A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Take the initial P and T of the air (before it is put into the tire) to be 1.00 bar and 298.0K. The final volume of air (after it is in the tire), is 1 L and the final pressure is 5.00 bar. Calculate the final temperature (be sure to state your assumptions).
P initial = 1.00 bar
V initial = ?
T initial = 298K
P final = 5.00 bar
V final = 1 L
T final = ?
moles = ?
Cval dT = P dV
P 1-γ T γ = constant
P internal = P external (since it is reversible)
The Attempt at a Solution
The biggest issue I am having is figuring out the volumes. My professor gave us a hint saying that we can assume constant volume, but what does he mean - I know we can assume the tire volume is constant, but the volume of air used to fill the tire can't be the same as the volume of the tire can it? Is that volume even relevant.
The first equation I derived but if volume is constant like my professor was saying, dV will be zero which ruins that equation. I found the PV=constant online but it seems way too easy. Is this assuming everything else is constant?
I don't care if someone comes out and gives me a direct answer I just need a little guidance. The homework is due Wens so I have a bit of time. Thank you!
There are just a ton of variables unaccounted for that could affected pressure which makes it really confusing to me - temp, moles, volume, etc.