(Solved): 3. (35%) The rigid tank below, with volume 0.4m3, contains air initially at 900K and 1000kPa. T ...

3. $(35\%)$ The rigid tank below, with volume $0.4{\mathrm{m}}^3$, contains air initially at $900\mathrm{K}$ and $1000\mathrm{kPa}$. The throttle valve is then opened; it allows the air to flow through the turbine and is adjusted to maintain the pressure downstream of the valve at $400\mathrm{kPa}$, independent of the pressure in the tank. The entire system is adiabatic, except for the tank which receives heat from a heat transfer reservoir with a temperature of $1200\mathrm{K}$. The heat transfer to the tank is such that the temperature in the tank remains fixed at $900\mathrm{K}$ while the air is exiting. After passing through the turbine, the air exits to the surroundings at a pressure of $150\mathrm{kPa}$. Air leaves the tank until the mass in the tank is one-half its initial mass, at which point the valve is closed. Take the air to be an ideal gas with variable specific heat. Assume there is negligible mass in the turbine, valve and piping at any time. Find: a) The initial and final mass of air in the tank $(\mathrm{kg})$. b) The amount of work done by the turbine $(\mathrm{kJ})$. c) The isentropic turbine efficiency. d) The heat transfer to the tank (kJ). e) The final pressure in the $\mathrm{tank}(\mathrm{kPa})$. f) The entropy generation for the entire system that includes the tank, valve, piping and turbine and considering that the system boundary extends to include a portion of the heat transfer reservoir through which the heat passes to the system $(\mathrm{kJ}/\mathrm{K})$. $0=$ 2)