Determination of the Boltzmann constant by the equipartition theorem for capacitors
Abstract
A new experimental setup for measurement of the Boltzmann constant is described. The statistically averaged square of voltage ≤ft<le {U}(2) right>le U 2 is measured for different capacitances C. The Boltzmann constant is determined by the equipartition theorem C≤ft<le {U}(2) right>le ={k}_{{}_{{B}}}T C U 2 = k
B T . For fixed capacitance, voltages could be measured for different temperatures. The setup consists of lownoise, highfrequency operational amplifiers ADA48982. 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 highschool students were able to measure the Boltzmann constant with the experimental setup 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 CallenWelton is given in an appendix at the level of introductory courses in physics studied by future teachers. To understand the work of the experimental setup, it is only necessary to know the equipartition theorem.
 Publication:

European Journal of Physics
 Pub Date:
 May 2019
 DOI:
 10.1088/13616404/ab07e0
 arXiv:
 arXiv:1801.00022
 Bibcode:
 2019EJPh...40c5102M
 Keywords:

 Boltzmann constant;
 equipartition theorem;
 voltage thermal fluctuations of a capacitor;
 Physics  Physics Education
 EPrint:
 Further minor corrections are made. Text in English 17 pages, text in Bulgarian 18 pages, 11 figures and 3 tables per language