Can an ideal gas feel the shape of its container?

Abstract

Thermodynamic quantities of an ideal gas enclosed in a finite container are examined. We use an asymptotic expansion for high temperatures to obtain the partition function of an ideal gas, both in two and three dimensions, showing the leading corrections to the internal energy due to a finite container. In the three-dimensional case, the first correction term depends only on the area–volume ratio, but higher order terms depend also on other geometric properties of the container. However, according to recent results, we show that the answer to the question posed in the title is negative.