List of Vacuum Pressure Measuring Devices [with formula]!

#### 1. Mercury Manometers:

These are of two types:

i. Differential and Optical Lever Manometers, which are modifications of the ordinary mercury manometers, with more sensitive methods of observation and measurement. These are suitable for measurement of pressures up to 10-3 mm.

ii. McLeod Gauge, which is a standard device of its type and based on the validity of Boyle’s Law at low pressures. It is suitable for accurate measurements of pressures, down to 10-5 mm.

#### 2.Viscosity Manometers:

The principle underlying these is that at low pressures, the viscous drag between two surfaces in relative motion is proportional to P/M, where P is the pressure of the gas and M is its molecular weight.

These are of two types:

i. The Damping or Decrement type, an example of which is Coolidge’s Quartz Fibre Gauge, suitable for the measurement of pressures, ranging between 10-2 mm, and 10-5 mm.

ii. The Molecular types an example is Langmuir and Dushman’s Molecular Gauge, suitable for the pressure range 10-3 mm to 10-7 mm.

#### 3. Mechanical Manometers:

These are based on the principle of mechanical deformation produced in a thin wall or diaphragm, due to pressure. These are calibrated against the McLeod Gauge and their range does not go below 10-3 mm.

The two widely used manometers of this type are:

i. The Bourdon Spiral Gauge, and

ii. The Aneroid Barometer type.

These are based on the measurement of the rate of transference of momentum from a hot to a cold surface due to molecular bombardment.

Widely used gauges of this type are:

i. Knudsen’s Absolute Gauge, a standard gauge of its type having a wide range, from 10-2 mm to 10-7 mm.

ii. Crooke’s Radiometer, suitable only for qualitative work.

#### 5. Ionisation Gauges:

These depend for their action on the change of electrical conductivity of a gas with pressure.

Two gauges of this type are:

i. Buckley’s type,

ii. Dushman and Found type, the latter one being suitable for measurement of pressures from 10-2 mm down to the lowest attainable pressure, and

iii. α-ray ionisation gauge.

#### 6. Conductivity Gauges:

The principle of these gauges is the effect of pressure on the rate of transfer of heat by conduction, their range is comparatively small, from 10-1 mm to 10-4 mm.

Among gauges of this type may be mentioned:

i. The thermocouple Gauges

ii. Pirani-Hall Resistance Gauge, and

iii. Gauges, based on linear expansion of metallic wires or strips.

#### 7. The Open Manometer:

The manometer consists of a U-tube, with both limbs open. One of the limbs is little shorter than the other, and bent at right angles. This is shown in Fig. 25.7. Depending upon the pressure a liquid of suitable density is poured into the tube, so as to be above the bend and at the same level in either limb. The shorter limb is connected to the gas-supply or the vessel, whose pressure is to be measured.

The level of the liquid in the shorter limb then rises above, or falls below than that in the other limb, according as the pressure of the gas is lower or higher than that of the atmosphere, as shown in Figs. 25.7(a) and (b) respectively. The difference of the levels in the two limbs is then read, and the pressure of the gas is calculated.

Let us consider that the difference of levels in the two limbs be h, and let the barometric height be H. Then in case- (a) pressure of the gas is (H-h) and in case (b), it is (H + h) cm of mercury column when mercury is used. If the liquid be oil or water of density ρ the pressure in the two cases will be (H-h.ρ.13.6) and (H + h.ρ.13.6) respectively, since 13.6 gm/c.c. is the density of mercury.

#### 8. The Closed Manometer:

This manometer is used for the measurement of high pressures. It is similar to the open manometer in construction, but with the longer limb closed at the top. This is shown in Fig. 25.8. It contains some air at atmospheric pressure in the closed space above the liquid, with the level of the liquid columns in the two limbs being same at the start.

When the shorter limb is joined to the gas supply, the level of the liquid column in the shorter limb is pushed down while that in the other pushed up, so that the air in it gets compressed. The pressure of this enclosed air being inversely proportional to its volume, it is determined by noting its new volume.

From this pressure and the difference in the levels of the liquid columns in the two limbs, the pressure of the gas-supply, in communication with the shorter limb can be calculated in the following way- We assume that the original volume of the enclosed air be V c.c., its pressure be one atmosphere or 76 cm of Hg. Then, if v be its volume, after the shorter limb connected to the gas-supply, we have, by Boyle’s law-

Hence, knowing the original volume V and the new volume v of the air H, the pressure of the enclosed air can be known. This is then the pressure at B in the longer closed limb. So if the difference of the levels in the two limbs be h, and the liquid used in the manometer be mercury, the pressure at A, i.e., the pressure of the gas-supply = H (H + h) cm of mercury column. If the liquid used to be oil or water of density ρ, then we can write,

#### 9. The Bourdon Gauge:

To measure very high pressures, a Bourdon Gauge is used. Its principle is same as that of Aneroid barometer, which is a modification of the gauge. As shown in Fig. 25.9 it consists of a tube ABC, elliptical in section, with the end A closed and the end C open, so that it can be put into communication with the gas-supply whose pressure is to be determined.

Due to the high pressure of the gas entering the tube, it becomes more circular in section. This results in the end A of the tube being forced away from C. This movement of A, moves the pointer P over a scale, graduated directly in atmospheres. The instrument is a direct reading one, and can be used to find low pressures also.

#### 10. McLeod Vacuum Gauge:

Simple manometer is not appropriate for the measurement of very low pressures. For the purpose, the McLeod Vacuum Gauge can be used. The form of the instrument is shown in Fig. 25.10. It consists of a cylindrical or spherical bulb B, of known volume, ending above in a graduated capillary tube CA and connected to a reservoir of mercury R and a side tube EF, which can be put into communication with the vessel or the pump where the pressure is to be determined.

As shown a side capillary tube G is attached to it, whose diameter is the same as that of CA. It is used to counteract the depression of the mercury column in CA due to capillarity for, being the same diameter as CA, the depression of the mercury column in it is the same as that in CA.

When the reservoir R is lowered until the mercury falls below the bend D, the bulb B and the vessel are put into communication each other and the bulb is filled with the gas, whose pressure P is to be determined. On raising the reservoir, mercury rises into the bulb and the side tube, thus cutting off EF from B the gas enclosed in the bulb is compressed as mercury rises more and more into it, until the whole of it is forced into the capillary tube CA.

The reservoir is raised further, until the whole of the bulb B and a part of the capillary tube CA are filled with mercury. The mercury in the capillary tube G, attached to EF, rises up in a level with the top end A of CA. Let the pressure of the gas in CA be h cm. Then if V be the volume of the capillary tube CA and the bulb B up to the bend D and v be the volume of the gas after the mercury has risen into it, we written-

Using Eqn (25.12) the pressure of the gas, P is determined. It is seen that greater the value of V and the smaller that of V, the smaller the value of P that can be measured. Hence the sensitiveness of the gauge depends upon the ratio V/v.

Practically all other types of gauges are calibrated with reference to it, however the performance of the McLeod gauge becomes somewhat erratic in the presence of easily condensable vapours. By introducing a liquid air trap in between the gauge and the high vacuum side this can be remedied. In fact, the liquid-air trap must be used even otherwise to prevent any mercury vapours entering the evacuated vessel.

There are a few other drawbacks in the instrument. It is inconvenient to manipulate the reservoir with a large amount of mercury in it, v. The mercury which remains in contact with the rubber of the flexible tube is likely to get contaminated due to the presence of sulphur in the composition of rubber.

Modification of McLeod Gauge:

In this modification of the gauge the tube D is made longer and fitted into a rubber bung in one mouth of a Woulff’s bottle W so as to dip inside mercury contained therein. This is shown in Fig. 25.11. Into the other mouth there is a side tube N connected through a stop-cock S to a small soda-lime tower T and a tube L leading to some simple form of a backing pump.

The tower T has a packing of glass wool at either end for preventing any particles of sodalime getting into the gauge. It is connected at the top to a long capillary tube J through a small rubber tubing provided with a spring-clip, to put into communication with or cut off from, the outside air as required.

The Woulff’s bottle first put in communication with the pump, through the stop-cock, so that the whole of the mercury in the gauge comes down into the bottle. The pressure throughout becomes same as produced by the backing pump and this very much lower than that of the atmosphere.

Then the communication between the bottle and the pump is cut off and that between the former and the sod-lime tower partially established by a slight rotation of S. As a result the air from outside gradually enters into the bottle, losing its moisture during its passage through soda-lime in the tower.

In a consequence, there increase of pressure on the surface of mercury in the bottle and it is forced up into D. The gauge is now conveniently used. The labour involved in moving the reservoir up and down for adjustment of the mercury columns in C and G, and the possibility of contamination of mercury are both obviated neatly by this procedure.

However, the McLeod gauge has its inherent detects of being rather unwidely in size and its inability to give a continuous record of pressure changes in the vessel. Moreover the use of the liquid-air trap affects seriously the rate of pumping and the readings obtained on the gauge.

Utility and Drawbacks of the Gauge:

Though the range of the gauge is small, between 10-2 to 10-4 mm of Hg, but it’s almost instantaneous action is extremely useful for the measurement of pressure fluctuations.

Its main drawbacks are:

(i) It is too sensitive to thermal or mechanical shocks and vibrations, which must be avoided as far as possible. As a safeguard it is usual to provide a shock-absorbing mounting for it;

(ii) It is unsuitable for use with organic vapours, as its filament gets ‘poisoned’ by them;

(iii) Pressures below 10-4 mm of Hg cannot be measured with its help with any reasonable amount of certainty;

(iv) At pressures below 10-3 mm of Hg the heat loss occurs more by radiation than conduction.

Like most gauges in the pressure range 10-3 to 10-5 mm of Hg this too requires some manual adjustments which are not as reliable as mechanical or automatic ones.

#### 11. The Pirani Resistance Gauge:

At high pressures, the thermal conductivity (K) of a gas is independent of pressure. At a pressure below 10-2 mm of Hg when the mean free path of the gas molecules is of the same order of magnitude as the diameter of the containing vessel, it becomes directly proportional to the pressure (p). Thus K is a linear function of p, i.e. K = α.p, where α is a constant.

This fact is the basis of the Pirani Gauge shown Fig. 25.12(a). It consists of a tungsten or platinum filament (F), enclosed in a small detachable glass bulb (B) similar in construction to that of the ‘cage-type’ incandescent lamp. This is maintained at a temperature, higher than temperature of the surroundings. The bulb is open at the lower end which is connected to the vessel where the pressure is to be found out.

With the change in the pressure of the gas in between the filament and the walls of the bulb the rate of heat conduction across the gas changes. This causes a change in the temperature of the filament and hence in its resistance. This change in the resistance of the filament is measured to the change in the thermal conductivity and so the pressure of the gas.

A calibration curve for the gauge is plotted measuring simultaneously the resistance of the filament and the pressure of the gas around it by a Wheastone’s bridge where a constant potential difference is applied to heat the filament to a temperature of about 120°C. The pressure due to any value of the resistance of the filament, can then be directly obtained from the curve. This calibration curve is straight line in nature so long as the pressure of the gas is below 10-2 mm.

At higher pressures, the relation between K and p no longer remains linear. Then K varies in a complicated manner with both the pressure of the gas and the temperature of the surroundings. To overcome this difficulty, Campbell suggested that instead of keeping the voltage across the bridge constant and to measure the resistance of the filament, the temperature and hence the resistance of the filament is kept constant for measuring the potential difference, required to be applied to the bridge.

Accordingly the Pirani gauge, shown as P.G. in Fig. 25.12(a) is connected in one arm of the bridge together with fixed resistance R1 and R2, and the variable resistance R3 in the arms. These resistance are made by an alloy like ‘manganiri and ‘minalpha’, having almost zero coefficient of temperature.

The potential difference is applied to the bridge at A and C, by a potential divider using a rheostat included in the battery circuit. Its value can be seen in the voltmeter V connected between A and C. The bulb of the gauge is placed in a thermostat at 0°C, to ensure constancy of the temperature of the surroundings of the filament.

Procedure:

i. By applying a known potential difference across A and C, the bridge is balanced adjusting the variable resistance R3, so that the deflection in the galvanometer becomes zero and there is sufficient current through the filament of the gauge to raise its temperature to about 100°C. The pressure changes, the voltage across A and C is adjusted every time to restore the balance of the bridge and to make the galvanometer deflection zero.

If θ be the excess temperature of the filament over the surroundings, the heat-loss long the leads L and L will be proportional to θ. Let it be equal to βθ, where β is a constant. If V be the voltage applied across the bridge, the heat dissipated per second in the filament is equal to αV2, where α is new constant. Again if p be the pressure of the gas around the filament, the heat lost per second by conduction across it is ƒ(p), where ƒ(p) is a function of pressure.

We may, therefore, write-

ii. In an actual case it becomes tedious to use Campbell’s method and so an alternative method is adopted sometimes. In that procedure the bridge is first balanced with only vacuum about the filament and then maintaining the voltage across the bridge constant the gas or air is allowed into the gauge. The balance of the bridge is thus upset to this out of the balance current, passes through the galvanometer.

The deflections in terms of scale divisions are noted for different values of pressure of the gas as indicated by a McLeod gauge. If N be the number of scale divisions through which the galvanometer needle is deflected for a pressure p of the gas surrounding the filament then we can write N ∝ ƒ (p). A graph between the two will be a straight line giving the required calibration curve for the gauge wherefrom the pressure of the gas for any deflection in the galvanometer can be directly obtained.

Some important points for the successful measurement of low pressure are:

(i) The material of the filament must have a high temperature coefficient so that its resistance change must-be appreciable for a small change in its temperature. So it is made of a tungsten or a platinum wire, of a diameter of about. 06 mm;

(ii) The heat losses along the filament- support must be as small as possible;

(iii) The filament must throughout be kept taut, so that the distance between it and the walls of the enclosing bulb remains same.

For getting the conditions- (ii) and (iii), a poor conductor of heat like a glass rod is used for the filament and it is taken round glass beads with its longer portions equidistant from the walls of the bulb on either side; (iv) in addition the falvanometer should have a high current sensitivity.

#### 12. Thermocouple Gauge:

This gauge is a variant of the Pirani Hot Wire or Resistance Gauge. Instead of measuring the resistance of the filament with it we measure the temperature of the hot junction of a thermocouple, attached to the filament. From the thermo-electric e.m.f. developed in it. The temperature of the hot junction depends on the thermal conductivity K of the gas in between the filament and the walls of the containing glass bulb, the outside of which is maintained at 0°C and is connected at its upper open end to the vessel in which the (low) pressure is to be determined.

In this arrangement the filament F, is a short ribbon of constantan and is heated by a current of up to 50 milliamperes. The hot junction of the thermocouple (T.C.) made of iron-constantan, chromelalumel or antimony-bismuth, is attached to the midpoint of the filament is connected through a rheostat to a low-voltage battery and a milliammeter.

The circuit includes a sensitive galvanometer, the deflections of which give an indication of the thermo-electric e.m.f. developed and hence that of the pressure of the gas. The gauge is calibrated against a McLeod gauge with the same gas in both, if proper accuracy is demanded.

#### 13. Ionisation Gauges:

Ionisation is the process of knocking out an electron from the outer shell of a gas atom. This may be done by a fast-moving electron colliding against the gas atom. The process is known as ionization by electron collision.

Before ionisation it must possess a certain minimum amount of energy depending on the gas and therefore it must be accelerated through a certain minimum potential difference, called the ionisation potential (Vi), for that particular gas. The energy acquired by the electron is determined in terms of electron-volts.

If an electron is knocked off from a gas atom, ionisation produces positive ions and electron. When these positive ions are collected on another auxiliary electrode, we get a positive ion current or an ionisation current, for a given value V of the accelerating potential above the ionisation potential Vi.

This ionisation current, at low pressures, below 10-3 mm of Hg, changes linearly with the pressure of the gas, because at that pressures, an electron is hardly collide with more than one atom on its way from the cathode to the auxiliary electrode.

So in an Ordinary triode valve, the grid may act as the auxiliary electrode, if it be given a negative potential with respect to the filament. Thus any triode valve may be used as an ionisation gauge. To avoid any possibility of electrical leaks between the electrodes, however, the triodes used as ionisation gauges are specially constructed. As the electrons are emitted on heating the cathode the gauge is called a hot cathode ionisation gauge. A modification, now in common use is shown in Fig. 25.14.

It is the tungsten filament F is here supported on a glass rod R with a co-axial grid G, around it and a nickel or silver coating on the interior of the glass bulb, enclosing the two, acts as the plate P, with a platinum wire w scaled on to it for enable it to be connected to the external electrical circuit. To prevent deposition of any metal film on it, the glass rod is provided with loose glass collars C, C, as shown in the figure.

The positive ions may then be collected either on the grid or on the plate. The electrical connections for the purpose are shown in Fig. 25.14(a) and (b), with the grid being given a negative potential in the former and a positive potential in the latter case, with respect to the filament, with the plate joined to the positive and the negative poles of the high voltage or high tension battery (H.T.) of about 120 volts, in the two cases respectively. A milliammeter mA is included in the plate circuit and a galvanometer G in the grid-circuit G’, in the first case and vice versa in the second case.

Working Principle:

First Case:

The plate being at a positive potential with respect to the filament, electrons emitted by the latter are attracted towards the plate and pass through the holes of the grid. On their way to the plate, they bring about ionisation of the gas between the grid and the plate.

The positive ions produced are collected by the grid which is at a negative potential with respect to the filament. A small lonisation current thus flows through the grid filament circuit and can be read on the galvanometer G while the electron current is obtained by the milliammeter mA.

Second Case:

As the grid is at a positive and the plate at a negative potential with respect to the filament, the electrons emitted by the filament are attracted by the grid but a number of them get through it on account of their momentum causing ionisation of the gas in the space between the grid and the plate.

The positive ions so released are collected at the plate, any electrons straying into the region being repelled back by it. The positive ion is then read on galvanometer G’ and the electron current on the milliammeter, as before. Out of the two arrangements discussed the latter method is more sensitive, but the first one is easier to work with.

This gauge is not an absolute one and has to be calibrated against a McLeod gauge, with the same gas in it. After calibration the galvanometer G’ is replaced by a microammeter, graduated in pressure units. The gauge can be used to measure much lower pressures, in the range 10-3 mm, 10-7mm of Hg. It has other advantages over the McLeod gauge, e.g., (i) it can be used to measure pressures of both vapours and gases and (ii) being very smaller in size, and it can be located in close proximity with the vessel being exhausted.

Drawbacks:

Its manipulation is complicated and it needs a lot of extra-electrical equipments. Moreover its sensitivity depends upon the nature of the gas, the arrangement of its electrodes and the electric circuit employed. Further organic vapours ‘poison’ its filament and reduce the emission of electrons from it. As a necessary precaution a ‘cold trap’ of carbon dioxide snow or acetone, is arranged in between the gauge and the exhausted vessel.

It case an oil diffusion pump is used to exhaust the vessel, some sort of a ‘baffle’ must be used for preventing any oil molecules streaming back into the gauge and thus vitiate it working. At higher pressures, the life of the gauge is shortened due to the bombardment of the filament by the ions as to the possibility of the chemical reaction with the gas around it.

α-Ray Ionisation Gauge:

It this is the latest form of an ionisation gauge in which the ionisation of the gas is brought about by α-particles from a radioactive substance. As no cathode heating is required here it is called a cold cathode ionisation gauge.

The gauge consists of a closed ionisation chamber C, inside an outer protective shell and perforated at its top and bottom to allow free access to the gas inside it. At the bottom of the chamber there is a small saucer-shaped plaque P, 1 cm2 in area, and with its upper surface made of an alloy of gold and radium. This is in equilibrium with its products of decay, viz., radon radium A and radium B. Out of them the first one is a gas.

To prevent any of this gas escaping out, the upper surface of the plaque is electrolytically coated with a layer of nickel. This also serves the additional purpose of preventing contamination by mercury vapour. The losses from the plaque due to radioactive emission are so small that the instrument requires to test only once in a number of years. This plaque forms a highly efficient α-ray emitter, with a slow emanating power.

The grid G consists of four wires spread or strected out. This limits the distance to be covered by the positive ions produced by the ionisation of the gas by the α-particles. This facilitates their ‘capture’ before they have time to cover longer distances. This is because the ions may re-unite and thus the linear relation between the ionisation current and pressure may not remain valid, with the whole basis of the gauge knocked out.

The small ionisation current produced is amplified and noted. The gauge may be used to measure pressures within a wide range from 10-3 mm to 1000 mm and it is a continuous reading one.

One serious drawback of the gauge is the extra-precautions are required to save from the hazards of exposure to the radioactive substance used.

#### 14. The Knudsen Gauge:

It is a very simple but efficient gauge, used to measure the lowest pressures yet produced. At high pressures, a gas behaves like a viscous liquid. Its flow through narrow tubes is followed by Poiseuille’s law, the rate of flow being proportional to the fourth power of the radius of the tube. It is limited by the frequency of intra-molecular collisions.

When the pressure is low, the mean free path of the molecules becomes greater than the radius of the tube. Under these conditions the flow of a gas is very suggestively called molecular flow by Knudsen. The mechanical force exerted between two surfaces, very close to each other and maintained at a difference of temperature, is known as radiometric effect.

Knudsen used the radiometric forces at low pressures in devising his absolute gauge. It enables us to measure pressure in an evacuated vessel, from 10-3 mm down to 10-7 mm, by noting the deflection of a cold plate suspended in the vessel, owing to its bombardment by the molecules rebounding from a nearby hot plate.

If the dimensions of the plates are very large in comparison to the distance between them so that all edge-effects could be ignored and also if this distance be small compared to the mean free path of the molecules the deflecting repulsive force on the cold plate is found to be proportional to the gas pressure in the vessel, right up to a pressure of 10-7 mm.

The essentials of the gauge is shown in Fig. 25.16. Here P1 and P2 are two fixed plates electrically heated and arranged on opposite sides of a cold plate A in the form of a rectangular picture frame, suspended by a quartz fibre carrying a mirror M for enabling its deflection to be measured by lamp and scale arrangement.

Let us assumed that the temperature of P1 and P2 be T1 and that of A be T2. If n1 and n2 be the number of molecules per cubic centimetre travelling from P1 to A and from A to P1, with root mean square velocities c̅1 and c̅2 respectively. Then, the rate of molecular collisions per square centimetre must be the same.

We can write-

Eqn. (25.21) shows that the force exerted on place A is independent of the nature of the gas in the vessel.

Further, if a be the area of each vertical strip of A, then the force acting on each strip = F.a. As these forces act in opposite directions on the two strips, they constitute a couple which is equal to F.a.2r, where r is the mean distance of each strip from the suspension wire.

Thus the frame is deflected, giving rise to a restoring torsional couple in the suspension wire. It comes to rest, when the two couples balance each other. Let then it has deflected through an angle θ. If τ be the torsional couple, set up in the suspension wire per unit twist in it the total torsional couple tending to restore the frame back to its original position θ; and we, therefore, have-

The pressure p of the gas in the vessel, can be evaluated using Eqn. (25.24).

The gauge possesses the following major advantages:

i. It is simple and easy to construct.

ii. It gives a continuous indication of pressure in the vessel.

iii. It does not require the use of objectionable liquids, like mercury.

iv. It is unaffected by any outside influences.

v. It can be used to measure the pressure of all kinds of gases and vapours, irrespective of their mass or condensability.

vi. It is stable and very sensitive of low pressure down to 10-7 mm.