Speedy oil provides a single channel automobile oil change and lubrication service. Customers provide an arrive rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability dist READ MORE »
- Responses: 204
- MSc, University of Utrecht, 1999
- PhD (IP), University of Amstedam, 2004
Derive the formula for the multiplicity (entropy) of the two state paramagnet in the large N limit and when the number of excess spins relative to N is small.
For a single large two-state paramagnet, the multiplicity function is very sharply peaked about N/2.
(a) Use Stirling's approximation to estimate the height of the peak in the
(b) Derive a formula for the multiplicity function in the vicinity of the peak.
(c) READ MORE »
Consider a classical particle moving in a one-dimensional potential well u(x). The particle is in thermal equilibrium with a reservoir at temperature T, so the probabilities of its various states are determined by Boltzmann statistics.
(a) Show that the average position of the particle is given READ MORE »
Polymers, like rubber, are made of very long molecules that tangle into a configuration that has lots of S. A crude model of a rubber band contains N links, all of equal length L, which can only point either left or right (2 possible states). The total length of the band is thus the net displacemen READ MORE »
Consider the semi-infinite square well given by V(x)=-Vo