Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 209

4.90 Gas Fluctuations (Moscow Phys-Tech)

a) We can disregard any particles from the high-vacuum part of the setup

and consider the problem of molecular flow from the ballast volume into

the vacuum chamber. The number of particles was calculated in Problem

where is the particle concentration and is the average velocity. Ex-
pressing via the pressure P and using (see Problem4.13)

we obtain

b) At the given pressure the molecules are in the Knudsen regime, the mean

free path Therefore, we can assume that the molecular distribu-

tion will not change and N can be obtained from the Poisson distribution.

The mean fluctuation (see Problem 4.94)

The mean relative fluctuation is given by

c) The probability of finding N particles as a result of one of the measure-
ments, according to the Poisson distribution (see Problem 4.35), is

Therefore, the probability of counting zero particles in 1 ms is

an exceedingly small number. This problem is published in Kozel, S. M.,
Rashba, E. I., and Slavatinskii, S. A., Problems of the Moscow Institute of
Physics and Technology.

4.14: