Pressure - temperature relationship in constant volume with high temperature and density

Question

For the coating, it is necessary to pour 40 ml of liquid in a closed container with a volume of 80 ml and place it in an oven at a temperature of 200-300 °C .My question is whether, given the high temperature and low volume and high gas density, the pressure to temperature ratio at a constant volume is the same as the ideal gas ratio .If not, what is the relationship between them at high temperatures? thank you very much

Answer 1

The ideal gas law is $PV=nRT$, and the ratio of pressure to temperature is seen to be

$\frac{P}{T}=\frac{nR}{V}$

For an ideal gas only (i.e., no liquid) in a constant volume container, the right hand side of the above equation is seen to be composed entirely of constants, so the ratio of $\frac{P}{T}$ is in fact constant under conditions of varying temperature and pressure. However, your container initially has 40 ml of water in an 80 ml container. As the temperature of the water increases, the vapor pressure of the water increases, so some liquid water evaporates and enters the vapor space of the container, increasing the pressure in the container according to the Antoine equation (see https://en.wikipedia.org/wiki/Antoine_equation). Thus, the number of moles in the vapor space, variable $n$, varies with temperature, so the right hand side of the "P/T" equation is not constant, and hence, the ratio of "P/T" is not constant in this case as temperature increases.

To find the relationship of pressure to temperature, you need to obtain Antoine constants in the temperature range that you are operating. At a given temperature, you can calculate the vapor pressure of water to obtain the pressure in your container is only water vapor is present. If air is also present, it will follow the ideal gas law and add to the pressure that you calculated from the Antoine equation alone.