- #36
the4thamigo_uk
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DaleSpam said:In the context of the conversation I don't understand this comment at all. In post 29 you specifically posited that you could get thermal energy transfer from a large cold blackbody to a small hot blackbody by using mirrors. That is inherently a geometrical argument. If you have passive radiative heat transfer from a cold blackbody to a hot blackbody then you are violating the 2nd law of thermodynamics by definition.
No, I wonder, does anyone here know what I am talking about? /
Im simply trying to show that it is theoretically possible to direct the radiative power from one source black body at fixed temperature T onto a second smaller black body, in order that the smaller black body achieves a 'steady state' temperature greater than T. The source black body is NOT passive, it is supplied heat from a hot plate. It all seems fairly obvious to me now, but some people disagree it seems?
Avoiding geometry, from only a thermodynamic argument, I 'could' simply state, that these two black bodies are the only things that exist in the world and that all the radiative power that each body emits is directed onto the surface of the other body. This is sufficient for the argument. There really is no need for geometry/optics.
Does anyone disagree with this on a 'purely thermodynamic' basis? This is what I want to find out. If its wrong, then its wrong, but exactly why is it wrong?
However, some people seem have countered that this is impossible, by invoking geometrical arguments about mirrors/lenses and such. Hence, to challenge this geometical argument, and 'only' in order to challenge this geometrical argument, we can use the enclosed black body example, which does not rely on mirrors/lenses. I think it is a fairly robust example.
Unfortunately again, some people may still think that this is an unrealistic counter-example even though it is a perfectly good enough example as far as I can see. We could easily build this experiment I believe.
In fact what the enclosed BB example shows is a perfect example, in that 'All' the radiative power from each body is directed to the other body. But, in fact you can relax this condition anyway. You 'dont even' need to capture all the radiation from the source body. All you need to show is that there is a way to increase the flux emitted from the surface of the source BB, such that it illuminates the entire surface of a smaller black body. This is what the mirrors example shows. You 'dont even' have to double/quadruple the flux, all you need to do is increase it by some amount. The flat BB is a sufficient example I think.
So, for a large BB maintained at T by a source of energy, it *is* possible to heat a smaller BB such that it achieves a higher temperature in a steady state. The two bodies do not have to be in thermal equilibrium as there is heat supplied.
If there is no heat supplied, then the black bodies will (eventually) achieve the same temperature, based on some system of differential equations like those given above.
Does anyone agree with this? ( or are you all bored by it? D ) ...
If you have passive radiative heat transfer from a cold blackbody to a hot blackbody then you are violating the 2nd law of thermodynamics by definition.
Second law of thermodynamics
'Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.' (Clausius)
For illustration take the enclosed black body example. The condition for steady state is that the (total power emitted by inner BB) = (total power emitted by the outer BB). There is *zero net heat flow* between the two BBs.
It might be the wording of the Clausius statement that is confusing, a BB at non-zero temperature will always emit radiation, yes? There is nothing to stop it? Its charges are jiggling about so it generates radiation. Radiative energy therefore is 'spontaneously flowing' from each body, it is just that they are exactly equal in the 'steady state'
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