting substances like water and ammonia. Using only each substance's basic properties, with no extra adjustable corrections, it achieved the lowest average error — 4.0% — in predicting liquid volume, versus 4.6% to 13.7% for four widely used existing equations.

The new parameter also carried real physical meaning: its size grew steadily from weakly interacting fluids like argon to strongly interacting ones like water, tracking the strength of molecular interactions, and it grouped the 76 fluids into four distinct chemical families. "Modern cubic equations of state are extraordinarily useful, but part of their success has rested on empirical mathematical structure rather than physical understanding," Lee said, adding that the more transparent method could also help design chemical processes for hydrogen energy, carbon capture and clean-ammonia fuels.