A constant-volume cylinder (see Figure 7-a) contains air at P_0 = 50 atm. T_0 = 29H K. At time t = 0. a valve opens and closes 20 ms later. When the valve is open, its effective flow area is given by A_f/A_f max = [sin 9pi t/T)]^1/4 where A_f max = 1.0 cm^2 and T = 20 times 10^-3 s. Assuming the heat transfer coefficient between the gas and the vessel walls is h = 100 W/m^2 K. find the pressure and temperature as a function of time during the valve-open period. How much mass escapes the cylinder? The air may be assumed to have constant specific heats with gamma = 1.4 and M = 29.0.