Consider a system of N particles that are restricted to move only along one axis, and so are trapped in a quantum well of length L. The energy change associated with an infinitesimal change in length is –tdL, where t is the tension and dL is the infinitesimal change in length. Treat this system as an ideal gas. Begin by writing down the partition function. Compute the entropy and the energy. Find also the tension t and thereby derive an equation of state for this system. You may use without proof the fact that the energy levels for one particle are given by: ,2 En | 2m L2

Consider a system of N particles that are restricted to move only along one axis, and so are trapped in a quantum well of length L. The energy change associated with an infinitesimal change in length is –tdL, where t is the tension and dL is the infinitesimal change in length. Treat this system as an ideal gas. Begin by writing down the partition function. Compute the entropy and the energy. Find also the tension t and thereby derive an equation of state for this system. You may use without proof the fact that the energy levels for one particle are given by: ,2 En | 2m L2