2051Ideal monatomic gas is enclosed in cylinder of radius a and length L.The cylinder rotates with angular velocity w about its symmetry axis andthe ideal gas is in equilibrium at temperature T in the coordinate systemrotating with the cylinder. Assume that the gas atoms have mass m, haveno 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?(MIT)

To answer: (a) What is the Hamiltonian in the rotating coordinates system? (b) What is the partition…

Answered: 2051 Ideal monatomic gas is enclosed in…

Similar questions

Problem Consider the ODE x = 2-3x with initial condition x(to) = 1 and to = 0. What is the value of the state x when t = 2? Estimate when the system will decay to a constant value using the time constant of the system (i.e., after 4 time constants)? 4
please answer c) only 2. a) A spinless particle, mass m, is confined to a two-dimensional box of length L. The stationary Schrödinger equation is - +a) v(x, y) = Ev(x, y), for 0 < r, y < L. The bound- ary conditions on ý are that it vanishes at the edges of the box. Verify that solutions are given by 2 v(1, y) sin L where n., ny = 1,2..., and find the corresponding energy. Let L and m be such that h'n?/(2mL²) = 1 eV. How many states of the system have energies between 9 eV and 24 eV? b) We now consider a macroscopic box (L of order cm) so that h'n?/(2mL?) ~ 10-20 eV. If we define the wave vector k as ("", ""), show that the density of states g(k), defined such that the number of states with |k| between k and k +dk is given by g(k)dk, is Ak 9(k) = 27 c) Use the expression for g(k) to show that at room temperature the partition function for the translational energy of a particle in a macroscopic 2-dimensional box is Z1 = Aoq, where 2/3 oq = ng = mk„T/2nh?. Hence show that the average…
Find the number density N/V for Bose-Einstein condensation to occur in helium at room temperature (293 K). Compare your answer with the number density for an ideal gas at room temperature at 1 atmosphere pressure.
5. Consider the two state system with basis |+) which diagonalizes the Pauli matrix 03. Generally the state of the system at time t can be written as |W(t)) = c+(t)|+) + c_(t)|-). (i) For the Hamiltonian of the system, first take H = functions c+(t) given the initial condition that at time t = 0 Eo03. Solve for the coefficient |W(0)) = |-).
c) How does the classical kinetic energy of the free electron compare in magnitude with the result you obtained in the previous part?
Answer in 90 minutes please. Count as double the questions if necessary.