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

1. Oct 25, 2012

### jolierouge

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????)
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!