# Planet X, Lord Kelvin, and the use of Structure as Fuel

On the nature of boiling
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Few people know this, but boiling is a cooling effect. If you somehow lower the boiling point of water below ambient temperature, you will get boiling water, as it quickly cools down to its current boiling point. The easiest way to do this, is to create a partial vacuum with a vacuum pump. A glass of water inside the bell will start boiling at room temperature, as pressure drops.

This is a fun demonstration I have shown students. I always ask “Is there anyone brave enough to get boiling hot water poured in their hand?” There is always someone. The shock is universal, each time newly boiled water is poured into a tense hand:

“It is cold!?”

Yes, the temperature has dropped significantly below room temperature. Energy (in the form of heat) was used to break those dipole bonds. Water will always reach for its boiling point temperature, if ambient temperature is higher than the boiling point. Decrease in pressure lowers the boiling point. However, the reverse is also true. For increased pressure, boiling point will rise.

The Second Law of Thermodynamics
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Lord Kelvin wrestled with the second law of thermodynamics through many iterations. His insights were profound, and it is amazing his work has still not been subsumed to a higher degree. In the year 1851 he coined one of the most profound and well cited formulations of the second law:

“It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects”.

The civilization on Planet X
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Lord Kelvin had never visited Planet X, though. Planet X has a uniform temperature of 500 K (227 degrees Centigrade). Planet X has the same atmospheric pressure as Earth. Planet X has no geology, no weather, but lots of buried pockets of highly pressurised liquid water.

Metal androids capable of handling the intense heat have built a civilization on Planet X. They get all the energy they need, but how? There is no weather on Planet X. No organic matter, no radioactivity. There is ONLY this pesky uniform heat on a rocky planet with no life. The androids, however, have the perfect answer:

“Drill baby, drill!”

Drill down to the pockets of pressurized water.

Water is a so-called 'incompressible liquid'. Yes, some high pressurised water may spill up, like at an oilrig, but not a lot. What will happen is it will start to boil. Steam will come steaming out of the drill hole, and the androids put a turbine in place. Water in the water pocket will boil and cool (just as in my vacuum pump). Eventually it will reach an equilibrium temperature (say 400 K, since the pressure will still be quite high inside the chamber).

At this point the water will continue to boil, transforming ambient heat into energy.

Implications
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Now consider Kelvins 1852 formulation: “It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects”.

The androids are drilling a hole, down to a “portion of matter” (the water). This “portion of matter” is “cooling below the temperature of the coldest of the surrounding objects” (since it is boiling in a uniform surrounding temperature of 600 K).

I am well aware that modern thinkers would not say the spirit of Lord Kelvins formulation has been broken, and I would agree. But if planet X, and the androids, don’t break Kelvins statement as interpreted literally, I do not know what does. Luckily there is also the Kelvin-Planck formulation:

“It is impossible to devise a cyclically operating device, the sole effect of which is to absorb energy in the form of heat from a single thermal reservoir and to deliver an equivalent amount of work.”

Clearly this has NOT been broken, although that “sole effect” part is doing a lot of heavy lifting.

A way of conceptualizing all of this may be to see what happens as a “structural potential” being irreversibly degraded. Planet X is clearly far from a perpetual motion machine. Eventually, all the water will become steam, and the android civilization must perish.

The DEG-theorem and my conclusion
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The closest, rigorously tested, mathematical framework capturing this may be the Degradation-Entropy Generation (DEG) theorem by M.D. Bryant. It provides rigorous mathematical grounding for connecting structural degradation to thermodynamic processes. Published in the Proceedings of the Royal Society (2008), the theorem states: dw/dt = Σᵢ Bᵢ Ṡᵢ, where w represents the degradation measure, Bᵢ are degradation coefficients, and Ṡᵢ are entropy generation rates for each dissipative process.

If we view the second law as “Entropy/disorder is always increasing”, Bryant’s framework seems to suggest a potential for using structure as an entropy sink in order to extract work from heat, exactly like the androids on Planet X do.

However: I think my own reformulation of the second law capture the android’s dilemma even more clearly, even if it is still speculative and unproven:

"Any extraction of energy within a closed system will over time degrade the system’s structural capacity to support such extraction. This degradation will, on average, cost more energy to reverse than the amount that was extracted."

Curious what others think. Why haven't I seen this thought experiment before? Clearly Lord Kelvin knew all of the underlying physics infinitely better than me. Yet, I do not think he would have formulated his 1851 statement exactly like he did, if he had thought of Planet X.

What do you think?

Oh, and if there is any appetite for it, there is more to come! If so, let me know.

**Sources**
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*Thomson, W. (1851). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam". Transactions of the Royal Society of Edinburgh. XX (part II): 261–268, 289–298. *

*Rao, Y. V. C. (1997). Chemical Engineering Thermodynamics. Universities Press. p. 158. ISBN 978-81-7371-048-3.*

*Bryant, M.D., Khonsari, M.M., & Ling, F.F. (2008). On the thermodynamics of degradation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2096), 2001–2014.*