# Why Doesn't Thermal Radiation Render Thermionic Conversion Unable To Approach Carnot Efficiency?

Physics Asked on January 6, 2022

Thermionic Conversion follows the classic Richardson-Dushmann Equation for thermionic current as a function of temperature squared:

$$J_{RD} = A_0 T^2 expleft(-frac{phi}{k_B T}right)$$
where

• $$J_{RD}$$ is the emission current density.
• $$T$$ is the emission temperature.
• $$A_0$$ is a material specific correction factor
• $$phi$$ is the material’s environment-mediated work function, and
• $$k_B$$ is is the Boltzmann constant

But thermal power loss is a function of the fourth power of temperature following the Stefan-Boltzmann law:
$$begin{equation} P=Asigma T^4 end{equation}$$
where

• $$P$$ is the power lost to thermal radiation
• $$T$$ is the emission temperature.
• $$A$$ is the area of thermal emission, and
• $$sigma$$ is the Stefan-Bolzmann constant

Although I see a lot of talk about space charge buildup being the limiting factor on thermionic conversion efficiency, the power of 2 disadvantage from thermal radiation losses seems to make thermionic conversion a fundamentally impractical approach to approximating Carnot efficiency.

What am I missing?

According to this article, "Thermionic Energy Conversion in the Twenty-first Century: Advances and Opportunities for Space and Terrestrial Applications", the thermal radiation actually is a design concern.

You mention two power laws, and yes it does imply that at high temperatures the efficiency must drop, but it also equally implies that at low enough temperatures, the effect of the thermal radiation must become negligible.

The power of the power law is not the only thing, and in evaluating whether a technology sinks or swims, it comes down to a practical question of what are the actual coefficients, etc., and what is the final tradeoff that gets made in engineering.

Answered by Nanite on January 6, 2022

## Related Questions

### Relation between stress and resonance

1  Asked on December 26, 2020 by kareem-ahmed

### Do time dilation and length contraction cancel out?

4  Asked on December 26, 2020

### Constant work function although changing Fermi energy

1  Asked on December 26, 2020 by dennis-tra

### Is number of photons undefined for a classical EM wave?

4  Asked on December 26, 2020 by ruslan

### Can we feel the electrons which move from one object to other during rubbing which caused charge?

1  Asked on December 26, 2020 by bora-ramireddy

### Heisenberg representation: why position operator has no explicit time dependance?

1  Asked on December 26, 2020

### What happens to heat waste produced by energy generation?

4  Asked on December 26, 2020 by user27515

### Entropy reducing power generator

1  Asked on December 26, 2020 by dallas

### Energy of exciton formation in semiconductors

1  Asked on December 26, 2020 by aleksejus-pacalovas

### Why does water ($mathrm{H_2O}$) only have two distinct fluid phases?

4  Asked on December 26, 2020 by jn-lalinsk

### Can one force the octupole moments of a charge distribution (neutral and with vanishing dipole moment) to vanish using a suitable translation?

1  Asked on December 26, 2020 by emilio-pisanty

### Right-Angle Lever Paradox where does the ang. momentum go?

2  Asked on December 26, 2020

### Can Thevenin voltage ever be negative?

1  Asked on December 26, 2020 by user56220

### Variations wrt. Time Derivatives

3  Asked on December 26, 2020 by chip

### Deformable body under a force and a moment

0  Asked on December 26, 2020

### Is the pressure in a pipe equal the pressure in the tank?

1  Asked on December 26, 2020 by physicsguy123

### SDE with drift multiplied by telegraph like random process

1  Asked on December 26, 2020 by ernst

### Energy dependence in density functional theory

1  Asked on December 26, 2020

### Potential Energy of a System of Point Charges

0  Asked on December 25, 2020 by iamsecretlyflash

### How do two light beams, one squeezed in phase and the other in amplitude, superposed on a beamsplitter, result in an EPR entangled state?

0  Asked on December 25, 2020 by quantum-journalist