A gun barrel is used to accelerate a projectile using high pressure/temperature air. It can be modeled as a horizontal frictionless piston/cylinder as shown below. It initially contains air at 1400 K, 40 MPa. The diameter of the cylinder is 0.01 m and is initially held in place by a pin at x1 = 0.01 m (or state 1). The piston is then released. The ambient pressure is 100 kPa. The mass of the piston is 0.008 kg. The designer wants to determine the length of the barrel (or state 2), when the piston exiting velocities are 100 m/s and 120 m/s, respectively. Ten experiments under different conditions are conducted. The measurements of pressure parameter as a function of distance x (or volume=3.14*D^2/4*x) are shown in the attached Excel file. Based on the Eqn. of Example 4, use MS Excel and two computer methods to determine the barrel lengths needed to reach the 2 exit velocities.