Free batch expansion of a compressible fluid, a tank with volume V = 10 ft3 (see Fig. 15.5-6) is filled with air (γ = 1.4) at T0 = 300K and P0 = 100 atm. At time t = 0 the valve is opened, allowing the air to expand to the ambient pressure of 1atm through a convergent nozzle, with a throat cross section S2 = 0.1 ft2.
(a) Calculate the pressure and temperature at the throat of the nozzle, just after the start of the discharge.
(b) Calculate the pressure and temperature within the tank when P2 attains its final value of 1 atm.
(c) How long will it take for the system to attain the state described in (b)?