DOC.
47
299
dQ = Tdn
(24)
is valid here
too.
We
now
have to
derive the
equations
relating the quantities
dQ,
n,
T
and
the
corresponding
quantities
dQ0,
n0,
T0
which
refer
to
a co-moving
reference
system.
As
far
as
entropy
is
concerned,
I
am
repeating
here the
reasoning
of
Mr.
Planck,1 noting
that
the
"primed"
and
"unprimed"
reference
systems
should
be
understood
as
the
reference
systems
S' and
S.
"Let
us imagine
that the
body
is
brought
by
some
reversible, adiabatic
process
from
a
state
in
which
it is
at rest
with
respect to the
unprimed
system
into
a
second state,
in
which
it is
at
rest with respect
to
the
primed
reference
system.
If
the
body's entropy
for the
unprimed
system
in the
initial
state
is denoted
by
n1
and
in
the final
state
by n2,
then, because
of the
reversibility
and
adiabatic
nature
of the
process,
n1
=
n2.
But
the
process
is reversible
and
adiabatic for
the
primed
reference
system as
well,
hence
we
will also
have
n2'
=
n2'."
"Now,
if
n1'
were
not
equal
to
n1
but,
say,
n1'
n1, this
would
mean
the
following: The entropy
of
a body
is
larger
for
the
reference
system
for
[84]
which
it is in
motion
than for the reference
system
for
which it is
at
rest.
But
this proposition
would
also
require
that
n2'
n2,
because in the latter
state
the
body
is
at rest
for the
primed
reference
system
while
in
motion
for
[85]
the
unprimed one.
However,
these
two
inequalities conflict
with the
two
equalities
established.
Similarly,
one
cannot have
n1'
n1; consequently [86]
n1'
=
n1
and,
in
general,
n'
=
n,
i.e.,
the
entropy
of the
body
does not
depend on
the choice of the reference
system."
Using our
notation,
we
must
therefore
put
n
= n0.
(25)
If
we now
introduce the quantities
E0,
p0,
and
V0
on
the
right-hand
side of
equation
(23)
by means
of
equations
(16c),
(18c), (20), and (22),
we
obtain
1M.
Planck, "Zur
Dynamik
bewegter
Systeme"
[On
the
dynamics
of
moving
systems].
Sitzungsber. d.
kgl.
Preuss.
Akad.
d. Wissensch.
(1907).
[83]