Uncertainty Analysis for a Simple Thermal Expansion Experiment

TL;DR

This paper presents a simple thermal expansion experiment for measuring a metal wire's expansion coefficient, analyzing measurement uncertainties and model applicability, and providing empirical results consistent with accepted values.

Contribution

It introduces a straightforward experimental approach combined with analytical and empirical analysis to explore model assumptions and measure thermal expansion coefficients.

Findings

Measured nichrome's thermal expansion coefficient as 17.1(1.3) ppm/K

Identified conditions where wire's mass and elasticity can be neglected

Validated measurement results against accepted values at 8% accuracy

Abstract

We describe a simple experiment for measuring the thermal expansion coefficient of a metal wire and discuss how the experiment can be used as a tool for exploring the interplay of measurement uncertainty and scientific models. In particular, we probe the regimes of applicability of three models of the wire: stiff and massless, elastic and massless, and elastic and massive. Using both analytical and empirical techniques, we present the conditions under which the wire's mass and elasticity can be neglected. By accounting for these effects, we measure nichrome's thermal expansion coefficient to be 17.1(1.3) ppm/K, which is consistent with the accepted value at the 8% level.