Stat mech Definition and 56 Threads

A circular cylinder of radius R rotates about hte long axis with angular velocity omega. The cylinder contains an ideal gas of atoms of mass M at temperature tau. Find the expression for the dependence of the concentration n(r) on the radial distance r from the axis in terms of n(0) on the axis...

I am supposed to show that N!/(N-n)! = N^n where 1<<n<<N I used stirling's approximation to show that N! = e^(NlnN-N) and (N-n)! = e^[(N-n)ln(N-n) - N + n]. I took the ratio of these two terms to get e^[NlnN-N-(N-n)ln(N-n) + N - n]. I canceled terms and get N!/(N-n)! =...

we have a hollow cubical box with sides of length a with perfectly conducting walls, such that the electric field tangential to the surfaces of the walls must be zero. we need to show that the system of standing waves: Ex = Ax*cos(Kx*x)*sin(Ky*y)*sin(Kz*z)*exp(iwt) Ey =...

we have to outline a proof to show that beta =1/(Kb*T) for a gas of fermions. we are supposed to put this system in thermal contact with a system obeying classical statistics, so that the two systems have the same beta, invoke the zeroth law to sat that they have the same temperature, and then...

A weight of mass m is fixed to the middle point of a string of length l and rotates about an axis joining the ends of the string. The system is in contact with its environment at temperature T. Calculate the tension R between the ends of the string in terms of its dependence upon distance x...

Cosma Shalizi has a brief paper in the arxiv: http://www.arxiv.org/PS_cache/cond-mat/pdf/0410/0410063.pdf containing a proof that if you use Bayesian degree of belief oriented probability in forming statistical mechanics a la Jaynes, entropy comes out non-increasing; the arrow of time...