1.4 Fast volume determination using a differential capacitance manometer

1.4 Fast volume determination using a differential capacitance manometer H N o r s t r 6 m , S Berg and L P Andersson, Institute of Physics, University of Uppsala, Uppsala. Sweden

The reliable pressure readings with a capacitance manometer are the basis for a new type of instrument designed for accurate and rapid measurements of capillary volumes. The basic measuring principle is based on expansion of air of atmospheric pressure enclosed in a known volume into a pre-evacuated cylinder so that the enclosed volume will cause a reduced pressure in the cylinder. The same is done with the air in an unknown volume into another identical pre-evacuated cylinder. A differential capacitance manometer is then used to measure the difference in pressure between the two cylinders with a high degree of accuracy. This difference in pressure is shown to be a linear function of the difference in volume between the unknown and the known volume. The accuracy and repeatability of the instrument is better than 0.5%.

1. Introduction

The need of rationalization in precision glass thermometer manufacturing was the original reason for designing this instrument. A glass thermometer contains the bulb with the mercury and capillary tube intended for the thermal expansion of the mercury. A certain bulb filled with mercury in combination with a specific capillary tube will give the desired expansion length difference L0 for a 100°C difference in temperature. The inner diameters of the capillary tubes are known from the glass tube manufacturing company, but deviations of several per cent from predicted values do frequently occur. The glass bulbs, however, are made manually by glass blowing. With this technique it is not possible to achieve better accuracy than - ~ 1 0 ~ in the predetermination of the manufactured bulb volume. It is thus obvious that such a glass bulb, in combination with a standard capillary tube will result in a thermometer with a predicted expansion length not better than -4-10~. Each manufactured thermometer, therefore has to be individually calibrated. Further problems arise when scales are to be attached to the thermometer. The manufacturer has to have a set of some 20 different scales to match the different expansion lengths obtained. If the bulb volume could be determined within 0.5 ~ accuracy, it is possible to combine this bulb with a capillary tube that gives the desired expansion length Lo. The possibility of making such combinations eliminates the individual calibrations in the manufacturing process. 2. Description

At room temperature and atmospheric pressure the air (oxygen and nitrogen) behaves as a perfect gas obeying Boyle's law 1 P0 V0 = Px V1 This is the basic principle of the instrument designed.* The * Swedish pat 741209-9, US pat 618161, German pat 2542838.

Vacuum/volume 27/number 3.

unknown volume (Vx) in a glass bulb contains air of atmospheric Po. This air volume is expanded into a large pre-evacuated cylinder with a volume I/1(1/1 ~ V~,). The pressure in the cylinder will then be

Po

"'

v.

In another branch of the vacuum system a glass bulb containing a known volume Vo of air at atmospheric pressure Po is expanded into another pre-evacuated cylinder with volume I/"2. The pressure in this cylinder will then be

P2

-

eo rh

• Vo

Now a differential capacitance manometer 2 (MKS Baratron 170M-6 instrument supplied with a type 145AH-10 head) is connected between the two cylinders thus indicating the pressure P = PI - P2 This pressure reading P can by electronic compensation be processed into a reading Uz = k(V:, -

Vo)

(appendix)

u2 is then a signal that tells the difference in volume between an unknown volume Fx and a well-known volume Vo. The technique of calibration of the instrument is pointed out in the appendix. A schematic diagram of the mechanical set-up of the system is shown in Figure 1. S1-S8 are electrically regulated valves that can be either closed ('0') or open ('1'). The mechanical pump (Edwards EDM2) has a pumping speed of 2 m 3 h - i and the total internal volume to be evacuated is about 0.5 I. This situation gives a total pumping time less than 1 min. The valves are operated according to Table 1.

Pergamon Press/Printed in Great Britain

99

H Norstr##m. S Berg and L P Andersson: Fast volume determination using a differential capacitance manometer

Voo I

S6 ~

verified that this 'error pressure' is a design parameter depending primarily on the valves (S1 and $2) used. This 'error pressure' also turns out to be constant and can therefore easily be eliminated as shown in the appendix. Further advantage of the differential measuring system is that the instrument is insensitive to the pressure reached (about 0.1 torr) during the 'evacuation' sequence. Non-symmetry of pumping speeds in the two branches of the system can cause a pressure difference of at most 0.005 torr at the end of this sequence. This difference adds a negligible error to the value measured during the 'reading' sequence. The instrument is designed to give a pressure difference of 1 torr between the two branches if the unknown volume deviates 0.35 cm 3 from the known standard volume Vo = 0.70 cm 3. In this pressure region the overall error of the gauge head is better than 0.1 ~o. Figure 2 shows the correlation between measured (with this instrument) volumes Vx in fraction of Vo and the same fraction (V,,/Vo) obtained from the manufactured complete thermometer.

Vxo Vo

Vx

MANOMETER-HEAD

I ~ S5

S8 I::

$7

11 ROTARY PUMP

Vx/Vo

Figure 1. Schematic of the mechanical set-up of the instrument.

1.50

Table 1.

W

3

Sequence

S1

$2

Valve $3 $4

0

$5

$6

$7

$8

~ 1.00 w re

Start Evacuate Read

1 0 1

1 0 1

1 0 0

1 0 0

0 1 1

0 1 1

1 1 0

1 1 0 0.50 I 0.50

The three operating sequences of the instrument are the 'start' sequence in which the unknown glass bulb Vx is attached to the instrument. Vo is constantly fitted to the instrument. The purpose of $3 and $4 is to maintain atmospheric pressure in Vx and Vo in this sequence. Then comes the 'evacuate' sequence in which all the internal volume of the instrument is evacuated to a pressure better than 0.1 torr by the rotary pump. Finally comes the 'read' sequence in which the two volumes Vx and Vo of air are expanded into the instrument and the corresponding pressure difference between the two branches is measured.

,

°

,

i

I

1.00

=

,

,

,

I

1.50

,1_

Vx/Vo/

MEASURED VOLUME

Figure 2. Normalized measured bulb volumes versus normalized real bulb volumes. The normalizing factor being the known standard volume Vo. The correlation is very good. The deviations from perfect correlation have been found to be mainly due to errors in the supplied diameter data of the capillary tubes, which thus at this moment limit the accuracy of predetermination of thermal expansion length of the thermometer.

4. Conclusion 3. Experimental results The actual volumes of the thermometer bulbs measured by this instrument have been in the range of 0.3-1.0 cm 3. To ensure the required accuracy, the instrument must be able to resolve a volume difference of less than 5 mm a. It should be pointed out that the actual volume of air of atmospheric pressure expanded into the instrument is Vx q- Vxo, where V~0 is the internal volume of the valve S1 at atmospheric pressure during the sequence 'evacuate'. The volume Vxo has been measured to be about 0.3 cm 3. The valve $2 has a similar added volume Voo. In the differential pressure sensing technique however, these two volumes almost compensate each other and cause only a small residual 'error pressure'. Experiments have 100

Volume determination using a differential capacitance manometer has proved to be very reliable. The symmetrical design of the two branches in the instrument has reduced the influence of 'extra added volumes' to the measured volume to a minimum since such volumes compensate each other. A further advantage is the independence of variations in the limiting vacuum reached by the mechanical vacuum pump. The instrument was designed to measure the volume of glass thermometer bulbs but it is expected to be used soon in a wide variety of applications.t t The instrument is commercially available under the name 'ITM-761-A Capillary Bulb Measurement Unit' and exported by Qvintus Inc, Box 408, 126 04 H~igersten, Sweden.

H Norstr6m, S Berg and L P Andersson: Fast volume determination using a differential capacitance manometer The d e v e l o p e m e n t o f this i n s t r u m e n t was financially s u p p o r t e d by the Swedish B o a r d o f Technical D e v e l o p m e n t .

The differential capacitance manometer reads the pressure P

(5)

P = P t -- P2 Combination of equation (2), (4) and (5) gives

Appendix Po

eo

= atmospheric pressure

Vx = unknown volume to be measured V~o = internal volume of valve SI at atmospheric pressure during sequence 'evacuate' V1 = extra volume to which Vx and V~o are expanded during sequence 'read' P1 = pressure reached in Vx during sequence 'read' 1/"o = thermometer glass bulb with known internal volume Voo : internal volume of valve $2 at atmospheric pressure during sequence 'evacuate' V2 = extra volume to which Vo and Voo are expanded during sequence 'read' P2 = pressure reached in V2 during sequence 'read' The volumes Vx + V~o of atmospheric pressure Po are expanded into the volume V~. Thus

Po(Vx + Vxo) = P~(Vx + V:,o + V1)

_/V,,o

P='~l'Vx~-l~°[~l

(1)

I,'o Voo] V2

V2]

(6)

Here

e IV~o

Vofi

°tr,

is the earlier mentioned 'error pressure'. Equation (6) shows that P is a linear function of Vx. The measured value P is available from the manometer unit as an analogue voltage u. Thus u=k.

Vx + l

(7)

where k and l are instrument constants. By electronically adding a constant voltage ux

u, = --(kVo + l)

(8)

to u one obtains a value (9)

U2 =

(V~ + Vxo) << Vx is always valid so

The value of ul is easily found by applying a volume Vo in the position of Vx and during the 'read' sequence adjust to zero output signal. Now u2 can be amplified to desired value to obtain full scale reading during sequence 'read' with a glass bulb of known volume 1.50 Voo in position of V~.

P1 = Po -~1 ("Vx -[- Vxo)

(2)

The other branch behaves identically, thus

Po(Vo + Iioo) = P2(Vo + Voo + V2)

t/1 -[- U =

k(V~ -- Vo)

but

(3)

and

References

(Vo + Voo) << V2, so Po P2 = ~ (Vo + Voo)

(4)

x A Roth, Vacuum Technology, North Holland, Amsterdam, 1976. 2 N G Utterback and T Griffith Jr, Rev Sci Instrum, 37, 1966, 866.

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