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*Thermodynamics*: Adding air to a bottle, finding internal energy and so on

  1. Oct 25, 2012 #1
    1. The problem statement, all variables and given/known data
    In class we saw a demo where a pop bottle was pumped up with extra
    air. If we consider the bottle was pumped up to a gauge pressure of 50 psi and let sit until
    it returns to room temperature. Describe what happens when the air is rapidly released (for
    example if the top suddenly popped off ). Treat this as a change in the volume the gas occupies
    not as a change in the number of moles of gas in the bottle.
    (a) What kind of process is this? Sketch a PV diagram.
    (b) Is there a change in internal energy, and if so, what sign does it have?
    (c) Calculate the temperature of the gas when all the excess pressure is released (i.e. the gas
    returns to atmospheric pressure).
    (d) How much work was done, heat transferred and change in internal energy of the gas that
    was contained in the bottle?
    (e) If instead there had been a slow leak in the cap, what would the change in internal energy
    have been? Add a dashed line to your PV diagram to represent this process.

    Volume of the bottle is 2L
    Pi=gauge pressure of 50psi=516630Pa
    Pf=1psi=101300
    T1=293K
    n=constant
    R=8.3145J/mol*K
    2. Relevant equations
    PV=nRT
    ΔU=nCvΔT
    ΔQ=ΔU+ΔW
    ΔW=PΔV
    3. The attempt at a solution
    a) I think the first process is isochoric (vertical line) because the volume of the bottle stays the same and there is air being pumped into it (causing pressure to skyrocket) I don't know how to show that they let it cool to room temperature and what happens when pressure is released. What I don't get is when they say treat this as a change in volume when the lid comes off. (Is volume continuously expanding????)
    b) internal energy is positive because all energy added as heat remains in the system. (kinda unsure about this)
    c)
    I can find the number of moles in this system which is (516630*0.002)/(8.311451*293)=0.42mol
    After that I don't know what to do
    d) Can't figure out c so I didn't think I could figure out this one
    e)Because there is a leak volume increase and pressure decrease (it will be a curve on the graph right?)

    My main problem is the part where the lid comes off and what volume it becomes and how to treat this when I am doing my calculations.

    Any nudge in the right direction would be awesome!
     
  2. jcsd
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