Acceleration of a slab driven by a constant pressure piston

The sequence of shock and rarefaction waves, which occur in a plane layer of ideal gas initially at rest when it is driven toward the vacuum by a very high constant pressure piston, is studied. In the rarefaction flow that relaxes the layer compressed by the first strong shock, a second shock is generated. The time and position of its formation are obtained by an exact analytical expression. The subsequent motion and intensity of the shock wave are approximated by the Chester--Chisnell--Whitham (CCW) method. Then, the Lagrangian distribution of entropy in the layer is analytically derived