For centuries, inventors have
attempted to create perpetual motion machines. Unfortunately, friction always
seems to get in the way. I read a book this summer called Maxwell’s Demon: Why Warmth Disperses and Time Passes by Hans
Christian Von Baeyer that discussed the possibility of building a machine that
could harness Brownian motion to lift a weight without depleting a source of
energy. The Brownian ratchet, or “ratchet and pawl,” perpetual motion machine
was popularized by Richard Feynman in the Feynman Lectures, and is shown below
in Fig. 46-1.
How does the ratchet and pawl machine work?
The particles in the container on
the right would move randomly because they are not at absolute zero. They would
hit the vanes attached to a rod that can rotate. The particles colliding with
the vane would cause the rod to vibrate counterclockwise and clockwise with
Brownian motion. In order to harness the Brownian motion, the other side of rod
is attached to a ratchet and pawl that make it so that the rod can only rotate
in one direction. The rod would theoretically rotate in one direction such that
it could lift a small mass, thus generating potential energy without depleting
an energy source.
Why doesn’t the ratchet and pawl machine work?
If the temperature of the gas in
both containers is the same, then the particles will have the same average
kinetic energy. Consequently, the particles in the ratchet and the pawl are
also subject to this kinetic energy and sometimes move such that the rod slips
backwards. It turns out that the particles in the container on the right
randomly cause the pawl to slip on the ratchet allowing the rod to slip
backwards just as often as the particles in the container on the right act on
the vane to rotate the rod forward. This equal probability makes it so that
there is no expected net torque on the rod from the particles randomly hitting
the vane when the temperatures of the two containers are equal. This phenomenon
is demonstrated mathematically in table 46-1.
L is the torque on the rod from the
weight. ϵ is the amount of
energy needed to lift the pawl off of the ratchet so that it can move forward
or backwards. It can come from the vibrating particles colliding with the vane
or it can come from the ones directly lifting the pawl. In order to rotate one
step forward such that the weight rises, Lθ work must be done to raise the
weight, and ϵ work must be done to raise the pawl such that the ratchet
rotates. The total amount energy provided by the vane in this case is Lθ + ϵ.
When the system moves backwards, Lθ + ϵ energy is given back to the vane. If
the energy threshold is the same on both sides, and the average energy of the
particles is the same because of the two containers having the same
temperature, then the mechanism should move forward and backwards with equal
probabilities.
The ratchet and pawl machine could actually work:
If the temperatures are different
in the two containers, specifically such that the container on the right has a
higher temperature, then the ratchet and pawl setup would successfully turn the
rod. However, the friction of the ratchet and pawl in the colder container
would heat up that container until it was the same temperature as the other
container. At that point, the machine would stop raising the weight.
Interestingly enough, this type of heat gradient is essentially how all
reversible engines work, and it does not violate conservation of energy.
Unfortunately, it appears that it
is impossible to build a perpetual motion machine, even if you really really
want to. Either the work done on the weight requires using up a temperature
gradient, or in the case that there is no temperature gradient, no work is done
on the weight at all and no gravitational potential energy is created.
Von
Baeyer, Hans Christian. Maxwell's Demon: Why Warmth Disperses and Time
Passes. New York: Random House, 1998. Print.
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