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 bigbear312 Dec 12th 2016 12:11 AM

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

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.

 ChipB Dec 13th 2016 11:09 AM

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 $\displaystyle n_w$.

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