Determination of the Boltzmann constant by the equipartition theorem for capacitors

Abstract

A new experimental set-up for Boltzmann constant measurement is described. Statistically averaged square of voltage U 2 is measured for different capacitances C. Boltzmann constant is determined by the equipartition theorem C U 2 = k 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. More than 10 high-school students were able to measure the Boltzmann constant with the experimental set-up in the 5 th Experimental Physics Olympiad with excellent accuracy compared to the price, conditions and available time for the experiment. A new derivation of the important for the statistical physics theorems by Nyquist and Callen-Welton is given in an appendix in the level of introductory courses in physics listened by teachers. For the understanding of the work of the experimental set-up, it is necessary to know only the equipartition theorem.

Set-up for observation thermal voltage noise and determination of absolute temperature and Boltzmann constant

“…Albert Einstein [5] was the first who suggested that Boltzmann constant k B can be measured using this relation if the thermally fluctuating voltage on the capacitor can be significantly amplified. However, our methodological experiment was made quite recently [20] and the set-up was given to the participant of the Experimental Physics Olympiad [3] The drift of the zero was the obstacle this method [21] to be used hundred years ago, but now the low noise operational amplifiers (OpAmp) allow the construction of a pre-amplifier with amplification Y = 10 6 = 10 60/10 (million times, 60 decibels in voltage or 120 dB in power) and to measure averaged square of the amplified voltage [3,20]…”

Nanotechnological Structure for Observation of Current Induced Contact Potential Difference and Creation of Effective Cooper Pair Mass-Spectroscopy

“…For the calibration of A = 10 6 amplifier is convenient to use shot 34 or thermal noise. 35 The rectified signal is collected on the lock-in capacitors for, say, ∆t = 5 s. Evaluating the electric voltage noise of the first operational amplifiers of the pre-amplifier to have spectral density parameter e N = 1.2, nV/ √ Hz, typical noise voltage can be evaluated as U N = e N √ ∆t = 2.68 nV we obtain Bernoulli signal to noise ratio r S/N = 3.39, which reveals that experiment is doable, and Cooper pair mass in cuprates can be determined using standard electronic equipment.…”

Scientific instrument for creation of effective Cooper pair mass spectroscopy

“…5. This pre-amplifier is reliable and we used it for education experiments for determination of the Boltzmann constant [21] and the electron charge [23]. The device is so robust that we reproduced in more than 300 samples for the set-ups of 5-th and 6-th highschool Experimental physics olympiads [22,24].…”

“…A reliable pre-amplifier for measurements of CPD after Refs. [21,22]. One can see a buffer and difference amplifier forming an instrumental amplifier which is sequenced by an non-inverting amplifier.…”