By conducting a comprehensive analysis on energy balance in the tank, determine an equation for the final temperature (TF), in terms of temperature and mass of air in compartment A (TA and mA), and temperature and mass of air in compartment B (TB and mB). (ii) Using the equation obtained in (i) and the ideal gas equation, calculate the final temperature (TF) and final pressure (PF). (iii) Compute the total boundary work, Wb done by the air inside the tank. Describe the nature of total boundary work obtained.
A 14 m3 adiabatic closed rigid tank is separated into two compartments by a membrane, as shown in Figure Q2(a). The volume size of compartment A is 2.5 times bigger than compartment B. Compartment A contains air at 435 kPa and 325°C, while compartment B contains air at 135 kPa and 68°C. The membrane then ruptures, where air from compartments A and B are allowed to mix and fill up the entire tank until the thermal equilibrium is established, at final temperature, TF, and final pressure, PF. Neglect kinetic and potential energies. Take cv = 0.718 kJ/kg.K for both compartments, and R = 0.287 kJ/kg.K.
(i) By conducting a comprehensive analysis on energy balance in the tank, determine an equation for the final temperature (TF), in terms of temperature and mass of air in compartment A (TA and mA), and temperature and mass of air in compartment B (TB and mB).
(ii) Using the equation obtained in (i) and the ideal gas equation, calculate the final temperature (TF) and final pressure (PF).
(iii) Compute the total boundary work, Wb done by the air inside the tank. Describe the nature of total boundary work obtained.
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