No, you don’t have to concentrate heat; you dissipate it, and make the dissipation work for you as it goes. You can bring a reservoir of cold matter alongside one that is already quite warm; cold water from an ocean trench, for example; the temperature gradient can be made to do work - you end up with a less organised system, but you get to take some energy out in doing so.
Again, we’re assuming a closed system, or rather one with a single thermal conduit (radiative emmision through the atmosphere to space) that is maxed out, hence our concern about dumping heat to space. Per the Stefan-Boltzmann law, the only way to increase radiant flux is to increase the temperature, but dumping heat into a high temperature reservoir requires dumping even more heat into a low temperature reservoir. Whether you do this by a mechanical refrigeration cycle or utilize existing environmental low temperature thermal masses (but remember, we’re at thermal saturation as it is; we don’t cool things off by radiation to space anymore) you’re playing a losing game, adding significantly more energy to the system than you’re rejecting. Ultimately, such a scheme wouldn’t work.
Refrigeration depends on an open loop system with an effectively infinite low temperature reservoir. Without that, your system will overload faster than it can reject heat.
Stranger
Which is why I said “bring it down slowly.” If you can cool a lump of rock to below -150C (you can do it in space, so you won’t warm up the earth in the process), then use a spacecraft to bring it to a complete stop at 100km altitude and drop it from there, the net effect would be to cool the earth (assuming it’s at 30C average).
You seem to be talking about a system in which the heat is evenly distributed and must be concentrated to create a thermal gradient. I’m not talking about such a system; I’m talking about one in which heat is NOT evenly distributed - that contains concentrations of heat and therefore already includes natural thermal gradients - these can be used to do work (and we would throw that work away).
The problem is, if you smooth out the thermal gradients on the Earth, that’ll decrease the amount of energy we radiate (since power radiated is not linear in temperature). I think your point is that if we use the thermal gradients to provide our energy needs, we’ll need less fusion, but in the long term, I think it’d still be worse (or at least, no better). Besides which, any thermal gradients which already exist on Earth must, in a situation like the OP posits, be considered a finite resource, and once those gradients are gone, they’re gone.
Mechanical transport of heat off-planet (shipping liquid water out to the Oort Cloud, say, and bringing back the same mass of ice), as some are suggesting, could in principle work, but I shudder to think of the cost. But hopefully, by the time we get to the point where we’d need to do it, it’d be a lot more feasible.
You don’t have to go that far. Just run a pipeline to geostationary orbit, and attach it to a huge radiator there.
Huge is relative. Remember, in the situation we’re positing, the entire Earth isn’t a big enough radiator. And the old trick of making a radiator with a lot of vanes, for high surface area, only works for conduction and convection: Try the same thing with a purely radiative radiator, and most of the surfaces just end up radiating onto other surfaces. So your radiator in geosynch orbit would have to be of a size at least comparable to the planet, to do any good.
Which might still be easier than going out to the Oort Cloud, I dunno. But remember, energetically, LEO is halfway to anywhere. And a planet-sized radiator would probably be a lot uglier than comet shuttles.
I guess I’m not clear on what you’re proposing. A process that actively radiates a high rate of energy–say, this hypothetical thermally-pumped laser–is going to require dramatic differences in temperature, more than that are going to be found in nature. You are going to have to concentrate heat energy into a high temperature reservoir, and this is a parasitic process; you’ll never reject as much heat as you create in the process. (You can’t “throw work away”; work either does productive kinetic movement, or becomes unrecoverable heat waste, which adds to your environment.) You seem to be suggesting something like a heat pump cycle, where you’re able to pump energy into a high temperature reservoir from a low temperature reservoir by adding work. The problem is that the work you do also creates heat, which has to be rejected somewhere; in an isolated system, you rejected it out into the outside wold where it doesn’t affect your system. In our scenerio, you’d still end up rejecting it to the environment. You might be able to make the radiative process somewhat more efficient, by increasing the thermal gradient, but in the end you’re stealing from Peter to pay Paul by dumping yet more heat into the environment. Assuming that we’ve already saturated our radiative output–that is to say, we’ve achieved the maximum greybody radiative throughput–the only way you can reject more heat is by either providing a more efficient radiative conduit to space, or by bringing in additional negative thermal mass.
Small thermal gradients (which will be being ever reduced by the heat you’re pumping into them as you attempt to extract energy to do work) like those found in nature are going to be inefficient to the point of being useless on this scale. Heat engines, like that in your car, require a couple of hundred degrees of thermal differential to get thermodynamic efficiencies in the 20% range. Aside from the rare geothermal vents, you just aren’t going to see those kind of gradients on any significant scale on the face of the planet.
Stranger
Of course. I think it’s perfectly plausible. If it’s a rigid structure, it can extend some distance in the radial direction without breaking up. And it can extend along the orbit as far as you want. A 4000-km wide ring extending all the way along geostationary orbit would have the same surface area as the earth, and would reduce earth’s absolute temperature by 19%, assuming it receives no sunlight and has the same albedo as the earth. Actually even if it receives sunlight, there are surface treatments available that minimize heat absorption and maximize radiation. (Something that looks white in visible light, but black in infrared.)
Even if you take the “coolant” to the Oort cloud, how are you going to cool it there? If you use a radiator it doesn’t really matter where in the solar system you are, as long as the radiator is in a shade or angled parallel to sunlight.
Anyway either way you do it, I think you need a pipeline or elevator to geostationary orbit. Otherwise the rocket engines would add a non-negligible amount of energy and pollution to the planet.
No. I don’t know why you keep saying that - it’s not what I’m suggesting and I’ve said so several times now; I’m talking about passively using existing heat gradients - making the flow of heat from a hot body to a cooler one do work for us - generating energy to power a laser. For example running something like a Peltier device or a Stirling engine on the temperature difference and using that to run the laser - I concede (and have already said so) that it might be horribly inefficient and pitifully ineffective, but it’s not outlawed by the laws of thermodynamics.
Doesn’t matter how slowly you bring it down - a big chunk of ice up there has potential energy - where does that energy go as you bring it down?
My calculation was based on the assumption that you can bring a block of ice down to 100km altitude without adding heat to the earth. I think it can be done you bring it down on a trajectory with a 100km perigee, and you use mass drivers right at that point to bring it to a complete stop. The “exhaust” from the mass drivers would travel away from the earth, and you have a block of ice motionless at 100km altitude. Yes, it does release potential energy as it comes down from there, but if it starts out at 150K temperature, it does not quite reach 300K before hitting the ground/ocean.
Admittedly I haven’t calculated the atmospheric friction losses at 100km so it may be non-negligible. I think cooling the ice even further before bringing it down would compensate though. Anyway I did say it isn’t an efficient method.
Ah. fair enough.
But if we’re assuming that we have enough waste heat that it can’t be naturally radiated to space, then any additional heat–including that produced by a heat engine like a Stirling engine–is going to contribute heat to the system, which above and beyond the maximum heat it is already radiating should be considered an adiabatic (thermally insulated) system. Any natural thermal gradients you have on the surface of the planet, or in the oceans, are strictly finite resources. Once you start using it to drive a thermomechanical cycle, they’ll heat up too, and without a low temperature reservoir to dump they’ll raise to the ambient temperature and become progressively ineffective, even aside from mechanical losses. Using work from within a system to extract heat from it is a losing game (hence, why air conditioners are mounted with the radiator to the outside of the building, i.e. outside our adiabatic system); you might get somewhat more efficiency, but if you’ve already maximized your ability to naturally radiate to space, you’re just buying a little bit more time, not ultimately solving your excess heat problem. Eventually, you’re going to run out of differential temperatures.
On the topic of tethered orbital radiators; as long as you could make the radiators more efficient–closer to true Planck blackbody with ? = 1 (and especially if you can shield them from absorbing energy from the Sun during their dayside exposure)–then you could significantly improve the radiative characteristics of the planet, and there’s no reason you couldn’t make it arbitrarily as large as you like, up to the point that the radiative temperature is equal to the 2.7 K microwave background. It would be like poking holes in the bottom of a water-filled tank. Of course, you’d want to keep it small enough that it doesn’t totally block out the Sun, or somehow keep it on station on the far side of the Earth. This would obviously be a massive engineering project only feasible for a space-going culture which could perform major construction and industrial operations in free-fall…which begs the question of why you’d leave such massive heat-dumping processes on the planet’s surface to begin with. Better to move it all into space, where it can radiate out into the cosmic background without having to burn through intervening layers of inconveniently thick atmosphere, and turn the planet into a Planetary Nature Preserve.
Stranger
If we assume that our overheating earth has small existing heat gradients, and the existence of a heat engine capable of exploiting them with high efficiency, then it would be possible to extract some energy from the system by allowing heat to flow from a hot reservoir to a cold reservoir through your engine. But doing so will increase the overall heat of the planet, since none of that heat has left the planet, and some of the extracted energy will be converted to heat by the inevitable inefficiencies in the heat engine. It doesn’t matter what you use the resulting energy for. Using it to power a laser doesn’t magically make heat disappear, and the laser will itself generate some additional waste heat on the planet. The laser refrigeration scheme used in Sundiver doesn’t actually work.
What you’re saying doesn’t make sense; if the overall heat is greater after we’ve extracted some energy and thrown it spaceward as a laser beam, where did the energy we threw away just come from?
The heat from the inefficiencies in the stirling engine (or whatever) is not new energy - it’s just wasted energy from the existing heat source.
Ah, I agree with this (and I said as much in my first post in this thread) - exploiting existing thermal gradients to extract energy, then throwing that energy away necessarily smooths out those gradients to the extent that they will no longer be exploitable, but as long as they exist, there is a way to take some of that heat and remove it from the system.
Possibly because that’s where people want to live. The same reason we have a lot of smog-producing processes in cities rather than in the countryside.
The energy came from the difference in heat between the hot sink and the cold sink. After you extract the energy from the system, the heat is still there, it’s just spread out more evenly. You can’t directly convert heat to energy. You can generate energy by allowing heat to flow from a hot sink to a cold sink through a heat engine. None of the heat is destroyed in the process, and some amount of additional heat will be created by the heat engine.
But when you generate that energy from the existing heat source, whatever cold sink you are using will gain at least as much heat as you removed from the heat source. You still end up with a net gain in heat. Otherwise, what you have done is convert waste heat directly into useable energy, which is in direct violation of thermodynamics.
Lasers won’t work! We’re trying to remove heat from the planet, not energy. Lasers have a high energy density, but a small amount of heat. Remember what a laser is: a coherent beam of electro-magnetic radiation. Thermal energy is incoherent!
Back to the drawing board…