Equation of State of Liquid Water Written by Simple Experimental Polynomials and the Liquid–Liquid Critical Point

Abstract

Experimental and theoretical evidence has been accumulating to support the liquid-liquid critical point (LLCP) hypothesis for water. However, no agreement has yet been reached on the pressure and temperature of LLCP. Here we made simple experimental equations that reproduced the volume of liquid water measured over a wide pressure-temperature range. They were polynomials that calculate pressure using volume and temperature as variables, and coefficients were determined by the method of least-squares. We analyzed the polynomials by changing the volume data and the number of terms in the polynomials and extrapolated them slightly to low temperatures. Consequently, the available experimental volume of liquid water indicated (but did not prove) the existence of LLCP at low temperature. Representative polynomials suggested that LLCP locates around 105 ± ∼ 9 MPa, 207 ± ∼ 5 K, and 0.993 ± ∼ 0.009 cm3/g.