# Oxygen Sensors Working Principles

The working principle of the zirconium dioxide O2 sensor measures the partial pressure of oxygen gas in a mixture of gases. Generally, this confuses SST’s customers as most oxygen sensors available on the market measure oxygen concentration.

However, what is partial pressure? It is a question SST is asked often where O2 sensor working principle is concerned. This article addresses the definition of partial pressure, the physics behind it, how to measure partial pressure, and how to convert the partial pressure of oxygen into volumetric content for users in oxygen concentration.

## Partial Pressure: The Definition

By definition, the partial pressure is the pressure of a single gas component in a mixture of gases. It corresponds to the total pressure which would be exerted by the single gas component if it alone occupied the entire volume.

## Daltons Law: The Physics

The details of the theory of the O2 sensor working principle are given here. The sum of the partial pressures (Pi) of the individual gases in a mixture of ideal gases is equal to the total pressure (Ptotal) of that mixture.

It can be derived from Equation 1 that the ratio of the number of particles (ni) of an individual gas component to the total number of particles (ntotal) of the gas mixture equals the ratio of the partial pressure (Pi) of the individual gas component to the total pressure (Ptotal) of the gas mixture.

. .
ni Number of particles in gas i
ntotal Total number of particles
pi Partial pressure of gas i
Ptotal Total pressure

Figure 1. Ptotal = P1 + P2 + P3 (Constant Volume & Temperature).

## Example 1

The atmospheric pressure at sea level (under standard atmospheric conditions) is 1013.25 mbar. At this point, the major components of dry air are oxygen (20.95% Vol.), nitrogen (78.08% Vol.), carbon dioxide (0.040% Vol.) and argon (0.93% Vol.). Since the above gases can be approximated as ideal gases, the volumetric content (%) can be equated to the number of particles (n).

On solving Equation 2 for the partial pressure of an individual gas (i), one gets:

The oxygen partial pressure then equates to:

Figure 2. Partial Pressure at 0% Humidity.

Obviously, this value is only applicable to dry atmosphere (0% humidity). In case there is moisture, the water vapor pressure takes up a proportion of the total pressure. Hence, the partial oxygen pressure (ppO2) can be calculated with more accuracy when ambient temperature and relative humidity are measured together with the total barometric pressure.

Figure 3. Liquid Vapor Pressure.

Firstly, water vapor pressure is calculated:

. .
WVP Water Vapor Pressure (mbar)
HRel Relative Humidity (%)
WVPmax Maximum Water Vapor Pressure (mbar)

Temperature (°C) Max water vapor pressure (mbar) Temperature (°C) Max water vapor pressure (mbar)
0 6.10 31 44.92
1 6.57 32 47.54
2 7.06 33 50.30
3 7.58 34 53.19
4 8.13 35 56.23
5 8.72 36 59.42
6 9.35 37 62.76
7 10.01 38 66.27
8 10.72 39 69.93
9 11.47 40 73.77
10 12.27 42.5 84.19
11 13.12 45 95.85
12 14.02 47.5 108.86
13 14.97 50 123.38
14 15.98 52.5 139.50
15 17.04 55 157.42
16 18.17 57.5 177.25
17 19.37 60 199.17
18 20.63 62.5 223.36
19 21.96 65 250.01
20 23.37 67.5 279.31
21 24.86 70 311.48
22 26.43 75 385.21
23 28.11 80 473.30
24 29.82 85 577.69
25 31.66 90 700.73
26 33.60 95 844.98
27 35.64 100 1013.17
28 37.78 110 1433.61
29 40.04 120 1988.84
30 42.42 130 2709.58

The maximum water vapor pressure is also called the dewpoint. As warmer air can hold more water vapor, it has a higher WVPmax.

Partial oxygen pressure then equates to:

. .
ppO2 Partial Pressure O2 (mbar)
BP Barometric Pressure (mbar)
WVP Water Vapor Pressure (mbar)

## Example 2

Example 2 below shows the effect of humidity reducing the partial oxygen pressure and thus the volumetric content of oxygen.

On a usual day, the following information is recorded from a calibrated weather station:

. .
Temperature: 22 °C
Humidity: 32%
Barometric Pressure: 986 mbar

Using the Water Vapor Pressure look up table above, WVPMAX = 26.43 mbar.

Partial oxygen pressure then equates to:

Since the oxygen partial pressure and the total barometric pressure are known, the volumetric content of oxygen can be calculated.

This information has been sourced, reviewed and adapted from materials provided by SST Sensing Ltd.

For more information on this source, please visit SST Sensing Ltd.

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