Generalization of Eight Methods for Determining R in the Ideal Gas Law

TL;DR

This paper reviews and generalizes eight different methods used to determine the molar gas constant R from experimental data related to the ideal gas law, highlighting their theoretical connections.

Contribution

It introduces a unified framework for understanding eight methods of estimating R, clarifying their relationships and underlying assumptions.

Findings

Eight methods are shown to be specific cases of a general approach.

The methods are compared in terms of accuracy and applicability.

A comprehensive analysis of parameter estimation techniques for R.

Abstract

The ideal gas law of physics and chemistry says that PV = nRT. This law is a statement of the relationship between four variables (P, V, n, and T) that reflect properties of a quantity of gas in a container. The law enables us to make accurate predictions of the value of any one of the four variables from the values of the other three. The symbol R (called the "molar gas constant") is the sole parameter or constant of the law. R stands for a fixed number that has been shown through experiments to equal approximately 8.314472. Eight methods are available to analyze the data from a relevant experiment to determine the value of R. These methods are specific instances of eight general methods that scientists use to determine the value(s) of the parameter(s) of a model equation of a relationship between variables. Parameter estimation is one step in the study of a relationship between variables.