# Predicting pressure inside a container based on temperature

I'm a mathematician and computer scientist, and for this particular problem I would benefit from some chemical expertise.

Suppose I fill a container up with some liquid propane. I believe this is done under very cold conditions so that the propane remains liquid while the container is being filled. It is then sealed off. Suppose now the inside of the container changes temperature. I would like to calculate the pressure that would be exerted on the walls of the container at any given internal temperature $$T$$.

Intuitively, I would think that the pressure would be a function of temperature and some initial conditions (how full is the tank initially)? If I filled up the tank to 95% capacity with liquid propane, and then heated the tank, I would expect the resulting pressure on the walls of the container to be much higher than if I filled up the tank to only 1% capacity and did the same thing.

However, the only resources I've been able to find so far relate to the vapour pressure, which is a function of only temperature and this seems incomplete.

Can anybody point me in the right direction on how to approach this problem? Some factors that seem to complicate things are:

• The containers always seem to contain some level of liquid (due to internal pressure?), the rest is gas. Does the liquid have an effect on the pressure exerted on the walls? Can I just ignore it?
• If, rather than fill up the tank with liquid at very cold temperatures, the tank is just directly filled with gas, how does this change things? My guess is that given the initial pressure and temperature you can predict the pressure at a different temperature, but I think the fact that some of the gas becomes liquid at some point is tripping me up and I'm not sure how to approach the problem.
• When your tank is 95% full, is the space above the liquid containing air? – William R. Ebenezer May 7 '19 at 10:33
• As the tank is not full then there is always some vapour in equilibrium with the liquid and so you will need to find the saturated vapour pressure vs temperature. If all the liquid evaporated (say if 1% full) then it will behave as a gas and then pressure is proportional to temperature say via the ideal or van der waals gas laws. – porphyrin May 7 '19 at 10:37
• @porphyrin , for the first case, the liquid would also contribute $\rho gh$ pressure on walls. – William R. Ebenezer May 7 '19 at 10:40
• @William E Ebenezer, yes I has assumed that that was small enough to ignore. – porphyrin May 7 '19 at 10:42
• Equations of State - of which the ideal gas law is the simplest, relate pressure, temperature and density to one another – Charlie Crown May 7 '19 at 12:18