A small particle of mass $m$ 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 $V$ such that $V \ll \frac{d L}{L} V_0$, where $d L$ is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct ?