Energy pumped into a water rocket? (soda bottle rocket)

[Head_Unit]

Homework Statement

So you're shooting off a water rocket, which has some water inside a 2L soda pop bottle. You're then pumping (for example, a bicycle pump) to compress more and more air inside to a higher pressure.

Homework Equations

Well, work = F*d. If you measure the stroke of the pump, and the force (ha ha, we pictured putting a bathroom scale on top of the pump handle), you could calculate that work. But you miss losses and heating through the system.

I'd prefer to think about the pressure in the bottle. From Boyle or Charles or one of those fellows, we can say P1/T1=P2/T2. If you have ambient temp and pressure, you could somehow measure or calculate the "under pressure" temperature.*

Temperature relates to energy (kinetic), and you can calculate the volume of the bottle.

So how can we calculate the new "under pressure" energy in the system??

The Attempt at a Solution

Ha, not much so far, that's why we need help. Can we calculate the moles and thus the number of molecules in the volume of the bottle, then multiply by delta temperature?

?



*ideas as to HOW welcome. So far we just pictured painting one side of the bottle black and using an infrared thermometer to read the temp.

 

[Head_Unit]

bump-no takers? Too much like Chemistry? Even WAG welcome...