Photo-Carnot engine

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A Photo-Carnot engine is a Carnot cycle engine in which the working medium is a photon inside a cavity with perfectly reflecting walls. Radiation is the working fluid, and the piston is driven by radiation pressure.

A quantum Carnot engine is one in which the atoms in the heat bath are given a small bit of quantum coherence. The phase of the atomic coherence provides a new control parameter.[1]

The deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.


Derivation

The internal energy of the photo-Carnot engine is proportional to the volume (unlike the ideal-gas equivalent) as well as the 4th power of the temperature (see Stefan-Boltzmann law).

U=\varepsilon \sigma T^{{4}}

The Radiation pressure is only proportional to this 4th power of temperature but no other variables, meaning that for this photo-Carnot engine an isotherm is equivalent to an isobar.

P={\frac {U}{3V}}={\frac {\varepsilon \sigma T^{{4}}}{3V}}

Using the First law of thermodynamics (dU=dW+dQ) we can determine the work done through an adiabatic (dQ=0) expansion by using the chain rule (dU=\varepsilon \sigma dVT^{{4}}+4\varepsilon \sigma VT^{{3}}dT) and setting it equal to dW=-PdV=-{\frac {1}{3}}\varepsilon \sigma T^{{4}}dV

Combining these gives us {\frac {2}{3}}T^{{4}}dV=4VT^{{3}}dT which we can solve to find {\frac {V^{{1/6}}}{T}}=const

....

The efficiency of this reversible engine must be the Carnot efficiency, regardless of the mechanism and so \eta ={\frac {T_{H}-T_{C}}{T_{H}}}

See also

Footnotes

  1. ↑ "Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence -- Marlan Scully, M. Suhail Zubairy, G. S. Agarwal, and Herbert Walther, 299 (5608): 862 -- Science". www.sciencemag.org. Retrieved 2008-06-18. 

Further reading


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