Determination of Boltzmann constant by equipartition theorem for capacitors

TL;DR

This paper presents a novel experimental setup using operational amplifiers and analog multipliers to measure the Boltzmann constant by analyzing voltage fluctuations across capacitors at different temperatures.

Contribution

It introduces a new low-noise, high-frequency measurement system for determining the Boltzmann constant via the equipartition theorem.

Findings

Accurate measurement of voltage fluctuations across capacitors.

Determination of Boltzmann constant consistent with accepted values.

Effective use of analog multipliers and operational amplifiers in thermal physics experiments.

Abstract

A new experimental set-up for Boltzmann constant measurement is described. Statistically averaged square of voltage $\left<U^2\right>$ is measured for different capacitances $C$. Boltzmann constant is determined by the equipartition theorem $C\left<U^2\right>=k_{_\mathrm{B}}T$. For fixed capacitance, voltages could be measured for different temperatures. The set-up consists of low-noise high frequency operational amplifiers ADA4898-2. An instrumental amplifier is followed by an inverting amplifier, square of the voltage is created by an analog multiplier AD633 and finally the averaged signal is measured by a multimeter.