Thermodynamics in static electric and magnetic fields

flinkexistenceMechanics

Oct 27, 2013 (3 years and 11 months ago)

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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