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There's no easy answer to your question as you don't define the nature of the gaz nor the nature of the cells. "Even if my understanding of the second law is incorrect, I don't understand why we can't extract heat energy from an object without a temperature gradient by placing it under certain conditions. For example, heat transfer via infrared radiation ...

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Bowlofred's answer is correct. You can get some insight by studying Feynman's Brownian ratchet - an attempt to get energy out of heat using statistical fluctuations (This also relates to your second point - that the Second Law is statistical in nature.) It consists of a tiny paddle wheel and a ratchet, and appears to be an example of a Maxwell's demon, ...

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There has been a new approach that you may consider. Your question involves the energy conversion between heat energy and Gibbs free energy. Since the two both are non- conserved quantities, the changes in heat energy and both Gibbs free energy can be divided into the two parts: one is the fluxes, the other one is the productions. For heat energy, $\delta Q$ ...

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If you work through the equations of a solar cell in detail, you find that the maximum possible efficiency of a solar cell is a function of the cell's own temperature and of the radiation brightness temperature of the light hitting it. If the two temperatures are the same, as they would be in your drawing, you find that the maximum possible efficiency is 0. ...

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"The gas would slowly radiate its heat through the glass to the ambient container housing the vacuum, and solar panels lining this surface could feasibly collect this energy." No. If we assume the gas inside and the cells outside are both at temperature $T$, then no (thermal) energy can be extracted. They will be in thermal equilibrium. Whatever ...

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The explanation is using an energy argument. That for the normal case of a submerged piece of wood, you can assume that if the wood and a parcel of water above it switch places, then the water (which is heavier/more massive) drops in the gravitational field releasing potential energy. This release is not offset by the rising wood since it is not as ...

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I suggest you build one in your kitchen. Cut a sponge into a J shape and hook it over a pencil, so that the straight edge dangles into a bowl of water. Put piece of tissue paper under the hook to catch drips and wrinkle, in case they come while you're asleep. Wait. I suspect you'll find that the top of the sponge never actually gets wet enough to drip. ...

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