The following section continues the analysis started in previous posts. =========================================== With reference to the volume change versus temperature relation shown in the third Figure on the page at.....
http://www.lsbu.ac.uk/water/strange.html#tv ......I now realise that Vesica Pisces is a bit of a red herring (pun intended) and that from a mechanics point of view [though not perhaps from a mystical pov ;-) ] there is a more revealing way of expressing this relation. The Vesica Pisces (VP) relation on Professor Chaplin's web-site is, V = a constant.(T)^(sq.rt 3) where V is the volume increase above the volume at 4 degrees Centigrade T is the temperature degrees above 4 deg C. Since, for practical purposes the specific heat of water is constant between 4 and 100 deg C we can substitute the variable Energy (E) for temperature in the above equation. V = a constant.(E)^(sq.rt 3) But V = L^3, so substituting for V and squaring both sides gives, L^6 = a constant.(E)^3 Taking the cube root of both sides gives, L^2 = a constant.E But L^2 (more specifically dL^2) is a linear strain energy epsilon squared, i.e. a one dimensional strain energy. How does this fit in with what has gone before in previous posts in this thread? I am delighted to say it fits like Cinderella's slipper. 8-) Allowing the volume of water to expand by lowering the Compreture (increasing the temperature} leads to a three-dimensional strain-energy requirement by the quasi-Solid phase (the molecular cell phase) in relative compression. But two of these strain- energy dimensions are provided by the compression of the quasi-Fluid two-dimensional phase in relative tension. This leaves a one-dimensional strain energy to be provided. To put it in another way. Two thirds of the energy needed to expand the water between 4 deg and 100 deg C is provided internally by a shift in the internal energy balances between phases and the remaining one third is provided externally by us. =========================================== The above is the technical bit - but it is worth while considering the implications of the way it was found. Now nothing is easier than playing around with the algebra in physics to get different forms. The trouble is, one has to have an insight into what the form means. For example, consider that famous expression [1 - v^2/c^2] If we rewrite it as [(c^2 - v^2)/c^2] then any mathematically unchallenged schoolboy will immediately want to recast the (c^2 - v^2) as (c - v).(c + v). But what does that mean physically. Until we can have some kind of physical model in our minds - something like a velocity strain, say [whatever that might mean ;-)] then there is no point is presenting it in that way. Now it is possible to go from the maths to the physics but it's easier to go from the physics to the mathematics and when one does the maths generally becomes so simple that it virtually disappears. Indeed its disappearance is a sign that one is looking at the phenomena face to face so to speak - and not through a glass, darkly. In the above case we have strain energy = a constant. calorific energy. If we measure strain energy and calorific energy in the same unit then the constant becomes 1 and the maths has completely evapourated. In the case of the VP relation above, it was an ability to visualise water as a cellular structure with the water molecules phase as the three dimensional material analogous to clay particles, and the cell interaction phase as the two-dimensional skin phase analogous to high pF pore water that gave insight into the need to recast the VP graph in simpler dimensional terms. Cheers Frank Grimer
