Is It Possible to Generate Energy with a Microscopic Gate Sorting Molecules?

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colin9876
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This baffles me, because the device outlined below could create energy ...

there's two tanks A & B with a microscopic gate between them

Air in A & B starts at say 25 degrees

whenever a faster than average moving molecule approaches the gate in A a sensor opens the gate and let's in pass into B
If a slow moving molecule approaches the gate from B, the sensor opens the gate and allows it into A

So perhaps after time t, the air in A is at 23 degrees and the air in B is at 27 degrees

In theory the 'sorting gate' could be a very low energy device.
The temp difference between A & B could be used to drive a heat engine and get energy out.

Where is the flaw in this theoretical argument? I can't find one. In theory particle sorting could be done to generate heat differences??
 
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