At 08:40 am 13/07/2006 -0700, Jones wrote: >----- Original Message ----- >From: Frederick Sparber > > > A fundamental law? > Energy is inversely proportional to radius? > > > Certainly true regarding photon wavelength > > - plus - Prof. Casimir sez: as you go smaller > and smaller in dimensions, then the increase > turns from cubic to fourth-power, > therefore ... one might suppose - that this > threshold of about 100 nm is (hypothetically) > the real advantage of a nanobubble over a > microbubble ? > > Jones > > The sequence of fourth powers of integers goes: > 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000,
That would be true for the solid vapour drop between 100° and the critical temperature but because vapour is a spherical shell between 0° and 100° I believe it should be an eighth power. The sequence for eighth powers of integers one to ten goes: 1 - 256 - 6,561 - 65,536 - 390,625 - .......... 100,000,000 which means its potential energy would increase by a factor of 100 million. 8-) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Since I wrote the above (which got bounced) I see that Fred is up to a sixth and seventh power - but let's not make an issue of it. The essential thing is that it is the equivalent of the adiabatic branches in the Alpha- atmosphere Carnot cycle. One might say that the "power" compression is the..... ================================================= et aliud cecidit in terram bonam et dabat fructum ascendentem et crescentem et adferebat unum triginta et unum sexaginta et unum centum ================================================= I now realise that Jones is the one who has really got the tiger by the tail in his recognition that as the scale decreases we meet with a discontinuity in behavior. Let's call it the Casimir phase boundary - or better still the Caspar boundary. <g> I must confess that in the discussion on the Yahoo site I was still thinking in terms of the working fluid inside the bubble being a gas - Jones was racing ahead and I hadn't managed to catch up. But I now see that the enormous change is scale means that we have crossed the boundary from a gas to a plasma of some kind. We have crossed a change in state boundary and the working fluid of the quasi-Carnot cycle is a Beta-atmosphere gas. Let's assume it is an exciton gas for now. As I have pointed out elsewhere one can go round the A-atm. Carnot cycle either by changing the space variable [switching insulation] or by changing the time variable [slow compression- expansion equals isothermal.....fast compression-expansion equals adiabatic]. Now assuming that the "conditioning" of the water that the enthusiasts seem to go on about has a real effect, it's not difficult to recognise what this represents in terms of a Beta-atmosphere exciton gas quasi-Carnot cycle. Conditioning has to be the equivalent of the slow isothermal arms of the Alpha-atmosphere Carnot. Have I caught up yet, Jones. 8-) Cheers, Frank ===================================== [Caspar] Frankincense to offer have I, incense owns a Deity nigh Prayer and praising, all men raising, Worship Him, God most high. =====================================
