Page 30 - 2020SEP30 Brief Booklet C

306 LEO SZILARD

it is transformed from a species that can pass long as we do not use the fact that the molecules
the seniipernieable piston A into a species for in the container BB’, by virtue of their co-
which the piston is imperiiieable), then the ordinate y, “remember” that the r-co-ordinate
parameter y retains its value 1 for the time for the molecules of this container originally
being, so that the “molecule,” because of the was in the preassigned inlerval, full conapensa-
value of the parameter y, “remembers” tion existsfor the calculated decrease of entropy,
during the whole following process that x by virtue of the fact that the partial pres-
originally was in the preassigned interval. sures in the two containers are snialler than
We shall see immediately what part this in the original mixture.
memory may play. After the intervention But now we can use the fact that all naole-
just discussed, we niove the piston, so that cules in the container BB‘ hatie the y-co-ordi-
we separate the two kinds of inolecules with- nate I, and in the other accordingly -1, to
out doing work. This results in two con- bring all molecules baclc again to the original
tainers, of which the first contains only the volume. To accomplish this we only need to
one modification and the second only the replace the seniipermeable wall -4 by a wall
other. Each modification now occupies the A *, which is seniipermeable not with regard
same volume as the mixture did previously. to x but with regard to y, naniely so that it is
In one of these containers, if considered by permeable for the molecules with the y-co-
itself, there is now no equilibrium with re- ordinate 1 and impermeable for the others.
gard to the two “modifications in x.)’ Of Correspondingly we replace B’ by a piston
course the ratio of the two modifications has B’*, which is impermeable for the molecules
remained w1 : wz . If we allow t,his equilibrium with y = -1 and permeable for the others.
to be achieved in both containers independ- Then both containers can be put into each
ently and at constant volume arid tempera- other again without expenditure of energy.
ture, then the entropy of the systeni cer- The distribution of the y-co-ordinate with
tainly has increased. For the total heat regard to 1 and -1 now has become sta-
release is 0, since the ratio of the two “niodifi- tistically independent of the r-values and be-
cations in x’) w1:w2 does not change. If we sides we are able to re-establish the original
acconiplish the equilibrium distribution in distribution over 1 and - 1. Thus we would
both containers in a reversible fashion then have gone through a coniplete cycle. The
the entropy of the rest of the world will de- only change that we have to register is the
crease by the same amount. Thcrefore the resulting decrease of entropy given by (9) :
entropy increases by a negative value, and,
the value of the entropy increase per mole- 3 = Ic(w1 log w1 + wt log wz). (10)
cule is exactly: If we do not wish to admit that the Second
Law has been violated, we must conclude
s = Ic(w1 log w1 + w2 log wp). (9) that the intervention which establishes the
(The entropy constants that we must as- coupling between y and x, the iiieasurenzent of
sign to the two “modifications in 5’’ do not x by y, must be accompanied by a production
occur here explicitly, as the process leaves the of entropy. If a definite way of achieving this
total number of molecules belonging to the coupling is adopted and if the quantity of
one or the other species unchanged.) entropy that is inevitably produced is desig-
Yow of course we cannot bring the two nated by Sl and Sz , where S1 stands for the
gases back to the original volume without mean increase in entropy that occurs when y
expenditure of work by simply moving the acquires the value 1, and accordingly Sz for
piston hack, as there are now in the con- the increase that occurs when y acquires the
tainer- which is bounded by the pistons value - 1, we arrive at the equation:
BB’-also niolecules whose x-co-ordinate lies WlSl i- w2s2 = s“
outside of the preassigned interval and for (11)
which the piston A is not permeable any In order for the Second Law to remain in
longer. Thus one can see that the calculated force, this quantity of entropy must be
decrease of entropy (Equation 191) does not greater than the decrease of entropy s, which
mean a contradiction of the Second Law. As according to (9) is produced by the utiliza-