1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Basic pressure change over time

  1. Feb 25, 2015 #1
    Im tryng to solve an equation for how pressure changes over time in a container. It goes something like this

    There is a 10 liter sealed container(V1) with x amount of initial pressure (P1), and a 1 liter container attached to it (V2) with one valve that opens between them, and then another valve that opens to atmosphere. The initial pressure in the 1 liter attachment is atmospheric (P2).

    For each cycle the valve opens between the pressureised 10 liter container and the one liter at 1 atm, the pressure then equalizes in both containers. Then the inner valve is closed and the outer valve is opened on the 1 liter container and pressure is vented to atmosphere (so the 1 liter container returns to 1atm) then the outside valve is closed and the cycle continues.

    I need to find out after how many cycles does the large 10 liter container reach a certain pressure above 1 atm...

    I can figure out what the pressure is in the container after they equalize each time which is
    P= (P1*V1 +P2*V2)/(V1+V2)

    So lets say the initial pressure is of P1 is 2atm after the first cycle the pressure would be P = (2*10l +1l*1atm)/(1l+10l) = 1.91 atm

    then the second cycle would be P = (1.91*10l +1l*1atm)/(1l+10l) = 1.83 atm

    etc etc

    so what would be the equation t describe this pressure drop over a certain number of cycles? i.e. P(c) = ?
    Last edited: Feb 25, 2015
  2. jcsd
  3. Feb 25, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Now try it.
  4. Feb 26, 2015 #3


    User Avatar
    Gold Member

    I'll have to accept your physics, because I don't know how to do that, but juggling your equation round and using V1, V2, and P2 as constants, I get a formula for Pn after n cycles, as

    ( (Pn ) -1 ) = ## (\frac {10}{11})^n ## ((P0) -1 )

    Edit - added excess brackets just to make clear
    Last edited: Feb 26, 2015
  5. Feb 26, 2015 #4


    User Avatar
    Gold Member

    Or in a more general form

    ( Pn - Px ) = ( P0 - Px ) ##( \frac{V1}{V1 + V2})^n##

    Where Px is the sink pressure, P0 is the container starting pressure and Pn is the container pressure after n cycles.

    Edit - BTW this looks so nice to me, that I think your physics must be correct!
    Edit2 - and it looks as if you could start with container pressure below atmospheric as well.
    Last edited: Feb 26, 2015
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Basic pressure change over time