Strange thermal efficiency at super low temperatures

[DIYStirlingGuy]

I was reading "An Introduction to Low Temperature Differential Stirling Engines" by Jame R. Senft and was messing around with the Carnot Thermal Efficiency equation and found something interesting. The formula goes like this T_h-T_c/T_h=Carnot Thermal Efficiency.

So if you're looking at a standard LTD Stirling that can run on the heat difference between the room temperature and your hand temperature the equation looks like this: 310K - 293K / 310K = .05483 or 5.5%.

So after fiddling around with some numbers I found a strange set of efficiencies at super low temperatures.

For example:

10K - 9K / 10K = .1 or 10%
9K - 8K / 9K = .1111 or 11%
8K - 7K / 8K = .1250 or 12.5%
7K - 6K / 7K = .1428 or 14.28%
6K - 5K / 6K = .1666 or 16.66%
5K - 4K / 5K = .2 or 20%
4K - 3K / 4K = .25 or 25%
3K - 2K / 3K = .3333 or 33.33%
2K - 1K / 2K = .5 or 50%
And of course it's impossible but you could use almost absolute 0K and get 99.99999999% efficiency.

Weird Stuff huh? OR am I doing the math wrong?

P.S. I know these are impossible temperatures to work with realistically. However, I do like to take things to the extreme to get a new perspective.
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My Stirling information site is http://diystirlingengine.com/

[vamoose]

Hey D.I.Y.
The closer to Zero K the better the theoretical efficiency of an engine, for the same Delta t.
Here's a webpage that might confirm your equations...
http://hyperphysics.phy-astr.gsu.edu/hb ... arnot.html
Maybe someone out there could explain the precise concept behind this for us, in layman's terms.
I could try, but i would just be makin stuff up!!
vamoose

[DIYStirlingGuy]

Thanks for the link, vamoose!

That's a great calculator! It really lets you play around with the numbers. This is a good one to add to my site.

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My Stirling information site is http://diystirlingengine.com/