A small particle of mass $\mathrm{m}$ moving inside a heavy, hollow and straight tube along the tube axis, undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $\mathrm{L}={\mathrm{L}}_0$ the particle speed is $\mathrm{v}={\mathrm{v}}_0.$ The piston is moved inward at a very low speed $\mathrm{V}$ such that $\mathrm{V}\ll \frac{\mathrm{d}\mathrm{L}}{\mathrm{L}}{\mathrm{v}}_0,$ where $\mathrm{d}\mathrm{L}$ is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?