An ideal gas undergoes a single-stage expansion against a constant external pressure P _external = P_f at constant temperature from T,P_i ,V_i , to T,P_f ,V_f . 

a. What is the largest mass m that can be lifted through the height h in this expansion?

b. The system is restored to its initial state in a single-state compression. What is the smallest mass m′ that must fall through the height h to restore the system to its initial state?

c. If h = 15.5 cm, P_i = 1.75 × 10⁶ Pa, P_f = 1.25 × 10⁶ Pa, T = 280.K, and n = 2.25 mol, calculate the values of the masses in parts (a) and (b).