Pressurized gas container gets opened

[dkeating]

Homework Statement

I have an empty 2-Liter bottle. It contains 3 g of air inside with an initial air pressure of 1105 mb. When I open it (which is an adiabatic process), I release the pressure which is instantaneous. The pressure then becomes standard atmospheric pressure. What is the temperature change associated with
this?

Homework Equations

W = ∫pdV | dU = Q - W | du + pdV = dQ | dQ = c_pΔU = -W^ad

The Attempt at a Solution

To be honest, I really don't know where to begin. My attempts have only led me to equations that have 2 unknowns.
I had two basic trains of thought: We assume that opening the 2 liter bottle leads to a new volume of air that expands out into the environment. In which case, I don't know the final volume OR the final temperature.
My other train of thought was: We assume that the 2 liter bottle is a system and that 2 liter volume doesn't change. In which case the integral of work comes out as zero (as we are supposed to integrate from final to initial volume) and I don't know how to proceed with that either.
Any insight would help, this has been stumping me for a day and a half!

 

[Chestermiller]

Is that 1105 mb milli-bars or mega bars?

When you ask, "what is the temperature change," do you mean the temperature of the air remaining in the bottle after the system has equilibrated? The temperature of the air that has escaped and mixed with the room air? The room air temperature?

Is the bottle insulated?

Does the air flow through a valve, or is it flowing through an unblocked 2 liter bottle opening?