ace PQ, and B will pass into
the space RS, and the gases will finally be completely separated;
similarly, by pushing the connecting rods together, the two gases will
be remixed in the space RQ. By performing the operations slowly enough
we may make the processes as nearly reversible as we please, so that
no available energy is lost in either change. The gas A being at every
instant in equilibrium on the two sides of the piston Q, its density,
and therefore its partial pressure, is the same on both sides, and the
same is true regarding the gas B on the two sides of R. Also _no work
is done in moving the pistons_, for the partial pressures of B on the
two sides of R balance each other, consequently, the resultant thrust
on R is due to the gas A alone, and is equal and opposite to its
resultant thrust on P, so that the connecting rods are at every
instant in a state of mechanical equilibrium so far as the pressures
of the gases A and B are concerned. We conclude that in the reversible
separation of the gases by this method at constant temperature without
the production or absorption of mechanical work, the densities and the
partial pressures of the two separated gases are the same as they were
in the mixture. These conclusions are in entire agreement with those
of the preceding section. If this agreement did not exist it would be
possible, theoretically, to obtain perpetual motion from the gases in
a way that would be inconsistent with the second law of
thermodynamics.

Most physicists admit, as Planck does, that it is impossible to obtain
an ideal semi-permeable substance; indeed such a substance would
necessarily have to possess an infinitely great resistance to diffusion
for such gases as could not penetrate it. But in an experiment performed
under actual conditions the losses of available energy arising from this
cause would be attributable to the imperfect efficiency of the
partitions and not to the gases themselves; moreover, these losses are,
in every case, found to be completely in accordance with the laws of
irreversible thermodynamics. The reasoning in this article being
somewhat condensed the reader must necessarily be referred to treatises
on thermodynamics for further information on points of detail connected
with the argument. Even when he consults these treatises he may find
some points omitted which have been examined in full detail at some time
or other, but are