# 1.2.1 Definition of vacuum

Pressure is defined as the ratio of force acting perpendicular and uniformly distributed per unit area.

$p = \frac FA$

 $p$ Pressure [Pa] $F$ Force [N]; 1 N = 1 kg m s-2 $A$ Area [m2]

Formula 1-3: Definition of pressure

In an enclosed vessel the gas particles perform thermal movements. In their interaction with the vessel wall, the atoms and molecules are subjected to a large number of collisions. Each collision exerts a force on the vessel wall. Where an enclosed gas is not exposed to outside influences, the numerous collisions that take place result in the same pressure occurring at any point within the vessel, no matter where and in what direction the measurement is carried out.

Figure 1.2: Definition of total pressure

In practice, it is very rare that only one gas is available. Mixtures of different gases are much more common. Each single component of these gases will exert a specific pressure that can be measured independently of the other components. This pressure exerted by the various components is called partial pressure. In ideal gases, the partial pressures of the various components add up to the total pressure and do not interfere with each other. The sum of all partial pressures equals the total pressure.

Figure 1.3: Definition of partial pressure

An example of a gas mixture is our ambient air. Its partial pressure composition is shown in Table 1.1 [3].

Gas type Chem. Formula Volume % Partial pressure [hPa]
Nitrogen N2 78.09 780.9
Oxygen O2 20.95 209.5
Water vapor H2O < 2.3 < 23.3
Argon Ar 9.3·10 -1 9.3
Carbon dioxide CO2 3.0·10-2 3.0·10-1
Neon Ne 1.8·10 -3 1.8·10-2
Hydrogen H2 < 1·10-3 < 1·10-2
Helium He 5.0·10 -4 5.0·10-3
Methan CH4 2.0·10-4 2.0·10-3
Krypton Kr 1.1·10 -4 1.1·10-3
Carbon monoxide CO < 1.6·10-5 < 1.6·10-4
Xenon Xe 9.0·10 -6 9.0 . 10-5
Nitrous oxide N2O 5.0·10 -6 5.0·10-5
Ammonia NH3 2.6·10-6 2.6·10-5
Ozone O3 2.0·10-6 2.0·10-5
Hydrogen peroxide H2O 2 4.0·10-8 4.0·10-7
Iodine I2 3.5·10-9 3.5·10-8

Table 1.1: Composition of atmospheric air. The partial pressures indicated refer to 1,000 hPa. Note: The value indicated for water vapor is the saturated state at 293 K (20°C). The values for carbon dioxide and carbon monoxide fluctuate depending on the place and time. The indication for carbon monoxide is the peak value for a large city. Other sources refer to a natural hydrogen concentration of 5 · 10-5 % and a partial pressure of 5 · 10-4 hPa.

In space, depending on the proximity to galaxies, pressures of under 10-18 hPa prevail. On Earth, technically generated pressures of less than 10-16 hPa have been reported. The range of atmospheric pressure down to 10-16 hPa covers 19 decimal powers. Specifically adapted types of vacuum generation and measurement for the pressure range result in subdivisions of the various pressure ranges as shown in Table 1.2.

Pressure range Pressure hPa Pressure Pa Number density per cm3 Mean free path in m
Atmospheric pressure 1,013.25 101,325 2.7·1019 6.8·10-8
Low vacuum (LV) 300…1 30,000…100 1019…1016 10-8…10-4
Medium vacuum (MV) 1…10-3 100…10-1 1016 …1013 10-4…10-1
High vacuum (HV) 10-3…10-7 10-1…10-5 1013…109 10-1…103
Ultra-high vacuum (UHV) 10-7…10-12 10-5…10-10 109…104 103…108
Extremely high vacuum (XHV) <10-12 <10-10 <104 >108

Table 1.2: Pressure ranges in vacuum technology

The unit for measuring pressure is the pascal. This unit was named after the French mathematician, physicist, writer and philosopher Blaise Pascal (1623 – 1662). According to Formula 1-3, the SI unit pascal is composed of Pa = N m-2. The units mbar, torr and the units shown in Table 1.3 are common in practical use.

Pa bar hPa µbar Torr micron atm at mm WS psi psf
Pa 1 1·10-5 1·10-2 10 7.5·10-3 7.5 9.87·10-6 1.02·10-5 0.102 1.45·10-4 2.09·10-2
bar 1·105 1 1·103 1·106 750 7.5·105 0.987 1.02 1.02·104 14.5 2.09·103
hPa 100 1·10-3 1 1,000 0.75 750 9.87·10-4 1.02·10-3 10.2 1.45·10-2 2.09
µbar 0.1 1·10-6 1·10-3 1 7.5·10-4 0.75 9.87·10-7 1.02·10-6 1.02·10-2 1.45·10-5 2.09·10-3
Torr 1.33·102 1.33·10-3 1.33 1,330 1 1,000 1.32·10-3 1.36·10-3 13.6 1.93·10-2 2.78
micron 0.133 1.33·10-6 1.33·10-3 1.33 1·10-3 1 1.32·10-6 1.36·10-6 1.36·10-2 1.93·10-5 2.78·10-3
atm 1.01·105 1.013 1,013 1.01·106 760 7.6·105 1 1.03 1.03·104 14.7 2.12·103
at 9.81·104 0.981 981 9.81·105 735.6 7.36·105 0.968 1 1·10-4 14.2 2.04·103
mm WS 9.81 9.81·10-5 9.81·10-2 98.1 7.36·10-2 73.6 9.68·10-5 1·10-4 1 1.42·10-3 0.204
psi 6.89·103 6.89·10-2 68.9 6.89·104 51.71 5.17·104 6.8·10-2 7.02·10-2 702 1 144
psf 47.8 4.78·10-4 0.478 478 0.359 359 4.72·10-4 4.87·10-4 4.87 6.94·10-3 1

Table 1.3: Conversion table for units of pressure