Pomeranchuk Cooling

Pomeranchuk Cooling - POMERANCHUK COOLING...

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Unformatted text preview: POMERANCHUK COOLING Isaak
Pomeranchuk
 (1913‐1966)
 3He

 •  •  •  •  •  
 Discovered
in
1933
by
Oliphant,
Kinsey
&
Rutherford
 Proved
to
be
stable
in
1939
by
Alvarez
&
Cornog
 Liquefied
in
1949
by
Sydoriak,
Grilly
&
Hammel
 Found
in
natural‐gas
sources
at
only
0.14
ppm

 Produced
by
β‐decay
from
Tritium:
 
 3 1 T → He+ e + ν 3 2 0 −1 
 
 
 
 
 
 € 3He
 Melting
Curve
of
 Clausius‐Clapeyron:
 dP SLiquid − SSolid ΔS = = dT VLiquid − VSolid ΔV Minimum
at:
 
 
 
 
 T
=
0.32K
 When
 
 T
<
0.32K
 
 
 
 d
P < 0 ∴ SLiquid < SSolid 
 
 
 dT 
 
 (The
difference
ΔV ≈ 1.3cm 3 / 
mol 
and
is
independent
of
T)
 


 € € € € 3He
 Entropy
of
Liquid
and
Solid
 3He
 Liquid
 •  Nuclear
spin
=
½
,
it
obeys
Fermi‐Dirac
Statistics
 •  Atoms
are
indistinguishable
like
conduction
electrons
in
a
 metal
and
wavefunctions
overlap
 •  Atoms
move
freely
and
there
are
strong
interactions
 •  Energy
levels
will
be
full
up
to
Fermi
energy
 •  This
‘ordering
in
momentum
space’
only
allows
surface
atoms
 (i.e.
near
Fermi
surface)
to
be
excited
and
there
is
a
reduction
 in
entropy:
 C 3 He ∝ T → S = ∫ dQ = T ∫ C 3 He dT T ∝T S ≈ 3RT € 3He
 Solid
 •  Atoms
are
tied
to
lattice
sites
and
vibrate
 •  At
low
temperature
kinetic
energies
and
phonon
excitations
 are
negligible
 •  The
atoms
are
distinguishable
and
independent
 •  The
entropy
of
the
solid
would
be
that
of
a
fully
disordered
 spin
½
system:
 S = R ln 2 •  Below
T
<
10mK
nuclear
interactions
become
significant
and
 the
entropy
is
no
longer
constant
 € Compression
Work
 Amount
of
heat
removed
from
the
 system
to
convert
1
mole
of
liquid
 into
solid
at
T
=
0.1K
 
 
 
 
 Q
=
0.42J
 
 
 
 
 
 

 

 

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Work
done
by
compression
to

 convert
1
mole
of
liquid
into
solid
 
 
 
 W
=
4.2J
 Compressional
Cooling
Cell
 Solidified
Liquid
Percentage
 Equation
of
State:
 
 
 
 F(P,
V,
T)=0
 For
a
Liquid‐Solid
mixture
of

 3He
this
reduces
to
 
 
 
 P2
=
Pm(T)
 Bulk
modulus
of
a
liquid
 
 Compressive
 ΔV P = −α V0 
 



Pressure

 
 3He
 P1
 P2




V
 Elastic
response
of
cell
 P2 = Pm (T ) = xP1 + α € (V f − V0 ) V0 Solidified
Liquid
Percentage
(cont.)
 For
a
reversible
adiabatic
process
 
 Δ
 System + ΔSEnv .
 = 0 
S 
 
 
 




where,
 ΔSEnv . = SEnv. (Tf ) − SEnv. (Ti ) Such
that
 SLiquid (Ti ) + SEnv. (Ti ) = n Solid SSolid (Tf ) + (1 − n Solid ) SLiquid (Tf ) + SEnv. (Tf ) € But
for
isentropic
process
 € SLiquid (Ti ) = n Solid SSolid (Tf ) + (1 − n Solid ) SLiquid (Tf ) = Const . 
 ∴ ΔSSystem = SSys. (T
f ) −
SSys.
(Ti )
= 0
 

 
 
 
 
 € and
 ΔSEnv . = 0 Solidified
Liquid
Percentage
(cont.)
 Initial

 P1
=
0,
nSolid
=
0
 
 
 1.
 
 
 2.
 (VLiquid (Ti ) − V0 ) Pm (Ti ) = α V0 Solving
gives
 € ( n Solid VSolid + (1 − n Solid )VLiquid − V0 ) Pm (Tf ) = xP1 + α V0 € α Pm (Tf ) − Pm (Ti ) = xP1 − ( n Solid ΔV ) V0 € 20mK
Temperature
Drop
 0.6
 0.5
 0.4
 nSolid

 0.3
 0.2
 0.1
 0
 0
 50
 100
 150
 200
 250
 300
 350
 Ti/mK
 Test
Data:
 P1
=
25atm,
x
=
1,
Ti
=
Ti,
Tf
=
Ti
–
20mK

 Bulk
Modulus
 180
 160
 140
 120
 α/V0
 100
 80
 60
 40
 20
 0
 0
 50
 100
 150
 200
 250
 300
 350
 Ti/mK
 Superfluidity
 Nobel
Prize
awarded
in
1996
jointly
 to:
 David
M.
Lee,
Douglas
D.
Osheroff
 and
Robert
C.
Richardson
 for
their
discovery
of
superfluidity
in
 helium‐3
 References
 •  R.
C.
Richardson,
“ The
Pomeranchuk
effect ”,
Reviews
of
Modern
Physics,
 vol.
69,
no.
3,
pp.
683–690
(1997).
 •  Anufriev
Yu.
D.,
Sov.
Phys.
JETP
Lett.
1,
155
(1965).
 •  David
S.
Betts,
“Pomeranchuk
cooling
by
adiabatic
solidification
of
 helium‐3”,
Contemporary
Physics,
15:
3,
pp.
227—247
(1974).
 •  Christian
Enss
&
Siegfried
Hunklinger,
Low
Temperature
Physics,
Springer
 2005.
 •  Frank
Pobell,
Matter
and
Methods
at
Low
Temperatures
2nd
Edition,
 Springer
1992,
1996.

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This note was uploaded on 02/27/2010 for the course PHYSICS 345 taught by Professor Chuker during the Spring '10 term at Chicago State.

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