claim 1 - Carnot is bogus
Tom has been slammed on other forums for claiming Carnot is bogus with cocky guys claiming he needs to prove Carnot invalid while Tom claims they need to prove Carnot valid. This leaves Tom hard pressed to prove a negative while these bozos miss a simple proof (1) heat=work (2) internal energy is linear absolute T (3) in isothermal process heat=work during compression or expansion.
Consider these temperatures where heat or work required for the same isothermal compression or expansion will vary by x
1200k 4x
_900k 3x
_600k 2x
_300k x
Yep, Carnot wins for any ideal regenerated Stirling cycle. The thing to remember with isothermal processes is that there’s no heat “leaving the gas” (either way)…it’s passing THRU the gas from source during expansion (where heat=work) and to sink during compression (where work=heat). Another thing to remember with isothermal processes is that the internal energy remains constant where each gas molecule has the same internal energy and same translational speed regardless of volumetric changes. Everyone seems to struggle with the reality that the internal energy remains constant despite our in/ability to gain usable work varies by volume variations. It is what it is.
claim 2 – no heat sink req’d
No heat sink sounds impossible. However, this time Tom offers video proof that appears to confirm his claim, but is largely dismissed as flawed (lacks NASA grade study).
- Carnot reveal via voodoo.png (19.51 KiB) Viewed 29770 times
Here’s my spin on a gamma cycle vs what I call a voodoo cycle. They’re each shown via distinct processes with PVT values chosen for clarity and including value “m” as relative density (abstract gas moles). Both cycles are shown with single-acting pistons where the upper piston is the power piston while the lower 2 pistons represent a displacer. The thing to remember here is that each figure is a freeze frame and that each process is between two figures.
Both cycles have the same input and output, 1-2 and 2-3, then everything differs. The gamma cycle has Cv regen 3-4 followed by isothermal compression 4-1. Meanwhile, the voodoo cycle has Cp regen 3-1 with simultaneous isometric transfer from power piston. Take a close look at these values and some weird stuff appears…gamma has external cooling while voodoo does not, yet both cycles have the same heat input from source and same work output at power piston. What’s up ??? I pondered this for a few hrs over a few nights trying to rationalize the whole work=heat buzz…
Then I was saved by a past comment Vincent made regarding buffer pressure where he said he favored vacuum. That did the trick and a mini altered state ensued. Review my values and you’ll see there’s no ambient or buffer pressure shown and this changes everything!!! The 3 bar Pmin coincides m values to gain whole m values gamma stg 4. Substitute 3 bar vs 1 bar vs 0 bar buffer pressure and you’ll discover something I’ve never seen anyone mention before:
The previous pseudo Carnot “proof” lacks buffer pressure consideration which is cross canceled and passes by unnoticed (sneaky academics). However, in reality, any 300-600k cycle with “x” expansion where the molar density is the same in working cylinder as buffer will lose to Carnot during this first process alone, since the buffer pressure is opposing the expansion. IOW we traditionally tally Carnot energy tax per cycle, but it’s actually paid per process.
If you toy with this enough, you’ll realize that only with zero buffer pressure (a vacuum) can all input heat become work during expansion (Vincent nailed it). Then, lacking any assist from buffer pressure (due to vacuum), completing the cycle will require all compression input from expansion via flywheel. So, the lower the proportional buffer pressure, the more proportional input is needed from flywheel, and vice-versa. Just think of crankcase or ambient pressure as feeble bounce gas.
Returning to my drawing, the gamma is .50 eff per Carnot, but the voodoo is ~1/3 less eff since it will require work for isobaric compression AND loses slight work gain gamma likely achieves during 4-1 process (depends on buffer pressure). Nevertheless, voodoo shows that a cycle is possible without external cooling, but this requires a specific relationship between volume ratio and thermal ratio, and common LTD hover around ideal ratios (maybe Senft knew this). The thermo gurus always say Wnet is path dependent, but sequence dependent is better buzz. As a sidebar, it’s worth noting that gamma Cv regen appears to create low pressure “cold hole” akin Tesla (vs voodoo Cp regen) but this is an illusion.