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## Homework Statement

A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Assume the initial pressure and temperature of the air before it is put in the tire to be Pi = 1.00 bar and Tf 287K . The final pressure in the tire is Pf = 3.75 bar.

Calculate the final temperature of the air in the tire. Assume that CV,m = 5R/2.

## Homework Equations

dU=nC

_{vm}dt

dU=dw...as q=0 adiabaitc

dw=-P

_{ex}dv

using these above equations my notes derive the following

V

_{i}T

_{i}

^{c}=V

_{f}T

_{f}

^{c}where c=Cvm/R

P

_{i}V

_{i}

^{[itex]\gamma[/itex]}=P

_{f}V

_{f}

^{[itex]\gamma[/itex]}where gamma=Cpm/Cvm

## The Attempt at a Solution

I am really stuck on where to even start this problem. It seems as if i am missing info, that i need a number of moles or a volume or something. I cant seem to find a way to rearange any of the above. In other problems it boiled down to using the boring old ideal gas pv=nrt to solve for one variable but again this leaves me with 2 unknows so im not sure what to do.

Any tips, hints, explanations anything would be a great help!

^{[itex]\gamma[/itex]}

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