Thermodynamics in static electric and magnetic fields
1
st
law reads:

so far focus on PVT

systems where
originates from mechanical work
Now:

additional work terms for matter in fields
Dielectric Materials
1

electric field inside the capacitor:
A
+

V
e
dielectric material
L
+q

q

displacement field D given by the free charges on the capacitor plates:
Source of D is density of
free charges.
Here: charge q on
capacitor plate with area A

Reduction of q
Energy content in capacitor reduced which means work W
cap
>0
done by the capacitor (
in accordance with our sign convention for PVT systems
)
(dq<0 and V
e
>0 yields W
cap
>0)
With
V=
volume of the dielectric material

When no material is present:
still work is done by changing the field energy in the capacitor

Work done by the material exclusively:
parameterized e.g., with time
(slow changes!)
With
Polarization=total dipole moment per volume
With
(
where V=const. is assumed so that PdV has not to be considered
)
Comparing
(
where work is done mechanically via volume change against P
)
With
we define the total dipole moment of the dielectric material
with
Correspondence
and

Legendre transformations
(
providing potentials depending on useful natural variables
)
making electric field E variable
H=H(S,E)
making T variable
G=G(T,E)
and
Magnetic Materials
2
I
N: # of turns of the wire
R
Faraday’s law:
where
Ampere’s law:
where
here
here
A:
cross sectional
area of the ring
magn. flux
lines
voltage V
ind
induced in 1 winding

Reduction of the current I
work done by the ring
work done by the ring per time
makes sure that reduction of B ( )
corresponds to work done by the ring

Again, when no material is present:
still work is done on the source by changing the field energy
In general:
where
M
is the magnetization = magnetic dipole moment
per volume
No material
M
=0
rate at which work is done by the magnetic material

Legendre transformations
(
providing potentials depending on useful natural variables
)
making magnetic field H variable
H
enth
=
H
enth
(S,H)
making T variable
G=G(T,H)
and
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