Rethinking the Ideal Gas Law Using Graphs

Abstract

The ideal gas law, PV = nRT, is one of the simplest physical laws in nature that is introduced to students as early as in high school and first year in college. In this equation, P stands for pressure, V is the volume, n is the amount expressed in mole, T is the temperature in Kelvin scale, and R is the ideal gas constant. The traditional approach of introducing the ideal gas law involves three historical experiments by Robert Boyle, Jacque Charles, and Amedeo Avogadro. They each observed that V ∝ 1/P, V ∝ T, and V ∝ n, respectively. Mathematically, we can put them together to yield V ∝ nT/P. Designating the proportionality constant as R, we have V = R . nT/P or PV = nRT as is mostly written. I call this the “bottom-up” approach in which we make individual measurements first and then consolidate them into one unified equation. In this paper, the author presents a logical way to unite the three gas laws together, a “top-down” approach where a systematic logical investigation is performed first, and then proposes a series of experiments that are both minimal and optimal. It provides a new theoretical perspective to the experimental facts and a new way of presenting the ideal gas law at the college intro level through a heuristic approach.