Finding Final temp for Adiabatic process

speny83

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=nCvmdt
dw=-Pexdv
using these above equations my notes derive the following
ViTic=VfTfc where c=Cvm/R
PiVi$\gamma$=PfVf$\gamma$ 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!

$\gamma$

Last edited:

speny83
can i say that So im thinking can i say that
(Tf/Ti)^c=Vi/Vf and (Pf/Vf)^(1/gamma)=ViVf

so that (Tf/Ti)^c=(Pf/Vf)^(1/gamma)

is this legit?

Mentor
can i say that So im thinking can i say that
(Tf/Ti)^c=Vi/Vf and (Pf/Vf)^(1/gamma)=ViVf

so that (Tf/Ti)^c=(Pf/Vf)^(1/gamma)

is this legit?
You have a couple of typos in there. Rewrite it more carefully.

Homework Helper

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=nCvmdt
dw=-Pexdv
using these above equations my notes derive the following
ViTic=VfTfc where c=Cvm/R
PiVi$\gamma$=PfVf$\gamma$ 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!

$\gamma$
Try expressing the adiabatic condition in terms of T and P. Think of the air in the tire at the end as a compression of a much greater volume of air at atmospheric pressure into the final volume of the tire.

AM