A precision balance has a weight hanging from it (the glass bulb below). The weight is
recorded, then a cylinder of water is raised from the floor so that the bulb is immersed. The
weight is again recorded. Now, the water is heated or cooled, and the weight measured as a
function of temperature. Following Archimedes' procedure this gives us the ratio of the density
of water to the reference density of the bulb. It traces out the equation of state shown in the
accompanying notes. If we knew precisely the volume of the bulb (say, by measuring the water it
displaces) we would know also the absolute density of the water at various temperatures.
Floating and buoyancy are key parts of gfd...being the basis of the hydrostatic pressure
balance, and buoyancy oscillations, etc. So, what is wrong with this picture above?
We did an experiment to show the curvature of the equation of state
of water by putting 2 layers in a flask: hot over cold. Then using a magnetic stir-bar
we mixed the 2 layers and the fluid 'shrank' down the thin chimney at the top: the volume
of the mixture is less than the total volume of the 2 layer fluid we started with. This
is described and the equation of state shown on the accompanying text. The same effect occurs
if we use two layers of salty and fresh water, for the same reasons. This effect leads to
an important instability in the oceans, called 'cabbelling'. Two parcels of water with the same
density yet different T and S, if mixed, will be denser than either was initially. So,
mixing will cause convective sinking.
A liquid crystal sheet shows temperature by color:
reds/oranges are cold, blues are warm (contrary to intuition). The range of temperatures for
this sheet is 20-24C Here Leif's warm fingers contrast the extreme cooling due to a mist of
sprayed water landing on the sheet...even thought the water was at room temperature.
This glass vessel has been evacuated to low pressure, with a little water left inside, then
sealed. It is a 'clinker'; that is, if shaken, the water breaks apart by boiling, forming vapor
bubbles. With no air cushion the water segments clink metallically against one another. If you
warm one bulb with your and, and put the other hand at the other end, you will feel a rapid
increase in temperature: vaporization at the end with a film of water cools there, but the
vapor condenses on the connecting pipe and second bulb, where the heat is deposited. The heat pipe
works very quickly.
It gives us a way of measuring the saturation vapor pressure of water quite accurately. If
one bulb is warmer than the other, the water vapor will drive the liquid column toward the cold
bulb. The hydrostatic pressure difference from top to bottom of the column is easy to calculate,
and it tells us the vapor pressure difference between the two temperatures (the bulbs can be
put in liquid baths to establish what those temperatures are). In the image below, we have about
15 cm of water height difference when one bulb is cooled to about 5 Celcius while the other is
warmed to about 25 Celcius. This is reasonably close to the predicted pressure difference from
the curve plotted below (Clausius Clapyron empirical equation from Gill Appendix 4, plotted with
Matlab).
The change of state seen in the 'clinker' tube or this vessel is a rapid form of boiling, and if it is held just right one sees bubbles forming and rising (and expanding in size rapidly because the scale height of the pressure is very small when the absolute pressure is near zero!).