A hollow cylinder is closed at the top end by a movable piston of mass \(M\) that can slide in the hollow part of the cylinder without friction. A flow of gas equal to \(\Phi=\frac{\Delta M_{\text {gas }}}{\Delta t}\left(\mathrm{~g} \mathrm{~s}^{-1}\right)\) is made to flow through a small tube. Gas molecules, of mass \(m_{o}\), can be considered to all have velocities \(v_{o}\) directed upward along the direction of the vertical and to elastically impact the piston. Determine the gas flow required to keep the piston in equilibrium against the force of gravity.