Three short counting exercises.

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Statistical foundations and the equilibrium ensembles · Statistical foundations and the equilibrium ensembles

Thermal Physics, Ch Microstates, multiplicity and the statistical entropy

Problem

Three short counting exercises. ((a)) A row of

5

distinguishable two-state units, each fixed in place and showing up or down, all arrangements having the same energy. What is the multiplicity of the macrostate with the largest multiplicity? ((b)) An Einstein solid of

4

identical oscillators at fixed sites shares

q = 4

indistinguishable units of energy

h\nu

. How many microstates has this macrostate? ((c)) A single xenon atom is a free point particle in a cubical box of volume

V

with rigid walls, its de Broglie standing waves giving allowed momentum components

p_i = n_ih/2a

with

n_i = 1,2,3,\ldots

along each edge of length

a

. What volume

V

makes the number of single-particle states with momentum magnitude below

p = 5.0\times10^{-24}\,\mathrm{kg\,m\,s^{-1}}

equal to

1.0\times10^{20}

Browse the problem library