Experimental determination of heat capacities and their correlation with quantum predictions

TL;DR

This paper presents an undergraduate calorimetric experiment to measure heat capacities of solids, compares results with quantum models, and discusses the Verwey transition in magnetite, emphasizing improved data accuracy through computer-based methods.

Contribution

It introduces a practical experimental approach for undergraduate labs to determine heat capacities and compare them with quantum predictions, including the Verwey transition.

Findings

Measured heat capacities of copper, aluminum, and graphite.

Data aligns with Einstein and Debye models.

Observed Verwey transition in magnetite around 120-140 K.

Abstract

This article demonstrates an undergraduate experiment for the determination of specific heat capacities of various solids based on a calorimetric approach, where the solid vaporizes a measurable mass of liquid nitrogen. We demonstrate our technique for the metals copper and aluminum, the semi-metal graphite and also present the data in relation with Einstein's model of independent harmonic oscillators and the more accurate Debye model based on vibrational modes of a continuous crystal. Furthermore, we elucidate an interesting material property, the Verwey transition in magnetite occurring around 120-140 K. We also demonstrate that the use of computer based data acquisition and subsequent statistical averaging helps reduce measurement uncertainties.