APPENDIX
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5. APPENDIX
5.1. Principles of Operation
When a cold gas molecule collides with a high temperature solid, it receives energy from the solid, is
heated and flies away, collides with a low temperature portion and returns to the original state. The
high temperature portion loses energy for the energy the cold gas molecule has obtained. This is the
mechanism of thermal conduction of gas and is called transport phenomenon of energy by gas
molecule.
In a pressure region (molecular flow region) in which collision of gas molecules is small, the amount
of energy carried by gas is proportional to the frequency of gas molecules colliding with the high
temperature portion. Thus it is also proportional to pressure.
Pressure can be measured by utilizing this principle.
Here, the following relationship holds between T and To [K] and the energy Q [J] carried away by
filament per unit area in unit time, given that T is the temperature of the sensor head filament and To
[K] is the temperature of the vessel wall.
Q = αΛ (T – To) P ................... (1)
In this equation, A is a coefficient referred to as free molecule thermal conductivity [m
3
·K
-1
] and its
value varies with the type of gas. "α" is a coefficient that corrects the imperfectness of exchange of
amount of energy at the time of collision of gas molecules and is referred to as an accommodation
coefficient, which is defined as follows.
α =
............................. (2)
where, T is the filament temperature, To is the temperature of gas molecule before collision and Tg is
the temperature of gas molecule after collision. If the exchange of energy on the filament surface is
perfect, α = 1.
The value α has complex properties that change with geometrical roughness, presence or absence of
adsorption layer, heat history, type of gas, temperature and others and is not yet fully explored. The
value α directly affects the accuracy and stability of the vacuum gauge.
The constant temperature type Pirani gauge supplies the energy lost by collision of gas molecules from
the heated filament and maintains the filament temperature constant all the time. The ULVAC Pirani
gauge is this type of gauge.
This type of gauge is less susceptible to change of α and more advantageous over other types of Pirani
vacuum gauges in terms of small change in α, stability and responsibility.
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