Transcript chamber B

Liquefaction of Gases : It can be accomplished in two steps :
(i)
The gas must be cooled to a temp. below its critical temp. as a
gas cannot be liquefied above its critical temp. however large
pressure may be applied.
(ii) Then pressure is applied so as to liquefy the gas. Lower is temp.
to which the gas has been cooled, lesser is pressure required to
liquefy it.
The following methods are used for production of very low temp.
(i)
Freezing mixture of salts in ice
(ii) By evaporation of a liquid under reduced pressure
(iii) Joule-Thomson Effect
(iv) Adiabatic expansion of a gas
(v) Regenerative Cooling : In this method a portion of the gas cooled
by Joule-Thomson expansion is used to cool other portions of the
incoming gas before the latter reaches the nozzle to suffer JouleThomson expansion .
(vi) Adiabatic demagnetization of a paramagnetic salt
Critical Temperature:
It is that temp. below which a gas can be liquefied by mere application of pressure.
The gas under critical temp. is called vapor and above this temp. is known as ‘gas’.
Note:
Ti = 6.75 Tc and Ti = 2 Tb
i.e. Ti > Tb >Tc
LIQUEFICATION OF AIR BY LINDE’S METHOD
Principle Joule-Thomson cooling coupled with
regenerative cooling.
Gas to be cooled is water cooled and then
made to suffer Joule-Thomson expansion
through a nozzle resulting in small cooling.
This cooled gas is used to cool the same
incoming gas,which again is made to suffer
Joule-Thomson expansion.
In this way cooling effect is made cumulative.
• Construction The apparatus
used is shown in the fig.1.
• P1,P2 are Compression
Pumps
• C1,C2 are Spiral Tubes
cooled by the cold water and
freezing mixture
respectively.
A is a Vessel containing
KOH soln.
• B,C are Chambers
terminating into nozzles
N1,N2
• D is a Dewar flask to collect
liquid air
Working
P1 compresses air to a pressure
of about 25 atm.
The compressed air is passed
through C1 surrounded by cold
water
.After getting cooled to temp. of
cold water air passes through
A.
KOH in it absorbs CO2 and water
vapours in air.
Then air enters P2 which further
compresses it to a pressure of
about 200 atm.
This air then enters C2 surrounded
by freezing mix. It is cooled to
-20o C and is allowed to come out
of nozzle N1 in chamber B
and suffers Joule-Thomson
effect thereby getting cooled to
about-70oC. Its pressure falls to
50 atmosphere.
From B it moves up and is
again led to compressor P2
where it is again
compressed to 200
atmosphere.
It is led to C2 to nozzle N1
and undergoes greater
Joule-Thomson cooling.
This process is repeated
and after a few cycles air is
cooled to sufficiently low
temp.
At this stage nozzle N2 is
opened and cooled air is
allowed to expand through it
to a pressure of about one
atmosphere and temp. of
-188o C in the chamber C.
It gets liquefied and is
collected in Dewar flask.
Any un-liquefied air is led
back to pumpP1 through
tube T.
LIQUEFICATION OF HYDROGEN
Principle Regenerative cooling
combined with Joule-Thomson
cooling.
But pre- cooling is required
below the temp. of inversion
which is -80oC for hydrogen.
Construction
P is a Compressor Pump.
C1,C2,C3,C4,C5 Coil tubes
placed in chambers A,B,C,D,E resp.
C5 terminates into nozzle which is
opened /closed by handle H
D is a chamber connected to an
exhaust pump E.P.
A is a chamber containing a mix. of
solid CO2 and alcohol.
F is Dewar flask placed in an
outer Dewar flask D F
If H2 is subjected to throttle expansion at ord. temp.
heating will be produced instead of cooling.
Actually H2 is brought to -177oC which is its Boyle’s temp.
Working:
Hydrogen enters compressor P through
inlet I and is compressed to a
pressure of 200 atmosphere.
It then enters coil C1 and is cooled by a
mixture of solid carbon dioxide and
alcohol in chamber A .
It is then freed of carbon dioxide and
moisture by passing through tubes of
caustic potash calcium chloride etc.
(not shown in the fig. ).
The dry and pure hydrogen then enters
coil C2 in chamber B, where it is
further cooled by outgoing cooled
hydrogen which has already suffered
throttle expansion ( i.e. regenerative
cooling takes place.)
The cooled hydrogen enters chamber C
and passes through coil C3.The
chamber has liquid air which cools
hydrogen to a temp. of -170 oC.
The cooled gas enters coil C4 in
chamber D.The liquid air from chamber is
kept trickling into D which is made to
boil under reduced pressure of about
10 cm. of mercury
The required latent heat of vaporization is
taken from gas itself which is thus
cooled to about -2000 C.
The gas finally passes through coil C5
and suffers throttle expansion at
nozzle N operated externally by
handle H. Thus gas further cools due
to Joule- Thomson effect.
This cooled gas moves up cooling
chambers D and C and enters
chamber B.This outgoing gas cools
the coil C2 and the gas is finally
brought back to compressor P
through tube T.
The whole process is repeated and after a
few cycles of operation the temp. falls
below -250oC. At this stage, after
suffering Joule- Thomson effect at
nozzle N , The hydrogen gets liquefied
and is collected in Dewar flask F.
Liquefaction of Helium ( K Onnes
Method):
Principle:Cooling by Joule- Thomson Effect
combined with regenerative cooling.
The inversion temp. of helium is -238oC i.e. 35K .
The critical temp. of helium is -268oC i.e 5K .
Boyle’s temp. of helium is -256oC i.e 17K .
However, for practical reasons the gas is precooled to a temp. of 17K(i.e. Boyle’s temp.)
in order to obtain cooling by throttle
expansion.17K of temp. is obtained by air
and hydrogen liquefiers.
Construction and Working:
The helium pre-cooled by air and hydrogen
liquefiers enters at C and reaches the
junction K, where it divides itself along two
spiral paths C1 and C2.
The spiral tube C1 is placed in the tube A, where
it is surrounded by the hydrogen boiling
under reduced pressure.
The portion of the gas in C2 is surrounded by
cooled outgoing helium gas in tube B.
After passing through these coils, the
gas is again led to two similar
coils C3 and C4 placed in tubes
A and B respectively where the
two portions of the gas are cooled
in the same way as in C1 and C2.
This helium cooled to a temp. below
17K is allowed to undergo JouleThomson expansion at nozzle N.
Helium,therefore, further cools
down.
This helium circulates round the
spiral tubes thereby further cooling
the gas inside these.
By this process of regenerative
cooling, the temp. of helium goes
on falling till it liquefies.
The liquid helium is collected in
Dewar flask.
Any un-liquefied helium is
compressed by the pump P and is
again sent to sets of coils.
Solidification of Helum:(below 4K):
Onnes tried to solidify liquid helium by evaporatig it under reduced pressure but did
not succeed although he attained a temp. as low as 1K.
Kessom was able to solidify it but under a very high pressure of 130 atmosphere.
He took the gas in a narrow bras tube placed in a bath of liquid helium.The gas was
allowed to expand. It solidified into a colorless transparent mass at 4.2K.The
solidification was confirmed from the fact that circulating liquid helium was
blocked by solidified gas.
Later experiments showed that pre-cooled helium at 3.2K solidified under a
pressure of 85 atmosphere and at 1.1K with pressure of 30 atmosphere.
Cooling due to Adiabatic Demagnetization (Production of low temp, by
magneto-caloric effect) :
Adiabatic Demagnetization of paramagnetic solid is an important process towards
attainment of 0K.
The process of magnetizing a substance involves doing work on it (in order to align
magnetic dipoles along the direction of magnetizing field) resulting in rise of
temp. It is called magento-caloric effect or thermomagnetic effect.
If a magnetized substance is suddenly demagnetized (i.e demagnetized
adiabatically) it will show a small decrease in temp. as the energy required for
demagnetization is drawn from the substance itself.
Discuss expt. Or method to produce low temp. : Principle of expt. Is cooling
due to Adiabatic Demagnetizatin as discussed above and on next page
.
The extent to which a paramagnetic substance can be magnetized by
magnetizing field is measured in terms of its susceptibility.It is defined
as ratio of intensity of magnetization and and the magnetizing field i.e.

Higher the value of
pm
H
 ,greater is the extent to which a paramagnetic
substance is magnetized by a magnetizing field .
From Curie law,

1
T
i.e.magnetic susceptibility of a substance is inversely proportional to its absolute
temp.
Assuming that this law holds good at all temps.,a magnetic substance will be highly
magnetized at low temps. If the substance is then adiabatically demagnetized ,large
cooling will be produced (approaching 0K) .
Experimental Verification:
The theoretical prediction was
experimentally verified by Simon
and others using the setup shown
in the fig.
A paramagnetic substance of high
susceptibility and low retentivity
(like gadolium sulphate) is placed or
suspended with a silken thread
in bulb B connected to diffusion
pump.The bulb is surrounded by
Dewar flasks D1 and D2 containing
liquid helium and liquid hydrogen
respectively. The whole apparatus is
placed between pole pieces of a
powerful electromagnet.
Helium gas is sent into bulb B so that
salt is in thermal contact with liquid
helium and attains the same temp.
 1.5K.
Electromagnet is switched on to apply magnetic field 10 4 gauss.
Hence specimen is highly magnetized. The large amount of heat thus
produced is conducted to liquid helium in Dewar Flask D1 by ciculating
helium vapours in bulb B . Hence the specimen is cold and highly
magnetized.
Bulb B is evacuated by pumping out helium gas. The specimen is thus
thermally isolated from flasks D1 and D2. Eletromagnet is switched off .
Thus the specimen is demagnetized adiabatically and the temp. falls to a
large extent.
To measure the temp. of salt ,magnetic susceptibility of the specimen is
measured before and after the experiment.
LetT1 and T2 be initial and final temperatures
and 1 and  2 be initial and final susceptibilities.
1 T 1   2 T 2
Then from Curie law,
Or
T 2


T

1
1
2
T2 is known as Curie Temp. or magnetic temp. A temp.of the order of 0.1K could be
obtained by this method thereby verifying production of very low temp.by adiabatic
demagnetisation.
THEORY OF THERMOMAGN ETIC EFFECT
If a paramagnet ic substance is placed in a magnetic field H and
the magnetic moment changes by dpm
then work done on the system is
dW  -H dpm
According to first law of thermodyn mics,
dQ  dU  dW
Using eqn. (1), eqn. (2) becomes
dQ  dU - Hdpm
For gases,
dQ  dU  PdV
Comparing (3) and (4), it is clear that
thermodyna mic relations of gases can be used
for thermo magnetic effect by replacing
' P' by '-H' and ' V' by ' pm'.
.....(1)
. ....(2)
.....(3)
......(4)
Consider Maxwell' s third relation,
 T 
 V 

 P 
 
  S  S  p
Replacing P by - H and V by pm, we get
 T 
 pm 


 H  S  S  H
or
1
 T 
 pm 






 H  S  T  H  S 
 T 
H
.....(5)
For paramagnet ic substances ,

 S 
T    CH is specific heat at constant magnetisin g field
 T  H
CH
 S 

 T 
T
Hence (5) becomes
T
 T 


 H 
CH
S
 pm 
 T 
H
If T is change in temp.
correspond ing to H change in magnetisin g field, then
T  pm 
H
.....(6)


CH  T  H
On heating all paramagnet ic substances tend to demagnetis e
T  
 pm 
i.e. pm decreases with increase in T i.e. 
is - ve

 T  H
Hence when magnetisin g field decreases, H is - ve then
T is also - ve.
i.e on adiabatic demagnetis ation
paramagnet ic substances are cooled.
From eqn. (6),
T  pm 
dT

dH
Ti



CH H  T 
Tf
0
C
T
where V is volume of the specimen,
 is susceptibi lity and Cis a constant.
CVH

pm 
T
pm
CVH
 2
T
T
Hence (7) becomes
But pm   VH and  
T  CVH 
dT

dH
2 
Ti


CH H  T 
Tf
Tf
or
0
CV
TdT


CH
Ti
0
 H dH
H
....(7)
CV 2
AH 2
or
Tf - Ti  H 
CH
CH
where CV  A is called Curie Constant
A
or
C  is Curie Constant per unit volume
V
AH 2

Tf  Ti CH
Above expression gives change in temp. during adiabatic
demagnetisation of a substance.
Obviously, Tf  Ti
2
2
2
2