Gas thermometer

A gas thermometer. The hose leads to a pressure gauge .

The gas thermometer is an expansion thermometer in which the state variable observed is the volume of an ideal gas . The temperature measurement is based on the measurement of the pressure .

Since there is a linear relationship between the change in volume and the temperature for an ideal gas , a two-point calibration and the use of a correspondingly divided linear scale can be carried out.

With a gas thermometer, as can be seen in the picture on the right, calibration is usually carried out with ice water as well as with boiling water . The melting point of ice is 0 ° C under normal conditions, while the boiling point of water depends very much on the air pressure. First, the air pressure is measured and the corresponding boiling point of water is determined. The internal pressure of the gas thermometer is then measured once in ice water and once in boiling water. The expansion coefficient of the gas in the thermometer vessel then results from the pressure difference : ${\displaystyle \alpha _{p}}$

${\displaystyle \alpha _{p}={\frac {1}{\vartheta _{s}}}{\frac {p_{s}-p_{0}}{p_{0}}}\left(1-k_{c}\right)}$

Here, the boiling point of water, the pressure in the thermometer bulb into ice water and the pressure in the thermometer bulb in boiling water. This is a correction term that is necessary to take into account the thermal expansion of the thermometer vessel: ${\displaystyle \vartheta _{s}}$ ${\displaystyle p_{0}}$ ${\displaystyle p_{s}}$ ${\displaystyle k_{c}}$

${\displaystyle k_{c}={\frac {\vartheta _{s}p_{s}}{p_{s}-p_{0}}}\left(3\alpha _{l}{\frac {\Delta V}{V_{0}}}{\frac {1}{T_{1}}}\right)}$

${\displaystyle \alpha _{l}}$is the coefficient of linear expansion of the thermometer vessel and the ratio of the volume of the capillary tube plus the hose to the manometer and the volume of the vessel. This is important because the vessel is being cooled or heated while the tubes and tubing usually remain at ambient temperature. is the ambient temperature in Kelvin . ${\displaystyle {\frac {\Delta V}{V_{0}}}}$ ${\displaystyle T_{1}}$

If the expansion coefficient of the gas in the thermometer vessel is known, the following applies to the measured temperature depending on the pressure:

${\displaystyle \vartheta ={\frac {p-p_{0}}{p_{0}\alpha _{p}}}}$

Either the pressure or the volume must be kept constant during the measurement. The range of application of a gas thermometer is between −200 ° C and +800 ° C. However, there are also applications down to −273.15 ° C.

Web links

• ChemgaPedia: Exact temperature determination : A flash animation clearly explains the individual steps of temperature determination with a gas thermometer. (German)