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Thermoelectrics: Reversibility and Efficiency at Maximum power. Tammy Humphrey Department of Theoretical Physics, University of Geneva. *Email: [email protected] Web: www.humphrey.id.au. Outline. Background The Physics of Thermoelectrics The Thermodynamics of Thermoelectrics
Department of Theoretical Physics, University of Geneva
*Email: [email protected] Web: www.humphrey.id.au
Finite thermal conductivity at open circuit means that heat is consumed but no work is done.
Zero efficiency at the crossover from power generation to refrigeration is the hallmark of an irreversible HE.
Feynman on reversible heat engines…The Feynman lectures on Physics, Chapter 44-3
“We need to find an analog of frictionless motion: heat transfer whose direction we can reverse with only a tiny change.If the difference in temperature is finite, that is impossible…”
Reversible electron transport requires equilibrium
“No thermoelectric device can ever reach Carnot efficiency”
H. Littman and B. Davidson, J. Appl. Phys., 32 (2) 217 (1961).
One energy where the effect of the temperature gradient cancels with that of the electrochemical potential gradient
One energy at which current reverses:
Constant occupation of states = Equilibrium
(despite temperature and electrochemical potential gradients)
“Reversible thermoelectric nanomaterials”, T. E. Humphrey and H. Linke, Phys. Rev. Lett. 94, 096601 (2005)
Other heat engines achieve reversibility in the same way…
T. E. Humphrey, R. Newbury, R. P. Taylor and H. Linke “A Reversible quantum Brownian heat engine for electrons” Phys. Rev. Lett. 89, 116801 (2002)
Loss Mechanisms in solar cells
1) Non-absorption of below band-gap photons
2) Lattice thermalisation losses
3) & 4) Junction and contact resistance losses
5) Recombination losses
Finite thermal conductivity between the sun and the cell at open circuit means that heat is consumed but no work is done.
Irreversible heat engine
Reversibility achieved at open circuit voltage eVOC,when a filter is used to limit photons exchanged to those with energy equal to the bandgap, EG. Then:
Efficiency of energy conversion is:
P. T. Landsburg and G. Tongue, J. Appl. Phys., 51, R1 (1980)
Efficiency at population inversion:
H. E. D. Scovil and E. O. Schulz-DuBois, Phys. Rev. Lett., 2, 262 (1959)
“number of electrons”
Ratio of efficiency at MP to Carnot efficiency
Efficiency at maximum power
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