# Homework Help: Questions on phase space and CanonicalMicrocanonical ensembles

1. Oct 9, 2012

### thermodynam..

1. Sketch the phase space of a weight free falling along the z coordinate (no
motion in other directions). Sketch the trajectory of the free fall including
impact on the ground.
2. Calculate the density of states, entropy, and temperature (all as a function of
energy) for the following model: Consider a 1 dimensional lattice with 3 elds
(periodic boundary conditions). Every lattice site can have the states ; 0; +.
Interaction energies are only between nearest neighbors and are E() = +4
E(++) = +3 E(+) = E(+) = 2 everything else E = 0. Sketch the highest
and lowest energy states.
3. Dierences: CanonicalMicrocanonical ensemble
Assume you have given a density of states as a function of energy
(E). This can be used to calculate canonical and microcanonical data.
(a) Discretize Energy in units of E and write down the entropy microcanoni-
cally.
(b) Give the partition sum in the canonical and the microcanonical ensemble
(as a function of the relevant observables).
(c) Assume you measure an observable as a function of energy A(E). Write
down its average canonically and microcanonically.

2.

3. I don't know how to sketch in problem 1 and for problem 2, I think maybe there are mistakes in the problem, otherwise, the highest energy should be +∞ and the lowest is -∞. Problem 3 I totally have no idea of it, and I want to know the difference and relation between Ω(the number of microstates) and Ω'(the density of states).

Last edited by a moderator: Apr 29, 2017
2. Oct 9, 2012

### HallsofIvy

Do you know the definitions of any of those things? Whoever gave you this problem certainly expects you to know them.

(And this problem is physics, not mathematics, so I am moving it.)