A nearly flat tire becomes noticeable warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression of an ideal gas. Assume the initial pressure and temperature of...

A nearly flat tire becomes noticeable warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression of an ideal gas. Assume the initial pressure and temperature of the air before it is put in the tire to be p_i
= 1 atm and T_i
= 25ºC and that C_V,m
= 3R/2. The final volume of the air in the tire is V_f
= 2.00 L and the final pressure p_f
= 90 psi.

Calculate the final temperature of the air in the tire (1 psi = 0.068046 atm, psi = pound per square inch).

Also, calculate ∆U and ∆S during this process.