Photo-Carnot engine

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):

${\displaystyle U=V\varepsilon \sigma T^{4}\,.}$

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

• Carnot heat engine
• Radiometer

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

• Marlan O. Scully, M. Suhail Zubairy, G. S. Agarwal, Herbert Walther (2003-02-07). "Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence". Science. 299 (5608): 862–864. Bibcode:2003Sci...299..862S. doi:10.1126/science.1078955. PMID 12511655.
• Zubairy, M. Suhail (2002). "The Photo-Carnot Cycle: The Preparation Energy for Atomic Coherence". Quantum Limits to the Second Law: First International Conference on Quantum Limits to the Second Law. AIP Conference Proceedings. 643. pp. 92–97. doi:10.1063/1.1523787.