There is an important difference between transfer of heat energy by conduction and radiation, which connects to the following different aspects of heat energy:
- radiative: possibly focussed in frequency but always spread out in space
- conductive: possibly focussed in space but always spread at high frequency.
Radiative heat can by itself only transfer from a blackbody spectrum with higher cut-off, that is from higher to lower temperature.
Conductive heat normally transfers from high to low temperature, but a body locally heated to high temperature, can locally heat a body of higher mean temperature.
Radiative heating is limited to transfer only to lower temperature, which forbids any form of backradiation. In the setting of the model of the previous post, this means that not only is
- sum (R_B(f)^2 - R_A(f)^2) non-negative
but also is each term
- R_B(f)^2 - R_A(f)^2 non-negative
for each individual frequency f, because the spectrum is given by Planck's Law. This means that
radiative heating by a single prominent frequency in a spectrum of low (mean) temperature, is physically impossible.
The erronous idea of backradiation may come from a confusion with conductive heat transfer,
where a form of backradiation is possible as indicated.
Inlägg
"Radiative heating is limited to transfer only to lower temperature, which forbids backradiation"
SvaraRaderaAs ever, you confuse macroscopic and microscopic phenomena. Obviously, the net flow of energy between two bodies is from the warmer to the cooler body. Also obviously, there is no physical means by which the cooler body can radiate only in directions which do not intercept the warmer body. And finally, obviously, a body which absorbs radiation gets warmer as a result. None of this contradicts the first obvious point.
This is such elementary stuff that it takes a special effort not to understand it.
Another example of a situation which is well established observationally which contradicts your ideas is that of close binary star systems. In a close binary, with two stars at different temperatures, each star heats the other. There are, of course, countless other examples.
When the observations contradict your theory, your theory needs revising.
I'd love to see an explanation for how you imaging heat can flow from a cold to a hot object through conduction.
SvaraRaderaI can imagine how the 2nd law is violated in a gravity field with a system B is above a system A and where the temperature in B is lower than in A. B simply lets some of its low-energetic molecules fall down into A, thus increasing the ensemble average of the kinetic energy in B while lowering it in A. But in this process heat goes from B to A, apparently contradicting the 2nd law. But this of course depends on which theoretical framework you prefer.
SvaraRaderaAnders, your example doesn't violate the second law. You just convert potential energy to thermal energy which increases entropy.
SvaraRaderaI agree that if entropy is increased the 2nd law is not violated, (interesting to see Claes agree on this point). I guess it works out fine if you treat both systems as grand canonical ensembles. There is of course a certain gain in kinetic energy if a particle falls down but i didn't quantify it and it can be made negligibly small. The main point is that a system can increase its temperature by getting rid of slow molecules and deposit them in a reservoir possibly at higher temperature. Is there a consensus that the temperature of an ideal gas is proportional to the ensemble average of the kinetic energy?
SvaraRaderaAnders, it seems I misunderstood your example. It just isn't possible to selectively get rid of the slow molecules to increase the temperature of an object without spending energy to do it, which increases entropy. You'd need a Maxwell's demon to do that, and those seems to violate the laws of nature as we know them. Gravity will just pull down all molecules by the same amount regardless of their velocity.
SvaraRaderaHeat is small scale kinetic energy, not kinetic energy.
SvaraRaderaThomas, you are right that gravity pulls on every molecule and that there will be exchange of particles in all directions. Maybe I could put it in a more precise form: The canonical equilibrium distribution of an ideal gas in a gravity field has a constant temperature curve and barometric pressure and density curves. Suppose you would instead prepare the (finite) system with a constant density curve and linearly decresing temperature. If you then leave the system to attain its equilibrium configuration I'm not so certain that the net heat flow would be from higher to lower temperature, if temperature is defined in the way prescribed by computational thermodynamics. I am pretty certain that one can cook up initial conditions where the flow would be from lower to higher temperature. This is of some interest (at least to me) since the statement of the 2nd law in statistical mechanics is quite categorical: "Heat flows spontaneously from higher to lower temeparture".
SvaraRaderaAnders, why don't you make an experiment proving your idea and collect the Nobel?
SvaraRaderaIt is not primarily an experimental question more conceptual, I'm sure it would be a piece of cake for Claes to simulate this.
SvaraRadera