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

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.