Fluctuations in the number of particles of the ideal gas: A simple exampleof explicit finite-size effects

The fluctuations in the number of particles of the ideal gas are calculated using the canonical and the grand canonical ensembles. The two results dif fer by a factor which accounts for the relative size of the total volume an d the subvolume where the canonical ensemble fluctuations are calculated. T his factor gives a simple example of explicit finite-size effects, because it arises from considering a fixed number of particles in the canonical ens emble. Our simulation results for the isothermal compressibility of the har d disk fluid with a finite number of particles are improved by applying thi s correction. (C) 1999 American Association of Physics Teachers.