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Dear all,

Here is a physics puzzle for your entertainment.

The puzzle has two parts: The first part is a description of a simple
experiment based on evaporation and osmosis. A seemingly reasonable
outcome of the experiment is given along with some justification.

The second part is a proof - or rather, a suggestion of a proof - that
the description must be fundamentally flawed. However, the proof gives
hardly any hints about where the error lies in the description.

Your job is to identify the error in the description - or in the proof
- - - or in how these two relate to one another, or ... Well, you go
figure it out!

Have fun! Let's hear your solutions!

Yours,
Sam Po

PART I: DESCRIPTION

Let us first set up some equipment: We take two pipes and equip
each pipe with a valve, which allows us to open or close the pipe
at will. In one of the pipes we place a semipermeable membrane so
that anything that goes through the pipe must pass through the
membrane.

Next, we take two containers that can hold vacuum. We insert one
end of the pipe that holds the membrane through a hole at the
bottom of one container and the other end through a hole at the
bottom of the other container. Then we take the other pipe do the
same thing but this time the holes are at the tops of the containers.

We will need some solvent and solute suitable for our purposes: The
solvent can pass through the membrane but the solute cannot. Also,
the solvent evaporates easily and the solute does not.

We pump all air out the containers and the pipes, make sure that
the lower valve is open and the upper valve is closed. Then we
inject a small amount of pure solute in container A and a large
amount of solution comprising solvent and solute in container B.
As a result, the lower pipe should be completely filled with liquid,
container A should be almost empty and container B should be
almost full. The surface of the liquid in the container B should be
much higher than in container A; high enough to ensure that the
solvent starts flowing from container B through the lower pipe to
container A.

The flow will stop when equilibrium of different pressures -
including hydrostatic, osmotic, vapor - is reached at the
membrane. Neither container is empty.

There is also equilibrium in each container between evaporation
and condensation.
The vapor pressure at equilibrium is smaller in
container B than in container A because of the solvent in container
B.

We open the upper valve and the solvent starts to move from
container A through the upper pipe to container B in vaporous
form. This is because evaporation dominates in container A and
condensation dominates in container B. This continues as long as
the valve is open and we do not run out of solvent.

We close the upper valve, when container A is almost empty. We
can then start the cycle over by opening the lower valve. The
solvent will once again flow from container B to container A, etc.

PART II: PROOF

By now it should be obvious that something is wrong because the
system would just keep on running forever. That is not necessarily
alarming because so does a spinning top, in theory, if you ignore
air resistance, friction, etc.

What is more alarming is that we can actually draw an infinite
amount of energy out of the process by, say, placing a rotor in
one of the pipes or buoy in one of the containers and use its
movement to generate electricity without ever causing the process
to stop.

A step by step analysis would show that the whenever energy is
drawn out of the system, it draws an equal amount of heat energy
from the surroundings. This is impossible because it would violate
the second law of thermodynamics.

PS: The description requires that air is pumped out of the
containers and pipes. This is optional, but simplifies the puzzle
a bit.

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Dear all,

Here is a physics puzzle for your entertainment.

The puzzle has two parts: The first part is a description of a simple
experiment based on evaporation and osmosis. A seemingly reasonable
outcome of the experiment is given along with some justification.

The second part is a proof - or rather, a suggestion of a proof - that
the description must be fundamentally flawed. However, the proof gives
hardly any hints about where the error lies in the description.

Your job is to identify the error in the description - or in the proof
- - - or in how these two relate to one another, or ... Well, you go
figure it out!

Have fun! Let's hear your solutions!