- Bob Armstrong <bob@...> writes:
>> Imagine a white metal sphere and a black metal sphere out in space at

You do, he does not.

>> about our distance from the earth. One half of each sphere is

>> illuminated by the sun and absorbs energy. One half is facing the rest

>> of the universe and is radiating it out by black body

>> radiation. Assume good heat transfer within the sphere. If both

>> radiate out freely on the same curves, but one absorbs more slowly,

>> then you end up with the one that absorbs more slowly at a lower

>> asymptotic temperature. Again, you haven't considered the entire

>> system.

>

> That is exactly the ultimate experiment I propose and will approximate .

> Kirchoff says they will be the same asymptotic temp and so do I .

Here is Kirchoff's law:

At thermal equilibrium, the emissivity of a body (or surface)

equals its absorptivity.

So lets analyze the situation, shall we? Since you keep invoking poor

Mr. Kirchoff, we'll use his law over and over.

Assume that we have two thin plates in space, one meter square, aimed

with one side squarely facing the sun, and the other side facing

space, at the same distance from the sun. For purposes of simplicity,

assume that space is at 0K instead of 3K -- it makes little difference

other than making the calculation simpler. Lets also assume the

distance from the sun is 1AU, so we can just use the earth's solar

constant.

We arrange for the front of one plate to be a perfect black body, and

for the the front of the other to reflects 90% of the incident

radiation. Let us further assume (for simplicity) that the rear of

each plate is a perfect black body (i.e. is painted exactly like the

front of the first plate). This will simplify our calculation.

The first plate is a perfect black body and therefore absorbs all

incident radiation. At equilibrium, therefore, it will be absorbing

1367W of energy. Based on Kirchoff's law, once we achieve thermal

equilibrium, the object must also be radiating 1367W of energy. The

surface area of the object is about 2m^2 (consider both the front and

the back), so it has to be emitting 683.5W/m^2.

The thermodynamic temperature of a black body can be measured by its

radiation by the Stefan-Boltzmann law, which states that the radiant

flux is equal to the Stefan-Boltzmann constant times the fourth power

of the temperature. Its value is 5.6704E-8.

So we divide 683.5 by 5.670400E-8 and take the fourth root. I'll save

you the trip to a calculator and note the value is 331.3K.

Now, lets consider the plate with one side 90% reflective and one side

a perfect black body. Total absorption is, by definition, 1367/10 or

136.7W. Total emission, by Kirchoff's law, must again be 136.7W. We

have to now emit from both sides -- but the corollary of Kirchoff's

law, we emit only 1/10th as much through the side that is 90%

reflective*, so we have the black body side emitting 124.3W/m^2 or

so. (We can't measure temperature directly from the other side because

it is not a black body -- it is emitting about 12.4W/m^2 or so).

We now note that by the Stefan-Boltzmann law, a black body emitting

124.3W/m^2 is at a temperature of 216.4K.

Please note that 331K and 216K are NOT the same temperature. (By the

way, for the Kelvin and Celsius challenged, 331K is about 136F, and

and 216K is about -71F -- different temperatures indeed.)

(*that's a slight lie -- no substance reflects in all bands equally,

so the emission in the much colder temperature band will be different

(and likely higher, resulting in an even lower temperature), but we'll

ignore that for this exercise, just as we ignored the fact that there

are no perfect black bodies.)

Anyway, if you have better math to present, please tell me about

it. Feel free to correct anything I did wrong.

> Otherwise you could transfer energy laterally ( not front to back )

Er, these objects CAN act as a heat engine, if you like. There is

> between them making a heat engine . That doesn't compute .

nothing wrong with that -- it doesn't violate the laws of

thermodynamics. Heat engines are just fine in an environment where the

heat is moving from a high heat spot (the sun) to a low heat region

(the entire universe).

>>>>First, we need to know the number we're starting with. The solar

So what? The question is whether there is a 100% correlation between

>>>>constant is 1367W/m^2.

>>>

>>> Of course , the solar constant is not 4 or even 3 digits constant .

>>> In fact at least half and estimate range to .8 and .9 and greater

>>> of total variance in mean earth temperature has been found explained

>>> by variation in solar radiance . I claim it will eventually be

>>> understood to be 1.00 .

>>

>>

>> I have my doubts on that. That would assume that there is no

>> greenhouse effect at all, and there very clearly is. That would also

>> assume there is no variance in albedo, and there very clearly is.

>

> Do a little web surfing or go to my http://cosy.com/views/warm.htm for

> links . The variability in solar output and it's correlation with

> earth's temperature is an established fact .

variance in the earth's temperature and solar radiance, not whether

there is a majority correlation.

> I used to think quite a bit about albedo because there are such extreme

Large scale environmental models are good ways of examining that problem.

> changes in it . How can the earth not get trapped in an ice age when

> that positively feedsback increases in the reflectivity of the planet

> so much ?

> I have come to believe that the energy density at this distance

We all have our personality quirks.

> from the sun is the only determinant of mean temperature ,

If you would like to bet money on this, even after I showed you the

math, please, by all means, bet me on it. We will need to come up with

an adequate statement of what we are betting on, of course.

>>> Of course in the same 24 hours an average nuke will produce 24,000

I note that you didn't catch my math error here, and it was a huge

>>> MWh versus your 3MW .

>>

>> 3MWh is one acre. The average nuclear installation covers many many

>> acres. If it covers a mere 8 acres (not unreasonable including

>> security buffers etc) you have the same output.

one-- 24GWh vs 24MWh. Still, 8,000 acres isn't really that much

space. The world is filled with wastelands.

Consider also that there is plenty of room in orbit, and you get both

an extra 25% (the amount of sunlight blocked by the atmosphere and

clouds), and the sun shines 24x7, and you can aim perpendicularly at

the sun at all times in orbit. Moving the power to the ground via

microwaves loses maybe 20% but you've more than made up for that here

already...

>> Also, we *will* ultimately produce multiple absorber panels, which

At the moment, yes, because of cost. However, manufacturing techniques

>> will have much higher efficiency still.

>

> I see your .3 efficiency being reached in labs . 0.2 seems to be

> about SoA commercially .

only improve with time, and with them, costs fall.

> But the talk is of doubling the lab efficiencies to .6 or more .

Not yet really. No one knows how to make a multiple absorber -- yet.

> That would change the area required to equal a moderate nuke from

My number is 12.5 square miles for a "worst case" 24GWh/day setup --

> 19 to 6 square miles .

the latitude of NY in wintertime. Nearer the equator is much

better. If we do get to .6 (multiple absorbers), we'd need about 6.25

square miles at that "worst case" latitude.

>> Consider also that

At the moment, yes. There are better things on the horizon. We can

>>

>> a) This is just a way of collecting energy. We can store it and

>> transport it in a variety of ways.

>> b) The price will only go down with time, and the efficiency will only

>> go up.

>

> Pumping water is hard to beat .

also move power around very efficiently over extreme distances if

we're willing to use superconducting cables.

--

Perry E. Metzger perry@... - Bonnie wrote:
> I kept meaning to get back to this thread, and am finally

Bore hole heat sinks are becoming a common feature in new

> doing it because I just saw a relevant blog posting to pass

> along.

>

> See:

> http://geddesblog.blogspot.com/2006/01/baloghblog-storing-summer-solar-heat.html

>

> That comment of Bob's kept resonating in my head as the days

> got shorter and therefore, colder: That the sun doesn't even

> give us enough energy to keep the ground from freezing for

> the winter. How true! (Despite the temporary January thaw we

> just got here.)

>

> Anyway, that blog posting mentions:

>

> 1. Capturing the winter cold, in the form of pykrete, to cool

> buildings in the summer

> 2. Borehole thermal energy storage (BTES), an in-ground heat

> sink for seasonal energy storage -- and a link to a Canadian

> community setting this up to heat a 52-house subdivision in

> winter

construction in NYC . You will find the caps of the 1600' bore

holes in front of all the Sciame reconstructed buildings along

Front St and Peck Slip by the Seaport .

> As for my yurt:

Likewise here in CO . We've got years of wood to burn just

> 1) My solar panels have arrived, I've got my batteries,

> but haven't done anything with them yet. But I'm not

> trying to heat the place with them, just provide a little

> light and music now and then!

> 2) For heating the yurt, I'm going to take advantage of

> some natural solar energy storage...in the form of downed

> trees on the property I'll be burning!

to clean up the property , especially because of beetle killed

trees . Our main need to enhance our solar efficiency is thermal

curtains to cover at night the picture windows which collect a

lot of sun in the afternoon .

We have some solar powered lights ( LED ) out on the front

gate , and would love to get a solar powered remote gate

opener . I got an ad for a solar powered freezer which seems

like a neat use because you get the power just when you need

it - winter takes care of itself . On some of the most remote

and severe curves between here and Denver , there are solar

powered warning flashers . These are the really practical uses

of a few square feet of solar panels ( a few watts ) and will

clearly dominate its use in temperate climates for a long time .

--

Bob Armstrong -- http://CoSy.com -- 719-337-2733

CoSy 2005 NewsLetter & MidWinter Party[ 19 ]

: http://CoSy.com/home.htm#20051231