Boerseun's Perpetual Motion Machine...

[Boerseun]

Haha - got you to look.

 

But consider this:

 

A dippy bird works thermally, and if you did not know that, it would look like a bona-fide perpetual motion machine.

 

Now here's my question:

 

If you were to put a dippy bird in a dark and sealed room so that no thermal induction can make the thing work, it should stand still. You can dip its head and it will wobble a little until it comes to rest again, because if your room design is all good, there's no energy coming from outside.

 

Now - microwave radiation is photons of a particular wavelength. Photons at the wavelength of visible light can be concentrated using parabolic mirrors, etc. Can you build a similar concentration device (lens, dish, or mirror) with some fancy material that can change the direction microwaves follow? If so, can you build a device that can concentrate CMBR to such an extent that it can make a dippy bird move in the absence of any other heat source? And will your device (for concentrating CMBR) be small enough to fit on the planet, at least?

 

This is merely speculation, of course - because the CMBR is so faint that I think a device to catch enough of it to make just a little dippy bird move will be so huge as to make the whole scheme impractical. But the CMBR is not 0 degrees - so there must be some usable energy there - it only needs to be concentrated by some mirror, lens or dish so as to be usably warmer than the environment and a heat-flow engine can use it.

 

Thoughts?

[modest]

If you were to put a dippy bird in a dark and sealed room so that no thermal induction can make the thing work, it should stand still. You can dip its head and it will wobble a little until it comes to rest again, because if your room design is all good, there's no energy coming from outside.

 

Yeah—that's my understanding too. You need a temperature gradient for it to work... like a heat engine.

 

Now - microwave radiation is photons of a particular wavelength. Photons at the wavelength of visible light can be concentrated using parabolic mirrors, etc. Can you build a similar concentration device (lens, dish, or mirror) with some fancy material that can change the direction microwaves follow?

 

Sure. Satellite TV dishes do that.

 

If so, can you build a device that can concentrate CMBR to such an extent that it can make a dippy bird move in the absence of any other heat source? And will your device (for concentrating CMBR) be small enough to fit on the planet, at least?

 

Absolutely.

 

If a person wanted to amplify the cosmic microwave background into something about as powerful as a cheap microwave oven then they would need a dish....

 

:confused: ....

 

Ok. The CMB is 2.735 K which can be converted to power in W/m² via the Stephan and Boltzmann law since it is blackbody. It comes out to 3.11 x 10^-6 W/m². That's how much power the CMBR has with no amplification. We'll need a gain of 800 W/m² / 3.11 x 10^-6 W/m² = 2.57 x 10⁸ to bump that up to 800 watts. The power gain on a parabolic dish is given by:

[math]G = \pi^2D^2/\lambda^2[/math]

so wes needs ourselves...

[math]D = \sqrt{\frac{G\lambda^2}{\pi^2}}[/math]

where

G = 2.57 x 10⁸

[math]\lambda[/math] = 0.0018 m (this is the wavelength and I think the CMBR peak wavelength is about 1.8 mm???)

[math]\pi[/math] = 3.14159 :D

[math]D = \sqrt{\frac{2.57 \times 10^8 \cdot 0.0018^2}{3.14^2}}[/math]

[math]D = 9.19 \ m[/math]

That can't be right :( A 10 meter dish would boil water at its focal point from cmb alone?.... no, that can't be right....

 

The power of the CMB is given on this page:

CMB uniformity

The power gain of a parabolic dish is given:

Parabolic antenna - Wikipedia, the free encyclopedia

 

I can't figure what I've done wrong but I find the answer unsatisfactory... Hummm....

 

~modest

[lawcat]

Edit: sorry I mesed up.

[Boerseun]

Awesome reply, modest - although I guess there must be a problem somewhere...

 

If you can convert CMBR to 800W using just a 10m dish, or a 30m dish as per lawcat, then using one helluva big dish, you can use CMBR commercially? :eek_big:

 

Commercially as in boiling water and feeding the steam through a turbine?

 

I don't know...

 

Somewhere, something doesn't gel...

[Boerseun]

...also, coming to think of it, the receptor at Arecibo should have been thoroughly cooked by now, if a 10m dish can concentrate CMBR to 800W?

[modest]

Right. That's what I was thinking. There are plenty of astronomy dishes which are larger than 10 m which—I would assume—achieve nothing like 800 watts / m^2 at their focal point even with all the local radio and microwave sources. So, I'm sure something has gone wrong with the numbers above. But, the power of the CMB (3.11 x 10^-6 W/m²) and the equation for the power gain of a parabolic dish look right... so I can't figure what I've done wrong :eek_big:

 

~modest

[Boerseun]

That's 3.11 x 10-6 W/m2, so wouldn't you need at least a million m² to get the ten-to-the-power minus six down to at least 1?

 

Which means a dish of a 1,000,000m² will yield 3.1W from CMBR?

 

That might be little closer... :eek_big:

[modest]

That's 3.11 x 10-6 W/m2, so wouldn't you need at least a million m² to get the ten-to-the-power minus six down to at least 1?

 

Which means a dish of a 1,000,000m² will yield 3.1W from CMBR?

 

That might be little closer... :shrug:

 

Yes. I'm such an idiot. That power gain equation is not meant for w/m^2, but rather just for watts. The total watts of the dish is divided by the area of a single wavelength. So a 10 meter dish could, with perfect efficiency, capture 800 watts and focus it onto something with a surface area of 1.8mm².

 

But, I also think I messed up in another way. The unamplified power of the CMB is 3.11 x 10^-6 W/m², but I think that is for the whole sky. A parabolic dish takes in only parallel rays, so it takes in a very small portion of the sky's available energy.

 

Both factors corrected for, it would probably end up being a rather large dish needed to raise the temperature enough to make our little dippy bird go.

 

I guess we could try this again.... To make our little bird go we probably need something like (total guess) 10 watts per square meter. The CMB is 3.11 x 10^-6 W/m², but our dish will have a very small field. How small is again going to be a complete guess... let's say... a thousandth of a percent of the full sky :shrug: :hihi: So... we need a gain of

 

10 / (.00001 x 3.11 x 10^-6 W/m²) = 3.2 x 10¹¹

 

... and since we started with a surface area of 1 meter then the above is the necessary surface area of the dish. As SA = 4 pi r² we need a radius of

[math]r = \sqrt{ \frac{3.2 \times 10^{11}}{4*3.14}} = 159 826 \ m[/math]

 

So... a dish of about 150 thousand meters in radius.... about the size of Iceland...

 

That seems like it could be in the neighborhood of being correct... but I haven't slept in a good long while and I could be making very little sense. :hihi:

 

~modest

[Qfwfq]

I a sealed room, the dippy bird's inexorable problem shouldl be the air reaching saturation, even if the latent heat of vaporization doesn't significantly decrease the room's overall enthalpy. The only thing to keep the bird going would be to keep the felt warmer, supplying the heat fro evaporation, and make the pool of water (or surfaces that drain into it) remain the most favoured place for condensation which requires absorbing the heat. In short, you need the water to evaporate from the beak more than it condenses on it and vice versa elsewhere.

 

Now - microwave radiation is photons of a particular wavelength. Photons at the wavelength of visible light can be concentrated using parabolic mirrors, etc. Can you build a similar concentration device (lens, dish, or mirror) with some fancy material that can change the direction microwaves follow? If so, can you build a device that can concentrate CMBR to such an extent that it can make a dippy bird move in the absence of any other heat source? And will your device (for concentrating CMBR) be small enough to fit on the planet, at least?

The CMBR is thermalized radiation and has what is presumably the lowest naturally occuring temperature in the universe. The idea of using it as a heat source for a thermodynamic engine makes less sense than using it for the heat sink, but even this strikes me as rather extravagant.

 

In any case, I see no reasonable way of tapping the CMBR as a profitable source of energy.

[Boerseun]

The CMBR is thermalized radiation and has what is presumably the lowest naturally occuring temperature in the universe.

Yes. Well. There cannot be anything colder, because anything colder will be heated by the CMBR, which is everywhere. Anything colder is artificial, and, as far as we know, because of human meddling.

The idea of using it as a heat source for a thermodynamic engine makes less sense than using it for the heat sink, but even this strikes me as rather extravagant.

I fail to see how you can use radiation as a heat sink. But being neither here nor there, this wasn't supposed to be feasible in the least - just interesting:

And will your device (for concentrating CMBR) be small enough to fit on the planet, at least?

In any case, I see no reasonable way of tapping the CMBR as a profitable source of energy.

Neither do I. It would be interesting to know whether a machine that can heat a dippy bird purely with CMBR will fit on the planet, though.

 

Anybody want to double-check Modest's calculation of a dish the size of Iceland? That's quite interesting, actually.

[Qfwfq]

I fail to see how you can use radiation as a heat sink.

Not the incident radiation, of course, in this sense you are correct. However, you could say the same about a pair of parallel flat surfaces of solid bodies, separated by a vacuum and yet, just as we say the warmer one cedes heat to the colder, so we say the colder absorbs it from the warmer. You would be equally correct in pointing out that, strictly, it's just that more heat is going one way than the opposite.

 

Now the way black body radiation works doesn't essentially depend on there being a solid surface except for these having a lower emissivity than perfectly black; they can be called grey bodies. So, the sky (between stars and things) is not much different and it isn't a matter of feasibility but rather one of principle and:

Neither do I. It would be interesting to know whether a machine that can heat a dippy bird purely with CMBR will fit on the planet, though.

The fact is that the CMBR would never heat it, no matter how big the parabola. Just as you agreed that anything colder would be heated, so could nothing warmer be heated by it.

 

Interesting question: could a material surface have an absorbtivity coefficient differeng from its one of emissivity? Don't cheat! Too easy to look it up, just reason upon it! :eek_big:

[Erasmus00]

Think of the CMBR as being (roughly) the temperature of the universe. The only way to get work from heat is to have something colder (if I have a hot brick, and want to power a heat engine, I need a cold brick for the other side).

 

So if you super cooled something to below about 3 kelvin you might be able to use the heat of the CMBR to power a device, but you'll certainly expend more energy cooling to 3 kelvin then you'll get out of the engine.

[sanctus]

Ok, now just wondering, what if you replace CMB with cosmic rays?

Intuitively, I think it would amount to the same, since the latter have higher energy but lower intensity...

[modest]

The fact is that the CMBR would never heat it, no matter how big the parabola.

 

 

The temperature of space is not given by the wavelength alone. It's also given by the flux. Put another way: the temperature of a photon gas is a function of the density of photons (among other things).

 

You can increase the flux with a lens or dish, and I'm pretty sure that putting 1,000 watts of microwave energy through a point will biol water at that point. I do it every day when I make tea.

 

...The only way to get work from heat is to have something colder (if I have a hot brick, and want to power a heat engine, I need a cold brick for the other side).

 

Yes, but you could create a temperature gradient with a lens or a dish even using only CMBR and even in a place as hot as our solar system. No?

 

~modest

[Pyrotex]

Make a CMBR antenna 1,000 km in diameter.

Refocus the energy and beam it straight down toward a small convenient black hole.

Just outside of the event horizon, put one of those paddle-wheels in a vacuum thingie that rotates when sunlight falls on it. Put a million of them.

The black hole gravity will shift the CMBR spectrum from the microwave to the near infrared, enough to spin the paddle wheels like crazy, driving turbines that supply electricity to a fantastic space city in orbit about the black hole.

[modest]

Make a CMBR antenna 1,000 km in diameter.

Refocus the energy and beam it straight down toward a small convenient black hole.

Just outside of the event horizon, put one of those paddle-wheels in a vacuum thingie that rotates when sunlight falls on it. Put a million of them.

The black hole gravity will shift the CMBR spectrum from the microwave to the near infrared, enough to spin the paddle wheels like crazy, driving turbines that supply electricity to a fantastic space city in orbit about the black hole.

 

That's clever But, I think you could avoid the black hole frequency converter by using a material in your heat engine which efficiently absorbs microwaves, like, water—rather than the fabric (or plastic??) of a paddle wheel.

 

But, if you were intent on using a paddle-wheel and didn't have a black hole you could also use a material to convert microwaves to infrared (rather than using a black hole). I think, again, water would be best since it absorbs microwaves and emits infrared

 

~modest

[modest]

You can increase the flux with a lens or dish...

 

I thought of a geometric proof which seems to disprove my own assertion.

 

At any given point in space the CMBR is isotropic making the probability that an incoming photon passing through that point comes from a certain direction equal to the probability that it will come from any other direction.

 

The points R1 through R5 in the following diagram would direct red rays to P with the blue lens and direct black rays to P with no lens. Since the red and black rays are equally likely and since the same could be said for any other point along the line of the lens there should be no greater or lesser number of photons passing through P with or without the lens.

The same principle should hold for a parabola. I therefore agree with Qfwfq,

The fact is that the CMBR would never heat it, no matter how big the parabola.

Since the CMBR is isotropic it would seem a lens or dish would not increase the luminosity at the focal point in the same way that it does for a directional source.

 

Sorry Boerseun

 

~modest