Uncertainty analysis for a simple thermal expansion experiment

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) µm/m·K, which is consistent with the accepted value at the 8% level.

Attending to experimental physics practices and lifelong learning skills in an introductory laboratory course

“…Prior to discussions, instructors seeded ideas about which assumptions of the model to question by making anecdotal observations during data collection, such as noting that the wire hangs in a triangle even at room temperature, which cannot be explained by thermal expansion effects alone. 27 These comments often referred back to the exploratory activities that students completed during the first class, such as the station which involved observing and documenting the shapes of hanging chains and wires, both in loaded and unloaded conditions.…”

“…27 The purpose of these experiments was to provide students with opportunities to engage in the iterative process of designing, conducting, and refining experiments, in alignment with our first course objective.…”

“…However, the wire's elasticity, mass, and kinks contribute to important systematic effects that may need to be taken into account depending on the desired accuracy and precision with which the thermal expansion coefficient is to be measured. 27 This experimental apparatus is appropriate for an introductory lab course because the underlying principles and concepts (gravity, tension, elastic stretching, thermal expansion, and Newton's Second Law) are accessible to students with an introductory physics background. The apparatus was the focus of several complementary activities in which students engaged during this first phase of the course: exploration of the apparatus and related concepts; development,…”

Building classroom and organizational structure around positive cultural values

“…The apparatus for the experiment [12] was designed by the teachers of the course, but the students use a consensus-based process to create the procedure that they will use to measure the expansion of a wire. After the first round of measurement, students work together to improve the experiment by making changes to the apparatus, procedure, or data analysis methods.…”

Bimetallic ammeter: a novel method of current measurement

“…Thermal expansion is a physical phenomenon happening around us all the time although it often goes unnoticed for most everyday objects. Albeit commonplace, it still is a vital aspect of the physical world as it has the potential to critically impact our lives -everything from the rise in sea levels to the structural integrity of infrastructure [2]. An object that interestingly exhibits thermal expansion is the bimetallic coil.…”