1. ### Partition Function of N particles in an assymetrical box

Homework Statement Consider a gas sufficiently diluted containing N identical molecules of mass m in a box of dimensions Lx, Ly, Lz. Calculate the probability of finding the molecules in any of their quantum states. Calculate the energy of each quantum state εr, as a function of the quantum...
2. ### I Sound in a gas of non-interacting particles?

Hi. In some statistical approaches (e.g. canonical ensemble), the particles of an ideal gas are non-interacting. Still, it's possible to derive the ideal gas law and other thermodynamic relations. Wikipedia gives an equation for the speed of sound in an ideal gas. How can there be waves in a...
3. ### Variation of system energy in Canonical Ensemble

A system is in contact with a reservoir at a specific temperature. The macrostate of the system is specified by the triple (N,V,T) viz., particle number, volume and temperature. The canonical ensemble can be used to analyze the situation. In the canonical ensemble, the system can exchange...
4. ### Derivation of the Boltzmann distribution (Dr. David Tong)

Hello! Dr. David Tong, in his statistical physics notes, derives the boltzmann distribution in the following manner. He considers a system (say A) in contact with a heat reservoir (say R) that is at a temperature T. He then writes that the number of microstates of the combined system (A and R)...
5. ### Grand canonical and canonical ensemble

Suppose that we have a system of particles (I am assuming a general system), and I want to find the ground state energy ##E_0##. We know that we can consider our system by canonical ensemble formalism OR by grand canonical ensemble so that ##H_G=H-\mu N## (in which ##H## is the Hamiltonian in...