Teaching ideal gas in a uniform field: exploring student preferences

An ideal classical gas under uniform gravity is a commonly discussed problem in statistical thermodynamics. At an introductory level, the condition of hydrostatic equilibrium gives rise to the barometric formula, which describes the variation of gas pressure with height. At an advanced level, the partition function can be used to find the density and the internal energy of the gas. These methods rely heavily on mathematical concepts, which may pose a difficulty to some students. This article presents teaching the problem via the virial theorem, emphasising the physical picture of the particle distribution. The virial theorem allows the internal energy to be expressed as an integral over the surface of the container. For the pedagogical purpose, visualisation of how the particles distribute themselves at extreme temperatures helps determine the internal energy of the gas. Student feedback is used as a basis for evaluating different approaches to the problem.