Chapter 2, Problem 2.29NP

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 ${\text{P}}_{\text{i}}=\text{1}.\text{00 bar}$ and ${\text{T}}_{\text{i}}=\text{28}0.\text{ K}$ The final pressure in the tire is ${\text{P}}_{\text{f}}=\text{3}.\text{75 bar}$. Calculate the final temperature of the air in the tire. Assume that $C_{v,m}=5R/2$.