A U-tube manometer is closed on the left end and open to the atmosphere on the right end, where P,atm = 10^5 Pa. The manometer is filled with mercury with density = 13546 kg/m^3. Initially the difference in the height of the two legs is 15 cm (higher on the open end). Trapped in the closed left end is a column of air with R = 287 J/kg*K, c,v = 716 J/kg*K, and initial height/length = 15 cm. The cross-sectional area of the circular glass tube is A = 2 cm^2. A volume of mercury equal to 40 cm^3 is then added very slowly to the open end of the tube. The trapped air is always in thermal equilibrium with the environment whose temperature is T,atm = 300 K.
Determine P2, V2, and T2 for the trapped air in the final equilibrium state, the work and heat transfer experienced by the air, and the final difference in height of the two legs of the manometer.