A single gas molecule of inertia \(m\) is trapped in a box and travels back and forth with constant speed \(v\) between opposite walls A and B a distance \(\ell\) apart. At each collision with a wall, the molecule reverses direction without changing speed. Write algebraic expressions for \((a)\) the magnitude of the change in momentum of the molecule as it collides with wall \(\mathrm{B},(b)\) the amount of time that elapses between collisions with wall \(\mathrm{B},(c)\) the number of collisions per second the molecule makes with wall \(B\), and

(d) the change in momentum undergone by wall \(\mathrm{B}\), per second, as a result of these collisions.