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Assume for purposes of discussion a closed container with a concentration of gas on one side and near-vacuum on the other. We could let the gas pressure equalise naturally, or we could construct a barrier with a turbine such that the gas moving from the concentrated side to the vacuum side spins the turbine and produces electricity. In both cases, the gas reaches equilibrium after some time, but in one of the cases the system performs work. My question is, what happens to the excess energy not used to produce electricity in the first example (with no turbine).

My intuition tells me that the answer has to be one of the following: Either the gas that drove the turbine is colder than the gas that did not, or that the electrical energy produced is actually less than the energy required to build the turbine so the electrical energy was actually input into the system by action of building the turbine.

Is either of my answer right? What else have I not accounted for?

Thanks.

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Your first intuition is correct. It is easy to see that the second cannot be right, because we can simply increase the size of the containers on each side. This will increase the amount of electricity generated, but the energy cost of building the turbine remains the same. –  user2963 Oct 1 '12 at 21:54
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1 Answer

up vote 3 down vote accepted

Zephyr's comment answers your question (Zephyr if you want to post it as an answer I'll delete this) but I think it's worth expanding (no pun intended :-) on it a bit.

Consider the microscopic view: assuming an ideal gas the internal energy is just the total kinetic energy of the gas molecules, and the temperature is a measure of their speed.

If you sudden remove the barrier in your system and let the gas expand freely the speed and kinetic energy of the gas molecules doesn't change. However if you have a turbine then gas molecules will hit the turbine blades and transfer some of their energy to the turbine. That means their speed and therefore temperature will decrease. If you were to measure the total kinetic energy of the gas molecules after expansion through the turbine you would find it had decreased by an amount equal to the energy generated by the turbine.

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Thanks John. The microscopic explanation of the gas molecules' speed was quite what I was missing. If Zephyr doesn't write back as an answer then I'll accept this one. –  dotancohen Oct 2 '12 at 11:23
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