I'm trying to find a analytical expression that describes the pressure-temperature function. The function that I want to describe is the pressure-temperature function where the water is in liquid state, as shown in this log-linear scaled figure:
https://upload.wikimedia.org/wikipedia/commons/0/08/Phase_diagram_of_water.svg
My target is: for each temperature,pressure, check if with that parameters water is in liquid state. I tried to compute approximately the function by fitting (by using Matlab, trying interpolation, using cftool and trying to improve the approximation) but I think that my result is wrong. On Matlab I gave vectors of temperature (Kelvin) and pressure (Pascal) and the best approximation characteristic that passes through points is described by:
$y=a \cdot e^{(b \cdot x)}+c \cdot x^6$
where a,b and c are respectively: [$3.51 \cdot 10^{30}$; $0.1092$; $0.208245204973289$].
I thought that, to see if a point(temperature,pressure) is in liquid state of water diagram, I must verify $y - a \cdot e^{(b \cdot x)}+c \cdot x^6 > 0$
I assumed that, since I don't overcome the critical point, the maximum temperature is 647 K, and I assumed that the maximum pressure is about 2000 atm ($2,0265 \cdot 10^8$ Pa).
Where did I wrong? Is there a better way to describe the function of the pressure-temperature characteristic and check if a given point (temperature,pressure) is in liquid state diagram (always in mathematical way)?
Thank you in advance