# McLeod Vacuum gauge Theory

McLeod vacuum gauge

The main parts of McLeod gauge are as follows:

A reference column with reference capillary tube. The reference capillary tube has a point called zero reference point. This reference column is connected to a bulb and measuring capillary and the place of connection of the bulb with reference column is called as cut off point. (It is called the cut off point, since if the mercury level is raised above this point, it will cut off the entry of the applied pressure to the bulb and measuring capillary. Below the reference column and the bulb, there is a mercury reservoir operated by a piston.

Operation of McLeod Vacuum gauge:

The McLeod gauge is operated as follows:

The pressure to be measured (P1) is applied to the top of the reference column of the McLeod Gauge as shown in diagram. The mercury level in the gauge is raised by operating the piston to fill the volume as shown by the dark shade in the diagram. When this is the case (condition – 1), the applied pressure fills the bulb and the capillary.

Now again the piston is operated so that the mercury level in the gauge increases.

When the mercury level reaches the cutoff point, a known volume of gas (V1) is trapped in the bulb and measuring capillary tube. The mercury level is further raised by operating the piston so the trapped gas in the bulb and measuring capillary tube are compressed. This is done until the mercury level reaches the “Zero reference Point” marked on the reference capillary (condition – 2).

In this condition, the volume of the gas in the measuring capillary tube is read directly by a scale besides it. That is, the difference in height ‘H’ of the measuring capillary and the reference capillary becomes a measure of the volume (V2) and pressure (P2) of the trapped gas.

Now as V1,V2 and P2 are known, the applied pressure P1 can be calculated using Boyle’s Law given by;

P1V1 = P2V2

Let the volume of the bulb from the cutoff point upto the beginning of the measuring capillary tube = V

Let area of cross – section of the measuring capillary tube = a
Let height of measuring capillary tube = hc.

Therefore,

Initial Volume of gas entrapped in the bulb plus measuring capillary tube = V1 = V+ahc.

When the mercury has been forced upwards to reach the zero reference point in the reference capillary, the final volume of the gas = V2 +ah.

Where, h = height of the compressed gas in the measuring capillary tube
P1 = Applied pressure of the gas unknown.
P2 = Pressure of gas at final condition, that is, after compression
= P1+h

We have, P1V1 = P2V2 (Boyle’s Law)
Therefore, P1V1= (P1+h)ah

P1V1 = P1ah + ah^2

P1V1-P1ah = ah^2

P1 = ah^2/(V1-ah)

Since ah is very small when compared to V1, it can be neglected.

Therefore, P1 = ah^2/V1

Thus the applied pressure is calculated using the McLeod Gauge.

1 Like