The conservation of etendué is merely a particular version of the second law of thermodynamics. Now, You are trying to invoke a multistep photovoltaic/microwave/rectenna method of concentrating energy, but you are still violating the second law of thermodynamics.
If one could concentrate the energy as you propose, one could build a perpetual motion machine.
I don’t see how they are violating the second law of thermodynamics—“all that conversion back and forth induces losses.” They are concentrating some of the power of the Sun in one small point, at the expense of further dissipating the rest of the power. No?
DK> “I don’t see how they are violating the second law of thermodynamics”
Take a large body C, and a small body H. Collect the thermal radiation from C in some manner and deposit that energy on H. The power density emitted from C grows with temperature. The temperature of H grows with the power density deposited. If, without adding external energy, we concentrate the power density from the large body C to a higher power density on the small body H, H gets hotter than C. We may then use a heat engine between H an C to make free energy. This is not possible, therefore we cannot do the concentration.
The Etendue argument is just a special case where the concentration is attempted with mirrors or lenses. Changing the method to involve photovoltaic/microwave/rectenna power concentration doesn’t fix the issue, because the argument from the second law is broader, and encompasses any method of concentrating the power density as shown above.
When we extrapolate exponential growth, we must take care to look for where the extrapolation fails. Nothing in real life grows exponentially without bounds. “Eternity in Six Hours” relies on power which is 9 orders of magnitude greater than the limit of fundamental physical law.
But in laboratory experiments, haven’t we produced temperatures greater than that of the surface of the sun? A quick google seems to confirm this. So, it is possible to take the power of the sun and concentrate it to a point H so as to make that point much hotter than the sun. (Since I assume that whatever experiment we ran, could have been run powered by solar panels if we wanted to)
I think the key idea here is that we can add external energy—specifically, we can lose energy. We collect X amount of energy from the sun, and use X/100 of it to heat our desired H, at the expense of the remaining 99X/100. If our scheme does something like this then no perpetual motion or infinite power generation is entailed.
How much extra energy external energy is required to get an energy flux on Mercury of a billion times that leaving the sun? I have an idea, but my statmech is rusty. (the fourth root of a billion?)
And do we have to receive the energy and convert it to useful work with 99.999999999% efficiency to avoid melting the apparatus on Mercury?
I have no idea, I never took the relevant physics classes.
For concreteness, suppose we do something like this: We have lots of solar panels orbiting the sun. They collect electricity (producing plenty of waste heat etc. in the process, they aren’t 100% efficient) and then send it to lasers, which beam it at Mercury (producing plenty more waste heat etc. in the process, they aren’t 100% efficient either). Let’s suppose the efficiency is 10% in each case, for a total efficiency of 1%. So that means that if you completely surrounded the sun with a swarm of these things, you could get approximately 1% of the total power output of the sun concentrated down on Mercury in particular, in the form of laser beams.
What’s wrong with this plan? As far as I can tell it couldn’t be used to make infinite power, because of the aforementioned efficiency losses.
To answer your second question: Also an interesting objection! I agree melting the machinery is a problem & the authors should take that into account. I wonder what they’d say about it & hope they respond.
Yeah, though not for the reason you originally said.
I think I’d like to see someone make a revised proposal that addresses the thermal management problem, which does indeed seem to be a tricky though perhaps not insoluble problem.
Ok, I could be that someone. here goes. You and the paper author suggest a heat engine. That needs a cold side and a hot side. We build a heat engine where the hot side is kept hot by the incoming energy as described in this paper. The cold side is a surface we have in radiative communication with the 3 degrees Kelvin temperature of deep space. In order to keep the cold side from melting, we need to keep it below a few thousand degrees, so we have to make it really large so that it can still radiate the energy.
From here, we can use Stefan–Boltzmann law, to show that we need to build a radiator much bigger than a billion times the surface area of Mercury. It goes as the fourth power of the ratio of temperatures in our heat engine.
The paper’s contribution is the suggestion of a self replicating factory with exponential growth. That is cool. But the problem with all exponentials is that, in real life, they fail to grow indefinitely. Extrapolating an exponential a dozen orders of magnitude, without entertaining such limits, is just silly.
The conservation of etendué is merely a particular version of the second law of thermodynamics. Now, You are trying to invoke a multistep photovoltaic/microwave/rectenna method of concentrating energy, but you are still violating the second law of thermodynamics.
If one could concentrate the energy as you propose, one could build a perpetual motion machine.
I don’t see how they are violating the second law of thermodynamics—“all that conversion back and forth induces losses.” They are concentrating some of the power of the Sun in one small point, at the expense of further dissipating the rest of the power. No?
DK> “I don’t see how they are violating the second law of thermodynamics”
Take a large body C, and a small body H. Collect the thermal radiation from C in some manner and deposit that energy on H. The power density emitted from C grows with temperature. The temperature of H grows with the power density deposited. If, without adding external energy, we concentrate the power density from the large body C to a higher power density on the small body H, H gets hotter than C. We may then use a heat engine between H an C to make free energy. This is not possible, therefore we cannot do the concentration.
The Etendue argument is just a special case where the concentration is attempted with mirrors or lenses. Changing the method to involve photovoltaic/microwave/rectenna power concentration doesn’t fix the issue, because the argument from the second law is broader, and encompasses any method of concentrating the power density as shown above.
When we extrapolate exponential growth, we must take care to look for where the extrapolation fails. Nothing in real life grows exponentially without bounds. “Eternity in Six Hours” relies on power which is 9 orders of magnitude greater than the limit of fundamental physical law.
But in laboratory experiments, haven’t we produced temperatures greater than that of the surface of the sun? A quick google seems to confirm this. So, it is possible to take the power of the sun and concentrate it to a point H so as to make that point much hotter than the sun. (Since I assume that whatever experiment we ran, could have been run powered by solar panels if we wanted to)
I think the key idea here is that we can add external energy—specifically, we can lose energy. We collect X amount of energy from the sun, and use X/100 of it to heat our desired H, at the expense of the remaining 99X/100. If our scheme does something like this then no perpetual motion or infinite power generation is entailed.
How much extra energy external energy is required to get an energy flux on Mercury of a billion times that leaving the sun? I have an idea, but my statmech is rusty. (the fourth root of a billion?)
And do we have to receive the energy and convert it to useful work with 99.999999999% efficiency to avoid melting the apparatus on Mercury?
I have no idea, I never took the relevant physics classes.
For concreteness, suppose we do something like this: We have lots of solar panels orbiting the sun. They collect electricity (producing plenty of waste heat etc. in the process, they aren’t 100% efficient) and then send it to lasers, which beam it at Mercury (producing plenty more waste heat etc. in the process, they aren’t 100% efficient either). Let’s suppose the efficiency is 10% in each case, for a total efficiency of 1%. So that means that if you completely surrounded the sun with a swarm of these things, you could get approximately 1% of the total power output of the sun concentrated down on Mercury in particular, in the form of laser beams.
What’s wrong with this plan? As far as I can tell it couldn’t be used to make infinite power, because of the aforementioned efficiency losses.
To answer your second question: Also an interesting objection! I agree melting the machinery is a problem & the authors should take that into account. I wonder what they’d say about it & hope they respond.
A billion times the energy flux from the surface of the sun, over any extended area is a lot to deal with. It is hard to take this proposal seriously.
Yeah, though not for the reason you originally said.
I think I’d like to see someone make a revised proposal that addresses the thermal management problem, which does indeed seem to be a tricky though perhaps not insoluble problem.
Ok, I could be that someone. here goes. You and the paper author suggest a heat engine. That needs a cold side and a hot side. We build a heat engine where the hot side is kept hot by the incoming energy as described in this paper. The cold side is a surface we have in radiative communication with the 3 degrees Kelvin temperature of deep space. In order to keep the cold side from melting, we need to keep it below a few thousand degrees, so we have to make it really large so that it can still radiate the energy.
From here, we can use Stefan–Boltzmann law, to show that we need to build a radiator much bigger than a billion times the surface area of Mercury. It goes as the fourth power of the ratio of temperatures in our heat engine.
The paper’s contribution is the suggestion of a self replicating factory with exponential growth. That is cool. But the problem with all exponentials is that, in real life, they fail to grow indefinitely. Extrapolating an exponential a dozen orders of magnitude, without entertaining such limits, is just silly.