Dear Franklin,

for the thermoelectric effect, the Carnot efficiency etaC limits the electrical energy, you can get. The efficiency eta for a thermoelectric elements equals to

eta = {(TH - Tc)/TH}*{[(1+ZT)0,5 -1]/[(1+ZT)0,5 + Tc/TH ]} < etaC

with TH the temperature of the hot contact and TC the temperature of the cold side. The factor ZT is the so called figure of merit, a dimensionless factor. For good thermoelectrics, a factor ZT >1 can be achieved. If ZT >> 1, the Carnot efficiency limits the efficiency. The factor ZT follows from

ZT = S²*T *sigma/lambda with

S the Seebeck coefficient, sigma the electrical conductivity and lambda the thermal conductivity. For 2 materials, this expression is somewise more complex, but in essentially, ZT increases for materials with high Seebeck coefficients, high electrical and low thermal conductivity.

Practically, the thermoelectric efficiency is lower, than the Carnot efficiency.

Therefore, the 2. principal theorem of thermodynamic cannot be avoided by thermoelectric.

With Regard

R. Mitdank

Dear Rüdiger:

Thank you for nice information. :)

However what I'm looking to learn is:

In the special case of the Thermoelectric Effect... lets regard the issue depicting solely the Thomson Effect:

I know the Carnot Efficiency is the maximum limit of the ratio of the Output Energy to the Heat/work Imput to the device. Therefore a device working with the TE Effect (as any other thermodynamic device) cannot produce more (even equal) Energy as that it had used to run for the first time...

But my question is What is the explanation , physically how we can explain these impossibilities ...

Or in more common words. What is the explanation which helps you to debunk ultimately the impossibilty of building a Perpetual Motion Machine using the TE ?

I know is impossible to build one , but to understand the physics and the First and Second Law of Thermodynamics in these scenario could lead us to a better understanding of classical termodynamics in the Thermoelectric Effect.

Another way to see the problem is:

Where are, and what exactly causes the Irreversibilities which create the Entropy production in a Thermoelectric device ... (supposing we are regarding this Perpetual Motion device as a device os the Second Kind).

Regards ! :)

Dear Franklin,

what causes the thermoelectric effect? You have a hot and a cold side. On both sides the electrons have an energy distribution (Fermi). The most electrons at T are in the ground state. Some electrons have energies higher than the Fermi energy. This is a low portion of all electrons. A very low portion of electrons at the hot side has higher energies than on the low side. This difference between hot and cold side generates the so called thermodiffusion of the "hotter" electrons to the cold side - and these electron charges induce the thermovoltage. The other electrons are not separated and they are useless for thermovoltage, because in both directions occurs the same process.

Yours

R. Mitdank

Dear Rüdiger ,

I follow you. So would you say that these transport processes will continue forever? Without any external driving force.

Consider from the point of view of a real material,

Regards,

Dear Franklin, the driving force is the temperature difference. But heat has a statistical character. Due to this, only a certain part of energy can be used.

A real material gives a worse result than an ideal. In the case of very high electrical and very low thermal conductivity the chargecurrent due to T-difference and heatcurrent (reducing this difference) can be well separated. In this case you get the Carnot efficiency.

Regards,

R. Mitdank

Dear Rüdiger Mitdank:

I understand, there is an internal driving force (not just a Temperature Gradient, but also an Electric Potential Gradient), and I understand; since heat and charge transport have a statistical origin/or behaviour , just a window of this function can be useful for transport phenomena.

I understand as well that the Carnot Efficiency will be higher than the maximum efficiency of a device of this kind,

But what I want to understand is; What is the reason, at the physical microscopic level. In otrher words: Where we can find those irreversibilities which make the device cannot continue running perpetually (in the case of a TE device , to continue generating a current and and generating a Temperature difference, and so on ...

I know, macroscopically we can advocate to the "efficiency less than the Carnot Efficiency" argument and this could be sufficient by practical terms.

But I want to go deeper. ¿What does cause this efficiency to be less than one?

If you think on a simple TE material (no contacts, no module, no p-n pair).

If dS/dT is different than zero, then we can observe a Thomson Effect in our material.

Now, lets imagine we can isolate this block of material, and place it into a closed circuit... made with a superconducting wire (rho=0) and isolate the wire as well (thermically and electrically), so the losses through the ambient nearly approach to zero.

Then, ideally, this material will generate its own Heat Flux (due to combination of the Ohm's Law and the TE Effect, and the Fourier's Heat Flux Law), and this Heat Flux will generate a Current .. and go on, continuously, ideally with no losses (when imagining the ideal case of idual insulation).

But we know this is impossible, because the First and/or Second Law of get on our way. And ultimatelly, if we can defeat the 1st. and 2nd. Laws of Thermodinamics using the most futuristic and advance combined isolation-vacumm-cryogenics-superconducting technology... Well, at the microscopic level, there will always be irreversibilities (friction, energy losses, etc.) and ultimatelly Quantum Mechanics won't allow us to build this perpetual motion device that runs forever, it is impossible to build a perpetual motion machine of any kind, and one using the Thomson Effect (or TE Effect) is no exception.

But what I'm saying is that the TE Effect (Seebeck and Peltier Effects combined) and the Thomson Effect, are two visions than particularly easily can lead to thoughs about a perpetual motion device, because the way I described these Effects above.

I was thinking to an answer to my question, but I have it far from clear, What I started to devise is the following:

Maybe the explanation is somehow in the Entropy generated by the carriers (holes and electrons) they transport in the crystal ... I have seen some approaches where an finite amount of Entropy can be assigned to the transport of a Particle , like and Electron or other fundamental particle. so It could be that at the microscopic level the transport of these charge carriers generates Entropy, which then this Entropy transforms into irreversibilities of the system at the nanoscale level.

But... I don't know if we can come up with a formal definition of Entropy for a particle at this level .. or a mathematical expression,

Besides, the other issue is... What is up with the Phonons? It could happen the same logic could be applied to them?... If so, What about the Entropy production of each Phonon? since Phonons make up a condensate of Phonons... So? then, the case for Phonons seems to be a little different.

I will stop here I hope we can summarize our disscurion, hope someone else provide more ideas to it .

Kind Regards Rüdiger Mitdank !

Franklin !