Determination of the Boltzmann constant by the equipartition theorem for capacitors

Abstract

A new experimental set-up for measurement of the Boltzmann constant is described. The statistically averaged square of voltage is measured for different capacitances C. The Boltzmann constant is determined by the equipartition theorem . 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, the square of the voltage is created by an analog multiplier AD633, and finally, the averaged signal is measured by a multimeter. More than ten high-school students were able to measure the Boltzmann constant with the experimental set-up in the 5th Experimental Physics Olympiad with excellent accuracy compared to the price, conditions and available time for the experiment. A new derivation of the important statistical physics theorems by Nyquist and Callen–Welton is given in an appendix at the level of introductory courses in physics studied by future teachers. To understand the work of the experimental set-up, it is only necessary to know the equipartition theorem.