Water's Unexplained Properties

Vapor pressure curves
Pressure-density relationship
Temperature-volume change relationship
Temperature-viscosity relationship

There are several properties of water that do not constitute anomalies but are still remarkable. Until they are fully explained, they may be considered to be the result of coincidences. These unexplained properties will be described on this page.

Vapor pressure curves

There are many formulations giving the vapor pressure of ice^a and water over various temperature ranges, mostly involving many empirical parameters. However, the following approximate formulae are curious and give approximately straight-line Log-Log plots of integral gradients 12, 8 and 4 with only physically meaningful parameters. The points are experimental data [70 ] and the lines show the equations (T is the scaled temperature given in the power expressions, see later, and the LogT values have been shifted so that the LogP values show a continuous function).

vapor pressure of water and ice with 'reduced' temperature, showing three approximate power laws, 12th over ice, 8th over water (-15C - 100C) and 4th over water (above 100C)

The vapor pressure of ice is approximately given by the following relationship between pressure (atm) and temperature (K). T₀ is 126 K which is approximately the temperature for the phase change between glassy amorphous ice and deeply supercooled amorphous water (136 K; the glass transition temperature). Bpt and Mpt are the boiling point and melting points of water.

P=((T-T0)/(Bpt-(Mpt-T0))^12

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The vapor pressure of water (-15°C - 100°C) is approximately given by the following relationship between pressure (atm) and temperature (K). T₁ is 162 K which is approximately the temperature for the phase change between glassy amorphous water and cubic ice (160 K).

P=((T-T1)/(Bpt-T1))^8

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The vapor pressure of water (100°C - 374°C, Critical point) is approximately given by the following relationship between pressure (atm) and temperature (K).

P=((T-Mpt)/(Bpt-Mpt)^4

I am grateful to Frank Grimer for pointing me at these relationships. [Back to Top ]

Pressure-density relationship

The density of liquid water tends towards an integral 6^th power relationship with respect to pressure.

where P is the pressure (MPa), P₀ is 378 MPa, T is the temperature (K), T₀ is 85 K and ρ is the density (g/mL).

This relationship is shown below (P' is the scaled pressure, that is, the left side of the above expression) as the dashed lines, with the colored lines being the experimental data. The lines for 20°C - 60°C fit well but the power increases from 6 at lower and higher temperatures. The best fit is thus around the compressibility minimum at 46.5°C. The extrapolated density at zero T and P is 1.28 g/mLl which is close to the density for very high density amorphous ice (1.25 g/mL) with P₀ and T₀ being close to the conditions required for its formation.

densities of water tend towards a 6th power law dependent on temperature and pressure

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I am again grateful to Frank Grimer for pointing me at this relationship. [Back to Top ]

Temperature-volume change relationship

The incremental volume change increases as the square-root(3) power of the temperature above the temperature (T₀, 3.984°C) of minimum volume (V₀, 1.00003 mL/g)

((V-V0)/V0)=0.272x((T-T0)/T0)^sqrt(3)

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as shown below, where the solid blue line follows the experimental data and the dashed yellow line shows the above equation.

Volume change increases as the square-root(3) power of the temperature

The square-root(3) term is related to the Vesica Pisces, being the ratio of the long to short diameter of intersecting expanded icosahedral water clusters (the short diameter being the distance between the centers of neighboring dodecahedra and the long diameter associated with a plane of water molecules between the two pentameric boxes (Figure 3h) joining them.

I am again grateful to Frank Grimer for showing me this relationship. [Back to Top ]

Temperature-viscosity relationship

The dynamic viscosity varies with the temperature above a baseline temperature, viscosity = (T-T₀)^-1.637 for H₂O and viscosity = (T-T₀)^-1.623 for D₂O; where T₀ = 225.4 for H₂O and 231.9 for D₂O, both these values being close to the respective homogeneous nucleation temperatures. The exponents are close to the golden mean, (1+√5)/2 (= 1.618).

log(T-T0) vs log(viscosity) data

In the graph above, H₂O values are shown by green squares and D₂O values are shown by blue diamonds. The red line is y = (T-225.4)^-1.632 for guidance. [Back to Top ]

Footnotes

^a A discussion of the vapor pressure of ice over its entire range is available [1099 ]. [Back]