How do I determine the amount of water in a sealed container to create a given pressu

Dec 2016
1
0
I have a sealed container with a volume of 1 liter. I want to go from an initial pressure of p1=1 atm and an initial temperature of T1=298 to a final pressure of p2=10 atm and a final temperature of T2=453 K.

I want to to use water to create the pressure. But I do not know how to determine the amount of water, how would I do that?

Thanks.
 
Last edited:

ChipB

PHF Helper
Jun 2010
2,361
289
Morristown, NJ USA
You can set up two equations in two unknowns:

1. For the initial condition you have gaseous air plus liquid water in the container. The number of moles of air from the Ideal Gas law is:

\(\displaystyle n_{a} = \frac {P_1 V_{a}}{RT_1} \)

where \(\displaystyle n_a\) is the number of moles of air and \(\displaystyle V_{a}\) is the volume of air in the container. The volume of water at this stage is then

\(\displaystyle V_{w} = V - \rho_{w} n_w \)

where V = size of the container or 1 liter and \(\displaystyle \rho_w\) is the density of water in terms of liter/mole.

Combining these two equations:

\(\displaystyle n_a = \frac {P_1(V-\rho_w n_w)}{R T_1} \)

2. The second equation is at the higher temperature, when the water has turned to gaseous steam. From the Ideal Gas law:

\(\displaystyle n_a + n_w = \frac {P_2 V}{R T_2} \)

So now you have two equation with unknowns \(\displaystyle n_a \) and \(\displaystyle n_w\).