Vacuum Technology Know How - Triumf

Pfeiffer Vacuum
Formula 1-4
General gas equation
Page 12
Formula 1-5
Gas pressure
Formula 1-6
Probable velocity
Formula 1-7
Mean velocity
Vacuum Technology
1.2.2 General gas equation
The following applies for gases: A volume of 22.414 liters (mol volume) at a temperature of
273.15 K (standard temperature = 0 °C) and a pressure of 101,325 pa (standard pressure)
contains 6.02 times 1023 particles (Avogadro‘s number). The mass of the gas thus enclosed
is its molecular weight in grams.
The general gas equation describes the state of a gas as a function of pressure,
temperature and volume.
Thus:
Where:
p = pressure [Pa; N / m²]
V = volume [m³]
m = mass [kg]
M = molar mass [kg / kmol]
R = general gas constant R = 8.314510 kJ / (kmol K)
T = thermodynamic temperature [K]
n = molecular number density [1 / m³]
k = Boltzmann’s constant k = 1.380 . 10 - 23 J / K
1.2.3 Molecular number density
As can be seen from Formula 1-4 and Formula 1-5 pressure is proportional to molecular number
density. Due to the high number of molecules per unit of volume at standard conditions,
it follows that at a pressure of 10 -12 mbar, for example, 26,500 molecules per cm3 will still be
present. This is why it is not possible to speak of a void, or nothingness, even under ultra
high vacuum.
1.2.4 Thermal molecular velocity
Gas molecules in a vessel move back and forth in different directions and at different speeds.
Their velocity distribution corresponds to a bell curve having its peak at the most probable
velocity
The mean thermal velocity is
m
p . V = . R . T = n . V . k . T
M
c w =
c – =
p = n . k . T
2 . R . T
M
8 . R . T
p . M
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