On 11/20/2014 3:57 PM, George wrote:
Thanks Bruno, Liz and Richard for your responses.
The topic is extremely controversial… It took me a few months of sleepless nights to
come to term with these ideas…. but let reason prevail. I am looking forward to an open
and rational discussion… a background in statistical thermodynamics would be helpful.
Bruno, you may not be able to download my pdf file because your Adobe Reader is not up
to date. If you wish I could simply attach these files to my email. Please let me know.
You asked me to summarize my post. The best way is with pictures taken from my
paper#2.https://sites.google.com/a/entropicpower.com/entropicpower-com/Thermoelectric_Adiabatic_Effects_Due_to_Non-Maxwellian_Carrier_Distribution.pdf?attredirects=0&d=1
(Currently under review)
Figure 7 shows what happens to the energy distribution of a Maxwellian gas (e.g. air) as
molecules rise from ground level (red) to a given altitude (blue). Kinetic energy is
converted to potential energy and the distribution shifts to the left.
Am I correctly interpreting this curve as showing that the kinetic energy probability
density function is an exponential; so that the most probable kinetic energy for an air
molecule is zero?? Why isn't it the Maxwell-Boltzmann distribution?
Brent
However when the distribution is renormalized as shown in Figure 8, the original
distribution is recovered, implying that the gas is isothermal with elevation. The
Second Law is upheld and Loschmidt is proven wrong….. but only with respect to
Maxwellian gases.
Now see what happens when a Fermi-Dirac gas (carriers in a semiconductor) is subjected
to a force field as shown in Figure 9. The distribution is shifted to the left as
elevation increases. However, renormalization does not recover the original distribution
because it is not exponential. The lower elevation has a higher temperature than the
higher elevation. The Second Law is broken. This effect can only be observed in high
quality thermoelectric materials (Caltech experiment).
I have made this calculator program and a simulator publicly available at my
web site.
*Figure. 7.* Un-normalized Maxwell distribution at ground (red/thick) and at non-zero
elevation (blue/thin) showing a shift to a lower kinetic energy, a drop in density and a
drop in temperature.
*Figure. 8.* Renormalized shifted Maxwell distribution at non-zero elevation (blue/thin)
is identical to original non-shifted distribution at ground level (red/thick).
**
*Figure. 11.* Un-normalized Fermi-Dirac distribution at ground (red/thick) and non-zero
elevation (blue/thin) showing drop in density and drop in temperature.
*Figure. 12.* Renormalized Fermi-Dirac distributions at ground level (red/thick) and at
elevation (blue/thin) are different. Elevation lowers energy and temperature of gas.
Please look on the right of the pictures for the temperatures at the ceiling and at the
floor.
George Levy
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