Counterpoint: all that is happening is that mechanical energy that kept the water pressurized (stored in the water itself and the surrounding rocks) is being released, and partially converted into work. Planet X is no different from a planet that conveniently comes with a lot of compressed springs buried underground. Nothing of which is particularly mind-blowing.
You seem to be missing the main point. Boiling pockets of water is a mechanism that over a long time convert ambient heat into something else, in a process were useful work can be extracted. In a steam driven train it is not just that you have a lot of initial pressure in your tank. Boiling is what makes the pressure remain over time. Please read my response to cousin_it for a deeper explanation for why the setup goes deeper than you think.
I'm not convinced any of this makes a significant difference. The reason why the water didn't boil already is that it was pressurized. This is slightly less intuitive than the compressed spring because unlike that example, it involves also configurational entropy, not just energy. And the boiling is prolonged because of the inherent kinetics of the process. But once you remove the pressure, the thermodynamic equilibrium goes from "a lot of liquid water" to "a lot of vapour with less free energy"; and you can use the energy flow that moves to make it happen to exploit that difference for useful work, as long as it lasts.
Case in point: we use this kind of compression and evaporation mechanism to cool stuff all the time, just not with water, it's called a fridge. In that case it's made cyclical by the compression step, and overall uses up free energy and produces entropy.
It made a difference for the androids on Planet X. They built their civilization around a novel initial condition on their planet (much like our usage of fossile fuel).
I want to plant a conceptual seed, though: Perhaps there are more structure to be found, that would allow us to convert ambient heat into useful energy, as the initial structure gets depleated. This post is also the starting point for introducing a more perplexing thought experiment in another post (that I can't post yet, due to lack of Karma).
I guess I have so much physicist-brain that to me it doesn't seem like there's a big difference - all I can spot is "thing has high free energy content, we can extract free energy from thing".
It just so happens that the densest free energy resources in our immediate neighbourhood hold it in either chemical or nuclear form. I really doubt there's any greater insights here to be found because anything that simply begs to roll to a lower free energy minimum will when given the chance. There's no large untapped reservoirs of low entropy stuff just begging to absorb heat from the environment so that it can undergo a phase change on Earth's crust or nearby space that I can think or speculate of.
Thanks! That seems like a fruitful way of looking at things, most of the time.
There's no large untapped reservoirs of low entropy stuff just begging to absorb heat from the environment so that it can undergo a phase change on Earth's crust or nearby space that I can think or speculate of.
That is not the only place one might look. I certanly do not know the future, but I do know this: Many a times have humanity dismissed things like novelity, that have later on turned out to be very important. The way I see it, you are a physicist, where as I am more of a head in the clouds visionary (with a Masters degree in Physics). I love interacting with those who know more than I do! My second thought experiment is still not useful, but perhaps you will find it more novel, once I post it.
Is boiling actually necessary for this scenario? Let's say the planet had pockets of pressurized gas instead. We drill into them, the gas expands, does work, and cools below ambient temperature.
This suggests Kelvin's formulation is actually ok, if we focus on the word "by". The work has to be extracted solely from cooling: something cools below the lowest temperature of surrounding objects, some work is extracted, and no other changes happen. If something else happens - for example a rock falls down, a spring is released, a container is depressurized, two fluids get mixed and so on - that doesn't count.
Boiling is the mechanism that absorbs ambient heat and lets you extract useful work. It gives you a process that can run for quite a while, converting ambient heat into energy.
Think of a classical steam engine: a train could run a long distance on a single tank of water. But if the tank just held pressurized gas, you'd barely get anywhere. Boiling keeps the pressure going, since water expands to about 2000 times its initial volume as it turns into steam. That expansion is what lets you siphon off useful work from the environment.
(Yes, at first that phase change goes into pressure rather than volume, but once the steam is released into the atmosphere, the expansion ratio stand.)
Eventually, the process ends. Unlike a steam train, the water pocket on Planet X can't be "retanked". Once it's gone, it's gone. You’ve spent the initial structure. But in the meantime, the boiling phase change acts as a clever thermodynamic lever, allowing you to trade ambient heat for work far beyond a single burst.
I'm a little confused what the goal is here? Are we trying to find the 'best' intuitive description of the Second Law? The best way to quantify its application to some specific type of physical process the way the 2008 paper cited does? Or are you claiming there is actually some flaw in the standard descriptions of how the Second Law arises from stat mech considerations?
As a matter of engineering, "How do we extract work from this system?" was the practical question that needed solving, starting from the days of Watt. We keep finding new and better ways to do that, using more kinds of power sources. We also get better at measuring and monitoring and controlling all the relevant variables.
As a matter of physics, Gibbs and Boltzmann 'subsumed' Kelvin quite nicely. Energy gets transferred between degrees of freedom in a system in all kinds of ways, but some arrangements are indistinguishable in terms of parameters we measure like pressure and volume, and the states that can happen more ways happen more often. It's just the counting principle. The rest follows from that. That's really all it takes to get to 'Entropy increases with time, and will not spontaneously decrease in a closed system or any appreciable size, and you can't extract work from a system while reducing its entropy or holding entropy constant.'
Few people know this, but boiling is a cooling effect.
True for the general public, but if there's anywhere that this is true of college juniors or seniors studying physics, chemistry, materials science, or at least several other fields, then I would say about the program that taught them what Feynman said about physics education in Brazil: there isn't any thermodynamics being taught there.
This is a fun demonstration I have shown students
It is a fun demonstration! What age are you teaching?
Also, I think you've set your Planet X example quite a bit farther from home than it needs to be. This looks like a perfectly normal thermodynamic half-cycle - basically half of the Otto cycle that our car ICEs are based on. The pressurized water boils due to the drilling-enabled pressure change creating a non-equilibrium pressure differential. Boiling converts the pressure difference into a temperature difference. The liquid undergoes isochoric heating, while the steam undergoes isentropic (adiabatic) expansion. It's an incomplete cycle because nothing is replenishing the heat or the water in the example as described, so over time the extraction of work cools the planet down and makes further extraction less and less efficient, and also eventually you run out of water pockets.
Are we trying to find the 'best' intuitive description of the Second Law?
Good call!
Perhaps not the 'best', but yes, I think a more rigorous version of my proposal could be intuitively useful. I do have a second thought experiment lined up, that may turn out to be a bit more significant, even if it is harder to parse what exactly is used as "fuel", and what is preventing the cycle from repeating. In such cases I think referring to structural degradation may turn out to be useful. A formulation giving some kind of clarity for important edge cases, that may turn out to be useful for us, by making it clearer what is allowed and what is not.
It is a fun demonstration! What age are you teaching? Also, I think you've set your Planet X example quite a bit farther from home than it needs to be.
Thank you! I was a high school teacher. Then I turned towards starting a company creating products (like parking pricing) based on predictive algorithms. You are right I didn't have to go into space for this example, but it felt fun, and it made the thought experiment clean and beautiful.
Ok, if we're talking about an audience of typical high school students (or equivalent general public) rather than upperclassmen in a college physics program or similar, then that's a bit harder, since you don't have the option to actually explain what entropy is, or even temperature, for that matter. For most people, temperature is the thing hot things have more of, that's all they know.
The thing that, IIRC, got most glossed over about this topic in high school physics and chemistry is that the Second Law isn't a law of physics at all. It's a law of combinatorics. And at least theoretically, the Counting Principle is something we got taught about in middle school, at least in more familiar contexts. S=k*ln(W), the rest is commentary - but that's not poetically satisfying like Kelvin's quote.
I think you are essentially looking for a not-too-mathy description of the equipartition theorem. If the energy in a system is distributed randomly among all the places it could theoretically go, then it is at equilibrium and cannot be do work. Otherwise, you can make the system do work as you allow it to evolve towards such a distribution.
Informally speaking, if there's some constraint keeping the system in a particular configuration, and you alleviate that constraint in a way that opens up more possibilities, then the system will spontaneously evolve in the direction of more possibilities, and you can (in principle, if you're clever) couple that spontaneous change to some other system to have it do work along the way. Maybe you want something like, "You can't make a system do work unless you expand the number of ways the system can be."
"You can't make a system do work unless you expand the number of ways the system can be."
Thanks! That is a beautiful way of putting it.
However, for reasons I will go into later, I have kind of come to think that Cosmological Degradation can be your entropy sink in rare edge cases. This may very well not be true, though the dimensional analyses for my more elegent thought experiment is compelling. If it is true, you will have cosmological degradation no matter what you do, so "you" do not expand the number of ways the system can be. The universe does.
I planed for the second thought experiment to be a separate post. For now I will state what I have come to believe might be a good formulation of the second law (a bit more precicely than in the Planet X text):
"Any extraction of utility within a closed system will over time degrade the systems structural capacity to support such extraction. This degradation will, on average, cost more utility to reverse than the amount that was extracted."
By utility I mean: things like usable energy, information, or function in general.
By structure I mean: “any state of order that is necessary for any particular extraction of utility”. In essence: “Total entropy will always increase”.
The distinction between what you wrote, and this, is exactly the edgecase were entropy increases no matter what you do. Will you be able to insert a metaphorical flywheel, and extract a bit of energy? I also think it may be a bit easier for innovators to look for structure that degrade as the price for turning ambient heat into work than to analyse the "number of ways the system can be". This would be analogous to the Android solution on Planet X.
By the way: It is obvious your technical knowledge in the matter exceed mine. I still hope I may have something of value to offer.
I think what you're saying is fine, and if it's useful to you or anyone else, then great! At heart I'm a scientist, not an engineer: I'm not so great at aiming for usefulness.
I do agree that I don't think engineers will be sitting around counting microstates in most cases. There are cases where they do some version of that, especially in high-end semiconductor devices and nanotech when you really have to account for quantum effects with as much precision as you can squeeze out of what you're working with. Otherwise it tends to be the kind of thing that gets abstracted away into practical approximations. Like how you can model the entropy of an ideal gas with N particles as the (unitless) volume of a 3-N-dimensional hypersphere, only that's an annoying formula and for high N the volume and surface area are almost the same, so instead you just use the surface area, and then the difference really doesn't matter because you take the ln() of it anyway. And after you see that derived one time in college you then just use the ideal gas law for the rest of your life.
"you" do not expand the number of ways the system can be. The universe does.
I would counter that the solution is: It is almost always an error (generally necessary and usually not an important error) to exclude "you" from the system being modeled. If you're setting it up or using it or measuring it or just present in its past lightcone, you're interacting with it and are part of it. You are also part of the universe. But in the cases where you're asking this question, then I think it's the answer. Also: if we're getting into cosmological questions involving entropy, then a lot of fun things might come into play. Consider that the entropy of a system is limited by its surface area. See: black hole entropy; cosmological event horizons; comparisons of the density of the universe to the density of a black hole the size of the universe; Dyson's eternal intelligence; entropic gravity; the "Omega Point"; and holographic universe models.
Also: I'm not sure your definition for 'utility' adds more than it obfuscates, but I look forward to seeing what you write next!
This is such a good answer. That last part goes straight into something that has been bugging me:
Consider that the entropy of a system is limited by its surface area.
Basically, I am considering interactions between a gas and the CMB. Usually, energy flux in the form of radiation scales like A*T4. With the CMB it is a bit different, since the CMB is present everywhere coming from all directions. If one could isolate the CMB photons in the atmosphere they would add energy based on atmospheric volume (I suspect), not area.
In the limit, however, with a sufficiently thick gas and large volume (if you could even get such a thing), you would get absorption of all CMB-photons deep inside the atmosphere, and then you would be limited by surface area, not volume. Rather than the CMB giving a volume based black body radiation you would get a more standard flux situation, limited by area.
Your insight about system entropy being limited by surface area was precisely one of the missing puzzle pieces I wanted to find. I do not yet know what to make of it, but perhaps it would be obvious to you.
Your reply in fact goes into many things that concerns my second thought experiment, and I wish to post it as soon as possible. Your take on “you” seems very relevant. Too little Karma, though. It seems as if I need two more Karma (somehow), or I will have to wait five days.
Regarding Dyson's eternal intelligence and the Omega Point: There may be a chance that the Cosmological Degradation is limiting conversion of utility in the long run. Maybe the reset time would diverge into infinity, and the last conscious thought, the last computation, will be broken, just hanging there, never finished. I have thought about this as well, based on my second thought example and my conceptual reframing of the second law. I planned to post that as a third follow up post.
It seems as if I need two more Karma (somehow), or I will have to wait five days.
Have some upvotes then :-)
Your insight about system entropy being limited by surface area was precisely one of the missing puzzle pieces I wanted to find. I do not yet know what to make of it, but perhaps it would be obvious to you.
The intuitive explanation for this is that a black hole is a maxentropy state, because you have the minimum possible information about its internal structure and composition. You can know its mass, momentum, and net charge, and that's it. You can't look at a black hole and infer anything else about the composition and structure of the matter that went into its formation. Hawking radiation complicates this a bit - I think there's some quantum information theory result that it necessarily somehow encodes the information about the matter that went in (IIRC because the virtual particles that cross beyond the event horizon annihilate normal matter instead of their virtual partners that escaped, in a way that matches the energy/charge/parity of the escaped matter?)? And you can theoretically, maybe, use something like the Penrose process to extract the energy from the rotational momentum and charge, thereby eliminating that gradient. At that point you only have the mass, and kinda (AFAIK) have to just wait the ridiculous amount of time it takes the black hole to evaporate into a similarly maxentropy gas in a post-heat-death cosmos.
With the CMB it is a bit different, since the CMB is present everywhere coming from all directions. If one could isolate the CMB photons in the atmosphere they would add energy based on atmospheric volume (I suspect), not area.
In the limit, however, with a sufficiently thick gas and large volume (if you could even get such a thing), you would get absorption of all CMB-photons deep inside the atmosphere, and then you would be limited by surface area, not volume. Rather than the CMB giving a volume based black body radiation you would get a more standard flux situation, limited by area.
I could be wrong, but I was under the impression that the CMB (a photonic gas) is composed of primordial photons; that they're not still being generated. In which case, for any concentration of matter (like the Earth's atmosphere), the CMB photons initially present will have either rapidly passed through and out (since the atmosphere is pretty transparent to microwaves) or else the local matter will have long since absorbed the local CMB photons and re-emitted their energy as part of a thermalized blackbody radiation of their own at the local temperature, such that there is no internal flux. Instead you have the gas emitting its own blackbody radiation out through its boundary, and the unabsorbed CMB passing out of the boundary, and the external CMB coming in across the same boundary. I think? In which case this is something that happens and reaches equilibrium very quickly - faster than you can actually form such a gas, since the CMB moves at light speed and matter does not. In any case it should all balance.
In the context of normal matter, the CMB sets a kind of minimum cold reservoir temperature for heat pumps that do net work - generating a colder cold reservoir takes more work than you can extract by dumping heat into them - but a minimum that decreases with time as the universe expands and cools.
Things get a little wonky with black holes, which are much much colder than the CMB. I am a bit unsure whether black holes break this in some way, since they get colder as you add matter to them. But I think that's balanced by the frictional heating and other effects that happen as matter approaches the event horizon? And also by relativistic effects that mean that matter takes infinite time (from the reference frame of a distant observer) to cross the event horizon as it falls in? We still don't have a good understanding of quantum gravity, either, which could have a lot of implications for the metric effects that happen near black holes and for the long-term future of the cosmos.
Maybe the reset time would diverge into infinity, and the last conscious thought, the last computation, will be broken, just hanging there, never finished.
Both of those thought experiments involve versions of this. Dyson's Eternal Intelligence assumes exponential slowing of computation over time, in order to produce infinite computation over even-more-infinite time using finite extropy. It is set in an ever-expanding,ever-cooling cosmos. Omega Point is set in a collapsing cosmos, performing infinite computation in finite time using finite extropy. Both involve decoupling objective from subjective time, since the computation/simulation happens much slower or faster than linearly, respectively. I don't think very many people seriously think that we, from within the universe, could set things up with the perfect precision needed to make either scenario work enough to do actually-infinite computation? More like you can stretch the efficiency of computation to be arbitrarily high the more precisely you can set things up.
Keep in mind I'm not any kind of cosmologist or theoretical physicist - just someone who once thought he wanted to be. I am a materials scientist, but one who hasn't worked in a lab in 15 years, and in any case we're way beyond that context now.
Thanks! Actually, your materials scientist perspective is perfect for a few of the questions I have been wondering about.
I could be wrong, but I was under the impression that the CMB (a photonic gas) is composed of primordial photons; that they're not still being generated.
This is my understanding as well. I switched into a thinking mode that explores limits without bothering with what can be achieved in reality. Kind of like how gas volume decreases as temperature goes down. Reality dictates the gas will turn solid at some point. But what if it didn’t? You are much more firmly rooted in reality compared to me, I think.
Since I can (thanks to you), I have now posted my next part here.
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,
Then it's not boiling hot water, it's boiling cold water.
Also, this sort of thing is not clever. Even if you leave out the word "hot", it amounts to "ha ha, you thought I was talking about a central example". People are justified in thinking you are talking about a central example.
The beauty of "hot" is that it is a relative term. Hot for whom? I love Veritasiums old video on melting ice cubes. From the ice's perspective a metal plate that feels cold to a human is more hot than a piece of cloth, that does not feel cold to a human. I love when things don't match with human intuition. It may turn into a learning experience.
The beauty of “hot” is that it is a relative term. Hot for whom?
It's implicitly relative to the speaker and/or the listener. Claiming that because you didn't specify one of those it's from the perspective of an ice cube is just another example of the same thing: being "clever" by deliberately pretending that there's no such thing as conversational implicature.
Having your words be literally accurate is not the spark of genius you think it is.
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.
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”.
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.
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 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.
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.