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Post by icefisher on Apr 17, 2012 20:52:23 GMT
 So here is the challenge. 1) What we have here are two spheres. One is slightly larger than the other (surface wise) but since the diameter of the inner shell is 8,000 miles and the outer shell is for TOA isn't much different say 8,020 miles we are going to disregard the differences for the purposes of this discussion. 2) The outer sphere is hollow (Sphere) and is made of some super material one molecule thick 3) the inner sphere is a solid ball (Ball) with a constant heat source sufficient to supply 341 watts/m2 to the surface of the ball. 4) All surfaces have a blackbody emissivity of 1.0, thus they are completely opaque and transmit and reflect no light. 5) Required equilibrium radiation power value for the outside of the Sphere is nominally 341w/m2 (though it would be very slightly less in the real world due to more rapid cooling given the Sphere has slightly more surface area). If that becomes a critical issue for anybody desperately trying to complete this assignment while holding current beliefs. . . . we can get to that later. 6) A vacuum exists between the Sphere and Ball. We may play with this parameter later also but for now the only means of heat transport between the Ball and Sphere is radiation. So what we must do is fill in the equilibrium radiation powers for A and B (These are radiation power vectors associated with nearby arrows) and provide any necessary temperature gradients and explanations where any temperature gradients exist between or within the surfaces themselves or cores. p.s.I will start and assign the value of 341w/m2 to both A and B. Those values are just my completion of the assignment and are NOT notated on the graphic. No explanation is needed as no gradients exist. . . .as well as zero greenhouse effect from absorption by the Sphere.
However, don't let this distract you. I am not requiring the use of my answer so if you don't like my answer provide another.
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Post by sigurdur on Apr 17, 2012 22:48:37 GMT
Sorry, but you totally lost me.
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Post by icefisher on Apr 18, 2012 0:21:22 GMT
Sorry, but you totally lost me. There is no argument above Sigurdur. Just a description of a starting condition of a thought experiment. A ball of specified attributes in the middle of a hollow sphere. The ball is internally warmed with 341watts times the square meter surface of the ball. Lets say it has a 1 square meter surface so the internal heat source is 341 watts. The Sphere (outer circle) is bigger but we are going to ignore that as in our earth/atmosphere system TOA is not of a materially larger number than the surface of the planet. It might in reality at earth/TOA scale reduce the outer radiation surface by a watt or two. The rest is just to make it easier so one does not need to consider reflectivity or emissivity and just use the easiest of equations. So two vectors are drawn the initial radiation of the ball and the amount of radiation the outer shell needs to radiate to keep in equilibrium with the internal heat source. The heat capacity of the outershell is negligible because it is only one molecule thick, radiatively speaking it doesn't matter what its made of beyond needing to be a blackbody. This is simply a very simple model of a greenhouse. The heat is trapped from radiating to space by the outer shell. The outer shell can only cool by radiating to space. The ball can only cool by radiating to the sphere. So the job is to fill in the radiation power figures in accordance with SB rules, and assign those values to vectors A and B. Explain any resulting heat gradients. All this does is capture my view of the greenhouse issue when boiled down to strictly radiation. Have at it. |
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Post by icefisher on Apr 18, 2012 0:30:13 GMT
Sounds like the usual incoherence 1. You say emissivity of B is 1. So B is a perfect black body absorber 2. You confirm you are saying B has zero reflectance so must be a perfect absorber 3. you say B has zero greenhouse effect from absorption so by definition it logically follows it must be a perfect reflector and a perfect insulator No B is the label for the radiation power vector from the inside of the Sphere (outer circle). It needs to be specified as a radiation rate in accordance with SB equations. 1. The Sphere which you seem to think is B is just the "Sphere". Sorry for not being more careful with the labeling and yes its emissivity is 1.0. 2. Yes its a perfect absorber. 3. I don't understand your statement. Reflectors have very low values of emissivity, like less than dot 1 (0.1). Blackbodies do not reflect. They absorb all light and emit. Your job is to calculate the temperature of the 2 surfaces facing inside the vacuum space, specify their radiation power in watt/m2 in accordance with SB equations. Make any adjustments from back radiation, and still have the system in equilibrium with its power source. |
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Post by icefisher on Apr 18, 2012 0:33:10 GMT
So now there are three objects.1.The shell that can only cool to space
2.The ball that can only cool to the sphere
3.The heated sphere
No just two objects. 1 and 3 are one object. Sorry for changing the nomenclature.
I have gone back and fixed the posts so nomenclature is consistent. Sorry for the confusion.
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Post by icefisher on Apr 18, 2012 0:54:52 GMT
as well as zero greenhouse effect from absorption by the Sphere..What does that mean? Thats the conclusion of my completion of the assignment. I could be wrong. I am interested in opinions of others and how they would complete the assignment. All this is is the simplest of greenhouses. We can't construct this but its perfect fodder for SB, or drawing temperature gradients through molecules and any other nonsense anybody can think of. |
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Post by icefisher on Apr 18, 2012 1:32:20 GMT
Thats the conclusion of my completion of the assignment. I could be wrong. I am interested in opinions of others and how they would complete the assignment. All this is is the simplest of greenhouses. We can't construct this but its perfect fodder for SB, or drawing temperature gradients through molecules and any other nonsense anybody can think of. So you are saying that you are demanding that no backradiation is allowed from the outer shell back towards the surface of the heated ball? And therefore you are demanding that no greenhouse effect is permitted for this simple greenhouse?? I am demanding nothing. I just created some initial conditions for a simple 100% radiation-based greenhouse. If its lacking I think thats part of the assignment (see item 6 in the initial conditions) |
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Post by icefisher on Apr 18, 2012 2:18:24 GMT
Your thought experiment needs to specify 1. Type of heat source 2. Temperature of surroundings or space outside of the outershell 1. Its a 100% efficient heat generator located evenly spread one molecule deep below the surface. It would have been uniform radiation above the surface but I moved it below the surface so as to avoid the problem of shining light through an opaque sphere. Lets just say in every way it behaves like sunlight but we are going to be well-behaved climate scientists (to keep our jobs) and completely ignore any losses on the way to the surface working its way through absorbing molecules in the atmosphere. 2. temperature of space: We have none. Assume zero kelvin. Or if you think that creates a problem then 3K will only produce a small fraction of a watt and can be disregarded. |
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Post by icefisher on Apr 18, 2012 2:38:13 GMT
Using the SB calculator hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c3You will find that 341w of heat loss occurs from a surface at 278.5K with surroundings of 3K Therefore 278.5K is the temperature of the outershell, since all of the energy of the 341W heat source has to be lost from this surface going back to the SB calculator we find for two surfaces where the colder surface is 278.5 and the heat loss from the hotter surface is 341W that the hotter surface is 331.2K So outer shell is at 278.5K Surface of heated ball is at 331.2K You are not done. You need to produce the radiation power vectors for these and show balanced flows and or temperature gradients with explanations for them. |
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Post by icefisher on Apr 18, 2012 3:42:09 GMT
Are you saying you want me to to tell you what the radiated power from each surface will be? using the calculator with 0K cold surface we get 341W from the outershell towards the heated surface 682W from the heated surface to the colder outershell What do you mean by balanced flows?? The net heat loss is 341W from the heated surface So 341W of backradiation is balanced by 341W of forwards radiation for a net result of no cooling from the heated surface for this particular half of the total 682W of cooling energy leaving the heated surface. Another 341W of cooling energy from the heated surface travels thru the outershell to space. OK your proposal is the SB blackbody surface temperature thing is wrong. We have a 682 watts radiating on to the inside surface of the blackbody Sphere and it will only heat to 1/2 the SB estimated temperature because 50% travels through the layer. Have I got that right? |
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Post by icefisher on Apr 18, 2012 7:06:17 GMT
Nothing is wrong with SB The cores surface is only heated by the powered energy from under the surface by an energy of 341WM2 for area of 1 The outer shell has twice the radiating area with 341 going upwards and 341 going downwards The maths will be an approximation because we are not dealing wth two flat surfaces and I used that calculator that assumes that. You have said though that effectively there is an infintessimally small vacuum gap and therefore all radiations leaving the surfaces will only travel to the opposite surface. The operating heating force for the outer ring is 682W The operating cooling force for the outer ring is 682W A radiation thermometer with emissivity set to 1 will record the temperature of the outer shell as 278.5 from either side. And for the surface of the Ball (inner sphere) each side of the top layer of molecules is radiating 682w/m2? and is 331.2K? |
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Post by icefisher on Apr 18, 2012 7:11:07 GMT
My explanation needs to be reworded/reworked At equilibrium the heating and cooling forces of the surface are in balance so that the temperature is constant A net 341W of energy is lost from the surface The one molecule thick hotter core surface layer actually receives 682W of energy from below the surface and sends 341W back below the surface. It then receives 341W downwelling for a total received energy force of 1023W
This received energy force is balanced by 1023W of cooling force for a steady temperature. The heat loss from the surface is: 682 upwards from below + 341 downwelling - 682 upwards towards the outer shell = 341W of heat loss So the hotter core layer has a heating force of 1023W and a cooling force of 1023W The cooler outer shell has a heating force of 682W and a cooling force of 682W Hmmm, I replied above before seeing this rework. I am not sure I understand it. Can you sketch it out? |
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Post by icefisher on Apr 18, 2012 8:36:45 GMT
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Post by icefisher on Apr 18, 2012 9:25:55 GMT
If we are now understanding each other if you could go back thru those earlier posts and tidy them up a bit then we can work thru some other areas as to why C02 might be fairly insignificant where we can both feel we are in the same team. I was sort of figuring maybe adding another outer sphere. Would that double the ball's surface radiating power? It appears each layer is doing that. |
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Post by icefisher on Apr 18, 2012 14:06:46 GMT
I was sort of figuring maybe adding another outer sphere. Would that double the ball's surface radiating power? It appears each layer is doing that. I tried this earlier:  Curiously if you add more layers with the same area and keep temperature gradients as zero it makes no difference other than to raise the height of hotter surface layers above the heated sphere. In climate science language the top colder outer shell has the 'effective temperature' that would have been present at the surface without the emitting atmosphere. All that will happen when you turn on the power of the heated sphere is it will take longer for the full amount of heat to reach the top layer as each physical surface warms with 682W of heating and 682W of cooling, where each of the lower surfaces 'sees' the same final temperature of 321.2, apart from the layer under the final outer shell. Quite counter intuitive that this is so. Looks like you have an error. You have different values radiating from the two sides of the molecule in the middle circle. 682 needs to be radiating to the ball at "A=", and that then cascades to the ball surface It looks like your model requires 682 watts increase for each absorption layer in order to maintain a 341 watt surplus. Could you check that? |
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