Does physics forbid such a device; a heat destroyer

philrainey

If one had a nuc reactor burning as hot as the surface of the sun and if there were materials that could withstand these tempertures. Could one drop a sphere into the burning mess that is in a complete vaccum. And if one had solar panels that could withstand the temperture could one have a sphere surrounded by them within the sphere in the nuc reaction receiving radiation from the hot bigger sphere surface and converting it to electricity without any heat been dumped in a cold sink?

Drakkith

We don't have these materials so it isn't possible. All machines that convert energy to something else will have losses. The cold sink WILL heat up.

TobyC

No one has ever said that it is impossible to remove heat from something without doing work, just that you need something colder for that to happen, then it happens by itself! Just put a hot thing next to a cold thing and watch the heat leave the hot thing, you can even get some useful work out of it.

Your post seemed to want to cool something down without having anything colder to dump the heat in. It is impossible to do that without putting energy in. DaleSpam came up with the neat idea of using space as your colder thing, putting the thing in contact with deep space, and if your machine is on a spaceship in deep space then that will be even easier. Like I said, the problem in that case is likely to not be cooling stuff down but keeping yourself warm.

Carnot efficiency has everything to do with it, it tells you how much energy you have to put in to take heat from a colder body and move it to a hotter body (which is what your machine will have to do if you don't have a colder reservoir handy) and importantly that energy is non-zero, it also tells you how much work you can get out if you're moving heat from a hot body to a cold body, but you don't seem to care about getting useful work out, just removing the heat. It also tells you that converting heat entirely into a 'useful' form of energy is impossible.

TobyC

No that would only work while the solar panels were colder than the hot sphere. I'm not sure how solar panels work so I can't tell you exactly why it breaks down when the solar panels heat up, but once everything is at the same temperature (which will eventually happen), you can no longer get any useful energy out of the heat in the reactor.

As the panels approach the temperature of the reactor they become less and less efficient (meaning more of the energy they absorb goes into heating them up rather than producing electric current).

DaleSpam

The second law of thermodynamics is about entropy. The point of talking about mechanical work is that it has no entropy. If you convert thermal energy to any other form with 0 entropy then Carnot's efficiency limit applies. It can be derived in a couple of lines directly from the second law of thermo and the definition of temperature, regardless of the actual form of the 0-entropy energy.

That isn't the question posed in the OP, but if your concern is merely to dump the heat then that is simply heat transfer, not a heat destroyer. In space the only mechanism of heat transfer is radiation. Heat transfer still requires a cold reservoir in order to follow the second law. Luckily, 2.7 K is a pretty cold cold reservoir for most purposes.

Please quote these false claims exactly, I think you are just misunderstanding or misquoting.

This question has already been answered in post 25. EM radiation has entropy, so if you radiate with any spectrum other than a black-body you will reduce the entropy which will involve the second law of thermo. In the limit of a very low entropy spectrum, like a laser, you can radiate a lot of energy quickly, but Carnot's limit applies.

DaleSpam

Roughly speaking there is a "band gap" between different parts of the semi-conductor. When a photon with energy higher than the band gap hits the semi-conductor then it can push an electron across the gap and generate a current.

As solar panels heat up, the electrons in the semi-conductor become more energetic, to the point where they posess enough thermal energy to jump the band gap. The problem is that with thermal energy they jump both directions. So what happens is that the energetic photon is absorbed, which pushes one electron across the band gap, but instead of generating a current a thermal electron just jumps backwards across the band gap.

This actually happens at much lower temperatures than thermal equilibrium. Keeping solar panels cool is a major design consideration wrt efficiency.

DaleSpam

Just to put some numbers on this. Suppose that the heat source is pretty hot, producing heat at 1000ºC (1273 K). And suppose further that the device is in thermal contact with deep space, as I suggested, and so it is using deep space as the cold reservoir (2.7 K). So the Carnot efficiency is 1-Tc/Th = .998. This means that for every 1 MW of heat produced, the device could capture 998 kW as work (or other low entropy forms of energy) and would have to dump 2 kW to deep space to satisfy the second law of thermo.

You can use the law for radiative power transfer for a black body, which is [itex]\dot{Q}= \sigma (T_h^4-T_c^4) A[/itex]. So to radiate 2 kW at 1273 K to a bath of 2.7 K requires an area of .014 m².

You can just scale those numbers up by however many MW you expect your power plant to produce.

The technological advances would be to use deep space as the cold reservoir while radiating at the hot temperature. That isn't something we could do now, we would use a radiator as the cold reservoir which would be at an intermediate temperature between 1273 K and 2.7 K, reducing the maximum efficiency of the engine and increasing the surface area required to radiate. But that would be the limit of what is possible according to the laws of physics as we know them, so that would be the limit of what you could get away with using "future tech" but not breaking the laws of physics.

mfb

Yes, if you have access to a cooler object (like space) and transmit a fraction of this energy to the cooler object. The required fraction depends on the temperature ratio.

It is possible to be faster than low-temperature radiators alone. You can use the temperature difference between "hot object" and radiators: A part of the energy has to go to the radiators, another part can be used to do something else - for example, power a laser which additionally emits energy. However, a higher temperature of the radiators would do the same (where the temperature of the hot object is the ideal value).

@DaleSpam: You already need contact to the 2.7K-bath to extract 998kW. You cannot get this and feed a 1000°C-surface with the remaining 2kW. Otherwise you could use this 1000°C-surface again, and extract .998 of the 2kW... you see the problem?

Dickfore

Your lead is wrong. Carnot's Theorem was proven by using the second law of thermodynamics.

The machine you are describing is exactly as the one in the Kelvin formulation of the second law.

So, the answer is that it is impossible!

DaleSpam

Certainly. I don't see a way around it, which is what I mentioned about the radiator at an intermediate temperature. I don't know how a heat engine could be in thermal contact with deep space rather than a radiator, but I don't know a law of physics that forbids it.

But the second law of thermo is satisfied as long as at least 2 kW/MW goes to space. So I think that anything else is fair game for "future tech". Although, maybe the "future tech" is a way of arbitrarily increasing the effective surface area of the radiator.

DaleSpam

Just out of curiosity I was playing around with this idea and optimizing the intermediate temperature such that the surface area of the radiator is minimized. For any given output power, the lower the intermediate temperature, the less energy needs to be radiated, but the less efficient the radiator. Conversely, the higher the intermediate temperature, the more efficient the radiator, but as the power plant becomes less efficient more energy needs to be radiated.

It turns out that there is a minimum at 955 K (64 m²/MW) which corresponds to a 25% efficiency on the engine. Any hotter than that and the engine becomes so inefficient that the radiator area needs to be larger, and any colder and the radiator itself becomes so inefficient that the area needs to be larger. However, there is a very broad range that is close to the minimum surface area.

Attached Thumbnails

 

mfb

Why does it grow so much above 1200K? Close to 1273K, the efficiency is ~0 and you have to dump ~33% more heat. However, the temperature is higher by 1/3, which leads to a radiation of (4/3)^4 =~ 3 times the 955K-value. Based on this, I would expect that the required radiator area does not have any minimum.

DaleSpam

That isn't quite how it works. Close to 1273 K you don't have to dump just 33% more heat, you have to dump an infinite amount of heat.

For example, at a radiator temperature of 1200 K the engine is terribly inefficient (~6.7%). So every 1 W of power produced requires 17.4 W of heat from the hot reservior and so you need to dump 16.4 W to the radiator. This is 448% more heat than the 955 K value (3 W), not just 33% more.

Remember, an engine is rated and designed for the power it produces, not the amount of fuel it burns. I suspect you are thinking of a constant heat input rather than a constant power output.

Dotini

Question: Is the interesting process which takes place on the sun - going from very hot interior to relatively "cool" surface to very hot corona - an example of the physical process the OP has in mind?

Respectfully submitted,
Steve

mfb

Oh, you fixed the amount of usable work. Sorry, I thought you fixed the thermal input power as Deeviant does.

Deeviant

These numbers get right at fundamentals of what a black-body cooling system would be looking at. But in the end, such a method is not what I was trying to get at. Don't get my wrong, I think using radiative cooling is super useful in space, but it is has been well hashed out in many different sci-fi worlds and it certainly isn't advanced technology, it really isn't technology at all; it's just how the universe works.

It may well be my fictional but physical law obeying spaceship relies solely on black-body emission for cooling, but I was looking for something a bit more... exotic.

Drakkith

Invent something! It's fiction! Make it logically consistent with known laws as best as possible, but in the end you're going to have to break a rule or two, so go all out!