A Pirani vacuum gauge utilizes the thermal conductivity of gases at pressures p of less than 1 mbar. Wire (usually tungsten) that is tensioned concentrically within a tube is electrically heated to a constant temperature between 110 °C und 130 °C by passing a current through the wire. The surrounding gas dissipates the heat to the wall of the tube. In the molecular flow range, the thermal transfer is the molecular number density and is thus proportional to pressure. If the temperature of the wire is kept constant, its heat output will be a function of pressure. However it will not be a linear function of pressure, as thermal conductivity via the suspension of the wire and thermal radiation will also influence the heat output.
The limiting effects are:
Thermal conductivity will not be a function of pressure in the range of 1 mbar to atmospheric pressure (laminar flow range)
The thermal conductivity of the gas will be low relative to the thermal transfer over the wire ends at pressures below 10-4 mbar, and will thus no longer influence the heat output of the wire. Consequently, the measurement limit is approximately at 10-4 mbar
Thermal radiation will also transfer a portion of the heat output to the wall of the tube