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.
dU=dw...as q=0 adiabaitc
using these above equations my notes derive the following
ViTic=VfTfc where c=Cvm/R
PiVi[itex]\gamma[/itex]=PfVf[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!