# In a liquid-in-glass thermometer, how does the gas pressure over the liquid affect the linearity of measurement?

In a common ethanol thermometer, the space above the alcohol column is filled with nitrogen. It also contains varying amounts of the alcohol in the gas phase.

At high temperatures, the gas phase volume decreases because the liquid expands. As a consequence, the pressure rises (lower volume, higher temperature, more ethanol in the gas phase because of the increased vapor pressure). Does this pressure increase contribute to the non-linearity of the measurement, i.e. position of the meniscus vs. temperature?

Even without a possible pressure effect, the rise of the liquid is non-linear with temperature because of the non-linear expansion coefficient of ethanol. I am wondering whether the pressure effect significantly contributes to the non-linearity. I am also wondering whether the expansion chamber (at the tip of the thermometer) helps to prevent excessively high pressures.

• Considering high values of Young modulus for liquids, I doubt there would be significant compression effect. Oct 25, 2022 at 8:50
• @Poutnik I just saw the claim that liquids don't have a Young modulus because they are isotropic. They do have different compressibility, and this is much lower than that of a gas.
– Karsten
Nov 1, 2022 at 18:51
• You are right. Ethanol has the bulk modulus 1.06 GPa and thermal expansion 750 ppm/K, what make 1 K temperature difference equivalent about 8 atm of pressure difference. Nov 1, 2022 at 21:48
• Here is a bit on how thermometers are built, filled, and given a scale: madehow.com/Volume-1/Thermometer.html, and a historic movie showing manufacturing of mercury thermometers.
– Karsten
Nov 1, 2022 at 22:02

[OP] Does this pressure increase contribute to the non-linearity of the measurement, i.e. position of the meniscus vs. temperature?

The main non-linearity is due to non-linear expansion of the body of the thermometer, and of the liquid in the thermometer (both expand with temperature, but the liquid expands more, leading to the rise of the liquid column). The graduations on a thermometer are equidistant, and the inside is built to have constant cross-sectional area. Therefor, you expect a non-linear response. This effect is smallest for a small temperature range, and largest for a large temperature range. If you look at the specifications of ASTM-certified thermometers, the temperature is supposed to be accurate to 0.01 °C for the smallest range thermometers (e.g. 18.9 to 25.1 °C, ASTM type 116C), up to 1 °C for the largest range thermometers (e.g. −6 to +400°C , ASTM type 11C).

Two other factors influencing the accuracy of the reading are the type of liquid (mercury, while highly toxic, has the advantage of not wetting the glass) and whether the thermometer is total immersion (more accurate) or not (less accurate because the temperature of the liquid above immersion depends on the ambient temperature).

So what about the gas pressure above the column? According to ASTM document E1-14,

[ASTM:] An expansion chamber is provided for relief of gas pressure to avoid distortion of the bulb at higher temperatures.

So the pressure is indeed a potential problem, but it affects the shape of the bulb (i.e. bends the glass) more than the volume of the liquid.