A Master Class in Dimensional Analysis: the Universal Gas Constant
Preprints are manuscripts made publicly available before they have been submitted for formal peer review and publication. They might contain new research findings or data. Preprints can be a draft or final version of an author's research but must not have been accepted for publication at the time of submission.
determination of the universal gas constant, R, in 35,712 different units. This large
number of units arises from a simple enumeration of possible pressure-volume unit
combinations and energy unit combinations covering SI (metric), Imperial (British), and
American units. In turn, various units for force and area used for defining pressure, and
various units for force and distance used for defining energy are explored. This
presentation serves as an excellent exercise for high school and undergraduate students to
master the skill of dimensional analysis, unit conversions, and basic combinatorics in
general chemistry and physical chemistry courses. Instructors can also use the described
exercise of constructing conversion matrices to train students in how to efficiently use the
Microsoft Excel spreadsheet program.