DOC.
39
225
Doc. 39
ON
THE
LIMIT
OF
VALIDITY
OF THE
LAW
OF THERMODYNAMIC EQUILIBRIUM AND
ON
THE
POSSIBILITY
OF
A
NEW
DETERMINATION OF THE ELEMENTARY
QUANTA
by
A.
Einstein
[Annalen
der
Physik
22 (1907):
569-572]
[1]
Let the state of
a
physical
system
be
determined
in
the
thermodynamic
sense by
parameters
A,
u,
etc.
(e.g.,
readings
of
a
thermometer,
length
or
volume
of
a
body,
amount
of
a
substance
of
a
certain kind in
one
phase).
If,
as we
assume,
the
system
is
not
interacting with
other
systems,
then, accord-
ing to
the
laws of
thermodynamics,
equilibrium
will
occur
at
particular values
A0,
u0, etc.
of the
parameters,
for
which
the
system's entropy S
is
a
maximum. However, according to
the molecular
theory
of
heat, this is
not
exactly
but
only approximately correct; according to
this theory,
the
value of
the
parameter
A
is
not constant
even
at
temperature equilibrium,
but
shows
irregular
fluctuations,
though
it is
very
rarely
much
different
from
A0.
At
first
glance
the theoretical examination of the statistical
law
that
governs
these fluctuations
would
seem
to require
that
certain
stipulations
regarding
the molecular
model must
be applied.
However,
this is
not
the
case.
[2]
Rather,
essentially it is sufficient
to
apply
the
well-known Boltzmann
rela-
tion
connecting
the
entropy
S
with the statistical
probability of
a
state.
As
we
know,
this relation is
S
=
R/N
lg
W ,
where
R
is
the constant of
the
gas
equation
and
N
is the
number
of
molecules
in
one
gram-equivalent.
We
consider
a
state
of the
system
in
which
the
parameter
X
has
a
value
A0+e
differing
very
little
from
X0.
To
bring
the
parameter
X
from
the
value
X0
to
the value
X
along
a
reversible
path at constant
energy E, one
will
have to
supply
some
work
A
to
the
system
and to withdraw
the
corre-
sponding amount
of
heat.
According
to
thermodynamic
relations,
we
have
A=fdE-fTdS,