# Brownian Ratchet with mechanism in vacuum

So first of all I want to state that I indeed understand Feynman's reasoning as to why the Brownian ratched fails. (At least what's written about it in Wikipedia.) I want to consider the following setup:

Now my question is: What would happen if we enclosed the ratchet mechanism (but not the paddle) in a vacuum?

I don't see how Brownian motion could now enable turning in reverse, so effectively we'd be left with usable work. This however contradicts the 2nd law of thermodynamics.

I'm only really interested the theoretical problem rather than practical challenges.

## 1 Answer

Even if the ratchet is enclosed in vacuum, the pawl is still at some finite temperature $T_2$, and so is still subject to thermal motion. So basically, the pawl, the only thing keeping the ratchet from going backwards, will move randomly and sometimes fail to catch, so the ratchet will move backwards. As the system tends to thermal equilibrium, this will happen more and more often until the ratchet no longer reliably moves forward.

Basically, any air in the mechanism chamber is irrelevant: all that matters is the temperature of the pawl.

• okay, I get it, thanks. I guess it's not theoretically possible to thermally isolate the mechanism from the outside, is it? – user3457338 Oct 10 '17 at 17:40
• @user3457338 In principle, you can isolate it from the outside. But you can't isolate it from the ratchet itself. If $T_1 > T_2$ differ, the ratchet will work momentarily, but as it works energy is transferred from the ratchet chamber to the pawl, and eventually the system reaches thermal equilibrium. Effectively what you end up with is just a normal heat engine: you produce some useful work from a temperature difference until that temperature difference goes away. – Chris Oct 10 '17 at 17:52
• Why couldn't you make the gear and pawl large enough so that the Brownian forces from all sides cancels out? And also very lightweight to limit their momentum. – EricP Oct 18 '19 at 4:36