2051 Ideal monatomic gas is enclosed in cylinder of radius a and length L The cylinder rotates with angular velocity w about its symmetry axis and che ideal gas is in equilibrium at temperature T in the coordinate system rotating with the cylinder. Assume that the gas atoms have mass m, have no internal degrees of freedom, and obey classical statistics. (a) What is the Hamiltonian in the rotating coordinates system? (b) What is the partition function for the system? (c) What is the average particle number density as a function of r?

2051 Ideal monatomic gas is enclosed in cylinder of radius a and length L The cylinder rotates with angular velocity w about its symmetry axis and che ideal gas is in equilibrium at temperature T in the coordinate system rotating with the cylinder. Assume that the gas atoms have mass m, have no internal degrees of freedom, and obey classical statistics. (a) What is the Hamiltonian in the rotating coordinates system? (b) What is the partition function for the system? (c) What is the average particle number density as a function of r?