DOC.
1
MECHANICS LECTURE NOTES
113
P
=
-
From the second
eq.
M
dv
8H
dT
dH
S=
-
T dT
=
-s
]
[p. 113]
-
dv
-
PdV
-
SdT
=
dH
-dT
-PdV+
TdS
=
dH +
d(TS)
=
dE
«
v
'
dE
dH
=
d(E
-
TS)
General
conclusions from
the
equations
for
cyclic
motion.
1)
If
one
considers
only
processes
in which
the coordinates
cyclic
velocities
n'
are
constant (currents,
temperatures),
then
the forces
can
be derived
from
a
potential.
2)
The
same
is also true if forces do not act
upon
the
cyclic
coordinates. In that
case
we
have
m
equations
dH
dit'
=
const.,
by means
of
which
one can
eliminate
the
n'
from H.
(Interaction
between
magnets
&
resistance-free short
closed circuits.
Adiabatic
processes.
3)
We
write down two
cyclical eq.
H,
_ d(aH
dt \o,r~'
a
82H
`ncr
d
(dH_
U°
dt
\dna'
_52H
OR0' 5Pb
Pb'
+
ôir9
ÔIVb
Rb
en;
dn""
dnp'dna'
dnp" dna'dnp
equal
to
each other
d2H
dn'dpat
^a
tt
So
far
as one can
disregard
an
independence
of
the terms
d2H
3ic'
3*'
fx
a
from
the
quantities
[p.
114]