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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]].
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| A quantum Carnot engine is one in which the atoms in the heat bath are given a small bit of [[Coherence (physics)#Quantum coherence|quantum coherence]]. The phase of the atomic coherence provides a new control parameter.<ref>{{cite web
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| |url=http://www.sciencemag.org/cgi/content/abstract/299/5608/862|title=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|publisher=www.sciencemag.org|accessdate=2008-06-18}}</ref>
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| 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.
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| '''Derivation'''
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| 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]]).
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| <math> U = \varepsilon\sigma T^{4}</math> | |
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| 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.
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| <math> P = \frac{U}{3 V} = \frac{\varepsilon \sigma T^{4}}{3 V} </math>
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| Using the First law of thermodynamics (<math> dU = dW + dQ </math>) we can determine the work done through an adiabatic (<math> dQ = 0 </math>) expansion by using the chain rule (<math> dU = \varepsilon \sigma dV T^{4} + 4 \varepsilon \sigma V T^{3} dT </math>) and setting it equal to <math> dW = -P dV = -\frac{1}{3} \varepsilon \sigma T^{4} dV </math>
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| Combining these gives us <math> \frac{2}{3} T^{4} dV = 4 V T^{3} dT </math> which we can solve to find <math> \frac{V^{1/6}}{T} = const </math>
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| ....
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| The efficiency of this reversible engine must be the Carnot efficiency, regardless of the mechanism and so <math> \eta = \frac{T_H - T_C}{T_H} </math>
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| ==See also==
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| *[[Carnot heat engine]]
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| *[[Radiometer]]
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| ==Footnotes==
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| {{reflist}}
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| == Further reading ==
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| *{{cite journal|url=http://www.sciencemag.org/cgi/content/abstract/299/5608/862|title=Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence|author=Marlan O. Scully, M. Suhail Zubairy, G. S. Agarwal, and Herbert Walther|journal=Science|date=2003-02-07|volume=299|issue=5608|pages=862–864|doi=10.1126/science.1078955|pmid=12511655|bibcode = 2003Sci...299..862S }}
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| *{{cite conference|url=http://adsabs.harvard.edu/abs/2002AIPC..643...92Z|title=The Photo-Carnot Cycle: The Preparation Energy for Atomic Coherence|author=Zubairy, M. Suhail|booktitle=QUANTUM LIMITS TO THE SECOND LAW: First International Conference on Quantum Limits to the Second Law. AIP Conference Proceedings|volume=643|pages=92–97|year=2002|doi=10.1063/1.1523787}}
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| {{Heat engines}}
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| [[Category:Hot air engines]]
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| {{physics-stub}}
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My name is Angie from Perpignan doing my final year engineering in Integrated International Studies. I did my schooling, secured 75% and hope to find someone with same interests in Scrapbooking.
Here is my blog post ... wordpress dropbox backup