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TRANSCRIPT
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CHAPTER VII
Thermometry
1. Introduction
Temperature is a measure of the degree of warmth or cold in a material. We can
perceive through touch that one bath of water is warmer than another. To make such a
concept precise we need to define a quantity called temperature in such a way that the
higher the value of the temperature of a body, the hotter it is. We also have to devise
practical and convenient methods of measuring temperature. The definition and methods
must be such as to lead to the same value of the temperature of a body measured by
different observers, using different methods.
A thermometer is a device to measure temperature. It uses a property of a material that
changes as it is heated or cooled. This property can be the volume of the material, or the
pressure of a gas at constant volume or some electrical property such as the resistance.
We have to choose two different baths and arbitrarily set a value for the temperature T1
for the cold bath and a value T2 , higher than T1 , for the temperature of the warmer bath.
We bring the thermometric device in contact with the bath, wait till thermal equilibrium
is achieved, and measure the value P of the property. Let P(T1) be the property value
when the material is kept in the cold standard bath and P(T2) be its property value when
the material is kept in the warm standard bath. If we now have a bath, the temperature T
of which is to be measured, the thermometer is brought to thermal equilibrium with this
bath and the property value P is measured. The temperature T of this bath is then defined
by the relation
T = T1 +{[P −P(T1)]/ [ P(T2) − P(T1)]} (T2 – T1) (VII.1.1)
The temperature of a bath defined in this way will depend both on the property that is
measured and the material of the thermometer. For example, if we take the property to be
the resistance of a metallic wire which forms the thermometer, there is no justifiable
reason to expect that the way the resistance changes with temperature will be the same for
wires of different material. This implies that temperature defined in this fashion will not
be absolute in the sense that measurements made with different material and using
different properties will generally give different values for the temperature of the same
bath. This will create chaos.
To define an absolute temperature, we have to look for a device and a property such that
the variation of the property with temperature will be independent of the working
substance used. The device may only be a theoretical one that will not be possible to be
realized in practice. Still, such an absolute temperature scale will be useful since it
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provides a benchmark against which the actual performance of practical thermometers
can be tested.
2. Absolute temperature
The Carnot engine is a heat engine in which the working substance undergoes a cycle of
changes in its thermodynamic state. In each cycle it absorbs a quantity, Q1, of heat from a
warm reservoir and delivers a smaller quantity, Q2, of heat to a cold reservoir. The
difference W = (Q1 − Q2) is available as work. The important feature of the Carnot cycle
is that its efficiency, η, defined by the relation
η = W/Q1 = (1 − Q2 / Q1) (VII.2..1)
is independent of the working substance in the heat engine or the nature of the property
used in converting heat to work in the heat engine . This is a consequence of the second
law of thermodynamics. So the efficiency of a Carnot engine can be used to define an
absolute temperature scale. If we take the temperature of the standard cold reservoir as
T2, and the warm reservoir has a temperature T, we may define the efficiency by
η = (1 − T2 /T) (VII.2.2)
The coldest reservoir that one can use must have a temperature T2 = 0 since the
efficiency of any engine cannot be greater than 1. This is called the Absolute Zero of
Temperature and all bodies must have a positive temperature on this scale. A scale of
temperature defined thus is called the absolute or Kelvin scale.
2. 1. Ideal Gas Scale
While it is nice to be able to define such an absolute scale, is there any practical way of
realizing the Kelvin scale? Here the ideal gas laws come to our help. Boyle and Charles
performed experiments on the pressure, P, of a given volume, v, of a gas in different
warm baths. They found that if the gas is at low pressure, the product of the pressure and
volume, Pv, remains constant in a given bath. This quantity increases as the bath
becomes warmer. One can therefore take a mole of a gas at low pressure and determine
the product PV (here V is the volume of 1 mole of the gas) in different baths. One can
define a practical temperature scale using this product PV. If we take the temperature of
a bath of melting ice as 0 and temperature of water boiling under atmospheric pressure as
100,1 we may define a gas scale of temperature by
T = {[PV(T) − PV(0) ] / [PV(100) −PV(0)]} 100 (VII.2.3)
This relation implies that on this scale
PV = C + RT (VII.2.4)
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The above constant, C, can be written as RT0. In such a case,
PV = R (T+T0) (VII..2.5)
Experiments show that (a) in the limit of low pressure all gases show the same behaviour
and (b) the constants R and T0 have the same values for all gases. The constant R has a
value 8.316 Joules/K and T0 has a value 273.15. We may now define a new scale of
temperature, called the Ideal Gas Temperature Scale, in which the ice point temperature
T2 ig = 273.15 and the temperature of boiling point water under atmospheric pressure T1 ig
= 373.15. This is also called the Celsius Scale. We may use any gas as our thermometric
substance and measure the pressure at a constant volume of the gas. The temperature of a
bath deduced from such a measurement, in the limit of pressure of the gas tending to zero,
will be the same. Also it will be independent of the gas. The relation
PV = RTig (VII.2.6)
is called the Charles law. At high pressures, the density of the gas becomes high and
interatomic interactions play a role in causing deviations from Charles law.
2. 3. Relation of ideal gas scale to the absolute scale
How does the ideal gas scale of temperature relate to the absolute temperature scale
based on Carnot cycle? If we use an ideal gas as the working substance in the Carnot
engine and calculate from Charles law the heat, Q1, absorbed at the warm temperature Tig
and the heat, Q2 , rejected at the cold temperature T2 ig we find
Q2ig/Q1ig = T2ig/Tig (VII.2.7)
And hence,
η = (1 − T2ig/Tig) (VII.2.8)
Comparing the equations (VII.2.2) and (VII.2.8), we find that the ideal gas temperature
Tig should be proportional to the absolute temperature TK. It is convenient to choose the
constant of proportionality to be unity. Hence we see that the ideal gas temperature scale
coincides with the absolute temperature scale. So the absolute temperature scale is
realizable in practice using a gas thermometer filled at very low pressure (i. e. in the limit
P tending to zero).
The ideal gas thermometer is called a primary thermometer. In actual practice a
gas thermometer can be filled only at a finite pressure and there will be small deviations
from Charles law. But one can apply corrections for temperatures measured by the gas
thermometer and obtain the temperature on the absolute scale. These corrections will
depend on the nature of the gas used.
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In practice one cannot use the gas thermometer in experiments. One will have to use
secondary thermometers that are small in size and weight and that are more convenient
for measurement and control. There are a variety of such thermometers available. These
are calibrated at a few fixed points using certain interpolation formulae as agreed upon by
International convention. We shall describe the International Temperature Scale currently
in use.
3. International temperature scale (ITS90)
The ITS90 was adopted by the International Commission on Weights and Measures in
1989. This scale supercedes the practical temperature scale of 1968 and the provisional
0.5 to 30 K Temperature Scale of 1976. The temperature measured on the ITS90 scale is
written as T90. The ITS 90 is defined in different temperature ranges as follows:
Between 0.65 to 5 K, T90 is defined in terms of vapour pressure of 3He and
4He. The
temperature T90 is represented in terms of the vapour pressure by the following equation:
9
T90 = A0 + Σ Ai{ [ln(P) − B]/C}i (VII.3.1)
i = 1
The vapour pressure P is in Pascals. Table VII.1 gives the constants for 3He and
4He and
the temperature range in which the constants are valid is indicated.
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Between 4.2 K to triple point of Ne, a 4He gas thermometer calibrated at three fixed
points (at the triple point of Ne, triple point of e-Hydrogen, and one other temperature
between 3 and 5 K as determined by vapour pressure thermometer) is used. The equation
to be used to obtain T90 is
T90 = a + bP +cP2
(VII.3.2)
Here P is the pressure of the Helium gas. The constants a, b and c are determined from
the calibration at the above three temperatures.
Between the triple point of e- hydrogen and melting point of silver, a platinum
resistance thermometer calibrated at specified sets of defined fixed points using specific
interpolations defines T90. We define W(T90) by the ratio R(T90)/R(273.16) where R(T) is
the resistance of the Pt thermometer at temperature T. The thermometer should be made
of pure strain-free Platinum wire satisfying at least one of the following two conditions:
W (MP of Ga) ≥ 1.11807 (VII.3.3)
and W (TP of Hg) ≥ 0.844235 (VII.3.4)
If it is to be used till the freezing point of Ag it must also satisfy the condition
W (FP of Ag) ≥ 4.2844 (VII.3.5)
From 13.8033 to 273.16 K the temperature can be calculated from W (T) by the relation
15
T90 = B0 + Σi Bi[{W1/6
(T) − 0.65)/0.35]i
(VII.3.6)
i=1
The constants Bi are listed in Table VII.2. Table VII.3 gives the temperature of a few
fixed points.
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4. Secondary thermometers
A secondary thermometer is a device of low thermal capacity having a property, which
changes with temperature. It should have a well-characterized and reproducible response
to variations in temperature. It will be useful if the response can be fitted to a well-
defined equation containing a few parameters that can be obtained by calibrating the
thermometer at a few fixed points. The sensitivity of the thermometer (i.e. the change in
signal for one degree change in temperature) should be high. At the same time the
thermometer should respond quickly to changes in temperature. This is achieved by
making the thermal capacity of the thermometer small and having a good thermal contact
with the object, the temperature of which is to be measured.
For cryogenic thermometry it is necessary to have long leads connecting the sensor at
low temperature to electrical leads at room temperature. One must take adequate
precautions to see that the heat leaking through the leads is small. Otherwise the
temperature indicated by the thermometer will be higher than the actual temperature of
the object. One should use as thin and as long leads as possible to increase the thermal
resistance of the leads. It will be good to anchor the leads to a point that is at the
temperature of the object at low temperature. Then all the heat from room temperature
will go to the cold object and ultimately to the refrigerating medium used to cool the
object. Heat leak to the thermometer will become small. This is indicated in Figure
VII.1.
The thermometer leads from the feed through (FT) at the room temperature flange is
wrapped round the specimen chamber and fixed to it with a thin layer of GE varnish
before being connected to the thermometer. Such anchoring is necessary in all
thermometric measurements at low temperature.
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5. Resistance thermometers
One of the most widely used techniques for measurement of temperature is resistance
thermometry. In this technique the resistance of a material is measured and the
temperature is deduced from the value of resistance. One can have materials with a
positive temperature coefficient (PTC) of resistance. In these materials the resistance
increases with increase in temperature. This is usually the behaviour of metals and
metallic alloys. The semi-conducting materials, on the other hand, have a negative
temperature coefficient (NTC) of resistance. In these materials, the resistance increases
(often by a few orders of magnitude) as the sensor is cooled. In the case of PTC sensors
one uses a constant current source to drive a constant current through the material. The
voltage across the sensor is measured with a digital voltmeter. As the temperature falls
the power dissipated in the sensor will decrease. With NTC materials, it is usual to use a
constant voltage across the resistor and measure the current. The power dissipated is
inversely proportional to the resistance. So, with this method of measurement, the power
dissipated will decrease in NTC sensors as the sensor cools.
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5. 1. Self Heating
Why are we worried about the power dissipated in the sensor? This power will have to
be conducted away to the cold object, the temperature of which is being measured. If the
thermal resistance of the contact between the thermometer and the object is ρcontact and P
is the power dissipated in the sensor during measurement, there will be a temperature
difference ∆T between the thermometer and the object given by
∆T = ρcontact P (VII.5.1)
If the object temperature is T, the temperature recorded by the thermometer will be T+∆T.
This is called the self-heating effect. The contact resistance increases as the temperature
falls and varies as T−3
below 1 K. It is therefore necessary to keep P small enough so that
∆T is a small fraction of T. The lower the temperature the smaller should be the value of
P. That is the reason for using a constant current mode of measurement with PTC sensors
and a constant voltage mode of measurement with NTC sensors. The power dissipated
depends on the square of the current while the measuring signal will be proportional to
the current. It is therefore possible to choose a current value that will give a large enough
signal to measure the temperature accurately and that, at the same time, will keep the
power dissipated small enough to make the error ∆T smaller than a pre-assigned value.
5. 2. Two Wire and Four-Wire Measurement:
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Figures VII..2(a) and 2(b) show the connections for a two-wire and a four-wire
measurement of the resistance of the sensor. In the two-wire measurement the DVM
measures the voltage across the resistance thermometer and the current leads. So the
resistance measured includes the resistance of the current leads, which will vary with
temperature in a manner different from the behaviour of the resistance thermometer.
Unless the resistance of the current leads is negligibly small compared to the resistance of
the thermometer, the measured temperature will be in error.
In the four-wire measurement the current and voltage leads are connected to the
terminals of RT. So the DVM measures only the voltage across RT and the resistance of
the current leads does not enter into the measurement.
5. 3. AC Measurement:
One can also measure the resistance of RT by AC methods using either a bridge
circuit or a lock in amplifier. This involves expensive instrumentation and is justified
only if one requires a very high sensitivity in measurement.
5. 4. Platinum resistance thermometer (PRT)
The platinum resistance thermometer is widely used in the temperature range 20K to
room temperature and above. The thermometer is made of a thin, high purity wire of
platinum mounted strain-free and encapsulated in a ceramic tube or a glass tube. It comes
with two leads. The PRT has a diameter of about 2 mm and a length varying between 5
to 20 mm. For four-wire measurement the voltage and current leads will have to be
soldered to the two leads of the PRT. The resistance thermometer usually has a nominal
resistance of 100 Ohms at 273.15 K. For such a thermometer the sensitivity is roughly
about 0.4 Ohm/K from 40 K to 500 K. Below 30 K the sensitivity falls off steeply. The
temperature variation of resistance is shown in Figure VII. 3.
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If the thermometer is calibrated, its accuracy in measuring temperature is around 5 to 10
mK and reproducibility is also of the same magnitude. The response time of the
thermometer depends on (a) its mass and (b) the temperature. The response time is a few
seconds at low temperature and increases as the temperature increases. The excitation
current is usually 1 mA, which will give a self-heating power of 100 microwatts at 273 K.
The Platinum thermometer can be used above 50 K in magnetic fields as the magneto-
resistance of platinum causes only an error of a few per cent in the measurement of
temperature.
5. 5. Rhodium-Iron resistance thermometer
The temperature variation of resistance of Rhodium-iron alloy depends on its
composition. It is possible to choose a composition for which the resistance increases
monotonically in the range 1.4 to 300 K as the temperature increases. Thermometers are
made either with a thin film of Rh-Fe alloy or with a thin wire. Because of the small
thermal capacity in the former case, the response time is much shorter (of the order of a
few milliseconds at 4.2 K to about twenty milliseconds at 300 K) than the response time
(a few seconds) with the wire wound thermometer. The sensitivity is high from 100-300
K. Below 100 K the sensitivity drops till 30 K. The sensitivity rises again to a high value
below 10 K. This thermometer is unsuitable for measurement in magnetic fields below
77 K.
5. 6. NTC Resistance Thermometers
5. 6. 1. Doped Germanium resistance thermometer
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Germanium (Ge) is a semi-conductor and appropriate doping can alter its electrical
conductivity. The resistance increases sharply as the temperature is reduced. Various
models are available with different suppliers, for use in the temperature range 0.05 K to
30 K. The rapid increase in sensitivity below 4.2 K makes it well suited for sub-milli
Kelvin control of temperature. A typical resistance temperature curve for a GRT is shown
in Figure VII.4.
It is seen that above 30 K the sensitivity of the thermometer becomes poor. It has to be
used with a constant voltage excitation. At 0.5 K the excitation voltage will be a few tens
of microvolts and this is increased to 10 mV at 100 K. This excitation voltage is chosen
so that the self-heating power at 4.2 K is about 0.1 µW and at 0.5 K is about 0.1 pico-
Watt. Typical thermal response time is a few hundred milliseconds at 4.2 K and a few
seconds at 77K.
5. 6. 2. Cernox Thermometers
These are ceramic oxides with a negative temperature coefficient of resistance. They
are useful in the temperature range 1.4 to 300 K. These thermometers are characterised
by a very low magneto-resistance and so are useful to measure temperature in the
presence of high magnetic fields. These are used with constant voltage excitation of a
few millivolts such that the self-heating power is about 10 µWatt at 300 K and 0.1 µW at
4.2 K. The thermal response time is a few milliseconds in the range 0.3 to 4.2 K. Figure
VII.5 shows the resistance temperature graph of commercial Cernox thermometers.
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5. 6. 3. Other NTC resistance thermometers
Carbon glass sensors, which consist of carbon fibres trapped in a glass matrix, can be
used from 1.4 to 300 K. They have a negative temperature coefficient of resistance.
Below 10 K they have a high sensitivity. However above 100 K their sensitivity falls
below 1Ohm/K. Above 100 K they can only provide rough temperature measurement to
an accuracy of 0.1 K. They have a low magneto-resistance, this being negative below
20K. They can be used in magnetic fields as high as 19T and the correction for the
temperature amounts only to a few per cent.
Ruthenium oxide sensors are thick film thermometers. They are useful in the range 50
mK to 30 K. The magnetic field dependence of resistance is small. Allen-Bradley carbon
resistors have been used for thermometry. They are inexpensive. But they need frequent
calibration.
6. Diode thermometers
At a constant current, the voltage across a forward biased p-n junction diode changes
with temperature. This property is used in diode thermometry. The advantage of diode
thermometers is their sensitivity (change in forward bias voltage for unit change in
temperature) is large and nearly constant from 300 K down to about 25 K in the case of Si
diodes and 40 K in the case of GaAs diodes. Below 25 K in Si diodes and 40 K in GaAs
diodes, the forward voltage increases rapidly as the temperature decreases.
Figure VII.6 Forward voltage of a Si diode and a Ga-As diode as a function of
temperature at constant current.
The forward voltage as a function of temperature at a constant current is shown in
Figure VII.6 for both Si and GaAs diodes. Si diodes are relatively inexpensive. Though
they are less sensitive than GaAs diodes they are more stable. Above 1 K one can
achieve an accuracy of about ± 25 mK in temperature measurement. The excitation
current is 10 µA. Problems can arise if there is an AC component of current from the DC
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source. One should take precautions like proper electrical shielding and grounding to get
precise measurements. The GaAs diodes can be used in moderate magnetic fields.
7. Thermocouples
Thermocouples have been used often in the past for the measurement of cryogenic
temperatures. They are inexpensive. When two dissimilar metals A and B are joined
together and the two junctions are maintained at different temperatures T1 and T2 an
electromotive force is generated which can be measured on a digital voltmeter. The
typical measurement arrangement is shown in Figure VII.7.
Figure VII.7: A and B are wires of two dissimilar metals joined together to form two
junctions maintained at temperatures T1 and T2.
The open ends of A are connected to the terminals of a DVM.
If T1 is different from T2 the DVM indicates an emf in millivolts. This is called the
thermo-emf. The thermo-emf is a function of temperature difference (T1 − T2) provided
the junctions of leads A and A’ to the terminals of the DVM are at the same temperature.
If T2 is a temperature of a reference bath such as melting ice then one can measure the
unknown temperature T1. Usually the reference bath is dispensed with. The open ends of
A and B are connected to the DVM. But at the junction to the DVM a resistance
thermometer measures the temperature and produces an appropriate voltage by a bridge
circuit.
Figure VII. 8: Thermo-emf of standard thermocouples with
the reference junction at 273.15 K
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There are three standard thermocouples used in the range of cryogenic temperature.
These are type E (chromel-constantan), type K (chromel-alumel) and type T (copper-
constantan). In Figure VII.8 the thermoelectric emf of these standard junctions are
plotted in millivolts against temperature T1, taking the reference temperature to be that of
melting ice (273.15 K). The slope of the curve gives the sensitivity. We see that the
curves flatten out at the low temperature end. The sensitivity falls at low temperature and
so these thermocouples are not usable below 30 K. For example the thermoelectric power
at 20 K for E, K and T type thermocouples are 8.5, 4.1, and 4.5 µV/K.
Since the wires find themselves in a region where temperature gradient exists, it is
essential that the wires A and B must be homogeneous. Otherwise the temperature
gradient along the length of the thermocouple wires will produce an emf of its own. The
Gold- (0.7 at %) Fe – Chromel thermocouple is suited for temperatures below 30 K as its
thermo-electric power remains high at 15 µV/K above 10 K.
One can measure the temperature to an accuracy of about 1 K. Relative changes in
temperature can however be measured more accurately. The advantage of thermocouple
thermometry is the low response time of the thermometer.
8. Capacitance thermometers
The dielectric constant of strontium titanate shows an appreciable variation with
temperature. A capacitance of a few nano-farads made with this material as the dielectric
medium can be used as a thermometer below 100 K. The capacitance will have to be
measured by an AC bridge with about a few volts of excitation. The disadvantage of
these thermometers is that the calibration changes after thermal cycling. They have to be
re-calibrated frequently. The advantage of the capacitance thermometer is that it is totally
insensitive to magnetic fields. The capacitance thermometer is useful for controlling
temperature in the presence of magnetic fields. Their thermal response time is high, of
the order of minutes.
9. Magnetic susceptibility thermometer
Temperatures of a few tens of a milliKelvin can be obtained either by adiabatic
demagnetization of a paramagnetic salt or with the help of the dilution refrigerator.. For
the measurement of such low temperatures the magnetic susceptibility thermometer can
be used. The paramagnetic susceptibility of a dilute system of of magnetic atoms varies
with temperature as
χ = C / T (VII..9.1)
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This is known as the Curie law. In a solid, two effects cause a change in the behaviour
of the susceptibility represented by Curie’s law. One is the exchange interaction between
neighbouring magnetic atoms, which cause the magnetic moments of the atoms to
become ordered below a certain temperature leading to ferro-, antiferro- or ferri-
magnetism. This interaction drops off rapidly as the distance between the neighbouring
magnetic atoms increases. Secondly the degenerate levels of the ground state of the free
atom are split by crystal field effect.
The paramagnetic salt should be in good thermal contact with the object the
temperature of which is to be measured. The magnetic susceptibility is measured by
using a Hartshorne bridge or a ratio transformer system. Cerium magnesium nitrate is the
thermometric substance commonly used below 1 K since its magnetic ordering
temperature is 4 mK. The other material is Pd containing a few parts per million of iron
atoms. The spin freezing temperature of this material is 0.1 mK and it has a giant atomic
magnetic moment of 10 Bohr magnetons.
10 . Vapour pressure thermometry
The pressure exerted by the saturated vapour over the liquid surface is a definite
function of temperature and hence can be used to measure the temperature of the liquid.
In fact, in the International Scale of Temperature (ITS90), the vapour pressure of 3He and
4He are used for defining the temperature scale between 0.65K and 5K. With a good
pressure measuring arrangement, the vapour pressure thermometer is an excellent
secondary standard, since the temperature response depends on the physical property of a
pure element. The vapour pressure is expressed by semi-empirical formulae with fit
coefficients. The vapour pressure equations for many common cryogenic fluids are
given in Table VII.4 and the constants in Table VII.5.
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The different fixed points of common vapour pressure thermometers are given in Table
VII.6.
The vapour pressure thermometer is useful for temperature measurement in the range
from the triple point to the critical point of the liquid. One of the important advantages of
vapour pressure thermometer is the extreme sensitivity in the range over which they can
be used. The disadvantage is that it is useful only over a limited temperature range. The
thermometers are most accurate in the range of the normal boiling point of the liquid
chosen. The constants for the vapour pressure equations are given in Tables VII.5 and
VII.6.
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The apparatus for vapour pressure determination is quite simple. There are many
variations of vapour pressure thermometers, but one described by Scott is shown in
Figure VII.9. The copper bulb having the liquid is connected to an accurate mercury
manometer through a thin walled vacuum jacketed stainless steel tube and a coiled copper
tubing. It should be obvious that the tubing between the bulb and manometer should
nowhere be colder than the bulb since this can cause refluxing and the pressure readings
will be low.
Also, the gas purity is quite important. With Hydrogen, the ortho / para ratio is an
important parameter due to the strong dependence of the vapour pressure on this
composition. In the case of helium, hydrogen is the possible source of impurity, since all
the other impurities will be solidified. As mentioned earlier, the vapour pressure
thermometry is quite sensitive. It also has good response and is not affected by magnetic
fields and does not need calibration.
11. Conclusion
There are other thermometric techniques like noise thermometry and nuclear orientation
thermometry which are outside the purview of the book. Since temperature measurement
is an important component of any low temperature measurement one must pay special
attention to thermometry.
110
REFERENCES
1. Thomas M. Flynn, “Cryogenic Engineering”, Mercel Dekker Inc., N.Y 1997.
2. Randall F Barron, “Cryogenic Systems”, 2nd
edition, Oxford University Press,
New York, 1985.
3. Scott, R. B., “Cryogenic Engineering”, D. Van Nostrand Co., Inc., Princeton, New
Jersy, 1959.
4. McClintock, M., “Cryogenics”, Reinhold Publishing Corp., New York, 1964.
5. Guy K. White, “Experimental Techniques in low temperature Physics”, 3rd
edition, Oxford University Press, New York, 1979.
6. A. C. Rose-Innes, “Low Temperature Technique”, The English Universities Press
Ltd., London, 1974.
7. S I Data sheets.
8. Lab Facility, U. K.
9. Lakeshore Cryotronics.