Quantity Calculus: Unambiguous Designation of Values and Units in Graphs and Tables

Abstract

The method of quantity calculus treats physical quantities as the product of a numerical value and a unit. This method, known for more than a century and internationally recommended for handling of physical quantities, is not used as extensively in textbooks and teaching as it could be. This paper gives some background to the methodology, and shows examples, suitable for teaching to undergraduate students, of the use of quantity calculus to provide unambiguous representations of physical quantities in tables and graphs.

Inconsistent Language Use in Online Resources Explaining the Mole Has Implications for Students’ Understanding

“…15 The quantitative calculus method treats each physical quantity as the product of a numerical value and a unit. 30 However, the addition of amount of substance as the seventh base quantity has caused confusion for chemistry educators with the official definition perceived as incompatible with practice in the analytical laboratory. 6 The definition remained unchanged until January 2018 when IUPAC recommended a new definition of the mole 16 that was adopted in 2019.…”

A New Model for Constant Fuel Utilization and Constant Fuel Flow in Fuel Cells

“…(Mathematically, the argument of logarithm is dimensionless (unitless). The propriety of taking the logarithm of a dimensioned quantity has long been debated [81][82][83][84]. In the fuel cell literature, however, it seems standard practice to do so (see, for example, References [1,3,4,85]).…”

Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions

“…The method of expressing the arguments of the logarithms in the Arrhenius equation shown in eq is recommended when tabulating or plotting data as it avoids potential ambiguities. In this manner, the numerical value of a (dimensioned) physical quantity is disengaged from its dimension, such that physical quantity/unit = numerical value as, for example, in Δ H f 0 /(kJ mol −1 ) = −285.9. This is known as quantity calculus , the importance of which has been underscored some time ago in this Journal and has been adopted as the Journal ’s conventional style .…”

“…as, for example, in ΔH f 0 /(kJ mol -1 ) = -285.9. This is known as quantity calculus, the importance of which has been underscored some time ago in this Journal and has been adopted as the Journal 's conventional style (11).…”

“…There has been a vigorous debate in the literature for over six decades about the fate of dimensions (and units) when quantities with dimensions are the arguments of logarithms (or exponentiation) ( − , see also ref ). The same issue has also been a subject of discussion and disagreement recently on the Internet .…”