Liquid oxygen expansion in vaccum

[anubodh]

Homework Statement

There are 2 containers.Outside temperatue is -190 degree celsius.(boiling point of liquid oxygen is -180 degree celsius).One is filled with vacuum and can have a minimum height of 6000m and other is filled with liquid oxygen (1140 kg/m3 density) at -190 degree celsius which can have a miximum height of half the height of the other container.Both have 1m x 1m base.I want to know how much liquid oxygen should be put in the vacuum container so that when it occupies the entire vacuum container it is distributed nearly equally at both upper and lower half [and not like that it has more mass at the base and very few at the top].[Inside vacuum container it would form gas as its boiling point woul decrease].
Please reply...
I need this answer for a national level competition..
Thanks

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Even for a national level competition, you must do your own work. Even if the answer won, I doubt you would share the prize with PF.

 

[anubodh]

Its not that answer to this question will get me a prize but it is a difficulty i am facing theoretically.So i want to clarify it before i start working on this project practically.