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.

中文翻译：

---

在均匀场中教授理想气体：探索学生的偏好


均匀重力下的理想经典气体是统计热力学中经常讨论的问题。在介绍性水平上，流体静力平衡的条件产生了气压公式，该公式描述了气压随高度的变化。在高级水平上，配分函数可用于查找气体的密度和内能。这些方法严重依赖数学概念，这可能会给一些学生带来困难。本文通过维里定理教授该问题，强调粒子分布的物理图像。维里定理允许内能表示为容器表面上的积分。出于教学目的，可视化颗粒在极端温度下如何分布有助于确定气体的内能。学生的反馈被用作评估解决问题的不同方法的基础。