a) An automobile tire contains air with initial pressure (P) at 3.2×105 Pa and initial temperature (T) at 20 °C. The stem valve is removed and the air is allowed to expand adiabatically against the constant external pressure (Pex) of 1.0x105 Pa until the final pressure of the system, P; = Pex. For air, Cy.m = 5/2 R. Cy.m denotes molar heat capacity at constant volume. Assume ideal gas behavior. i) Estimate the heat change (q) (in unit J). ii) Express the relationship of internal energy (AU) (in unit J) and Cv,m. iii) Calculate the final temperature (Tr) (in unit K) of the gas in the tire.

a) An automobile tire contains air with initial pressure (P) at 3.2×105 Pa and initial temperature (T) at 20 °C. The stem valve is removed and the air is allowed to expand adiabatically against the constant external pressure (Pex) of 1.0x105 Pa until the final pressure of the system, P; = Pex. For air, Cy.m = 5/2 R. Cy.m denotes molar heat capacity at constant volume. Assume ideal gas behavior. i) Estimate the heat change (q) (in unit J). ii) Express the relationship of internal energy (AU) (in unit J) and Cv,m. iii) Calculate the final temperature (Tr) (in unit K) of the gas in the tire.