Imagine a cubical cell of edge marked out inside a room full of still air at and

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 The grand canonical ensemble, ensemble equivalence and fluctuations

Problem

Imagine a cubical cell of edge

10\,\mathrm{nm}

marked out inside a room full of still air at

T = 300\,\mathrm{K}

and

p = 1.01\times10^{5}\,\mathrm{Pa}

. The cell has no walls: molecules cross its faces freely, so the surrounding air acts as a reservoir that fixes

T

and

\mu

while the number

N

inside the cell wanders. Air is treated as an ideal gas. ((a)) Estimate the mean number of molecules

\langle N\rangle

in the cell and the relative width

\sigma_N/\langle N\rangle

of its number distribution. ((b)) Estimate the edge length of such a cubical cell for which the relative width falls to one per cent.

Browse the problem library