An Expression for the Displacement of a Piston with Time in an Expanding Gas

Abstract: The problem of a piston movement in a confined space filled with gas, say a cylinder, is of interest in many engineering problems. This paper formulates a simple expression for the movement of a piston in a cylinder of expanding gas. A second order differential equation relates the displacement of the piston against time, in terms of the work done (say explosion in the system) and the mass of the piston. This equation has been numerically solved for certain illustrative values.

Keywords: Internal Ballistics, Gaussian Error Function, Numerical Solution, Explosion, Boundary Conditions, Third equation of motion