The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference
American Journal of Physics and Applications
Volume 7, Issue 1, January 2019, Pages: 21-26
Received: Dec. 15, 2018; Accepted: Jan. 11, 2019; Published: Feb. 22, 2019
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Yun-Sok Shin, Sejong Academy of Science and Arts, Sejong, Republic of Korea
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We report an observer effect in an Einstein solid, a quantum-mechanical system, induced by fluctuations of an observer’s frame of reference; which has been studied so far under the assumption that the observer’s frame of reference remains constant throughout the performance of a measurement, thus, what is actually measured throughout the performance of a measurement is an unresolved problem during which the observer’s frame of reference is assumed to fluctuate. We investigate the average energy and molar specific heat at constant volume of an Einstein solid measured by an observer with fluctuating frame of reference. The Einstein solid consists of N identical non-interacting simple harmonic oscillators per mole, where N is the Avogadro’s number at temperature T. The average energy and molar specific heat at constant volume of the Einstein solid are formulated for two types of fluctuations of the observer’s frame of reference in order to consider pedagogical and experimental demonstrations. The average energy of the Einstein solid is formulated from the definition of canonical ensemble average and the molar specific heat at constant volume of it is calculated by differentiating the average energy with T. The molar specific heat at constant volume of the Einstein solid exhibits novel features at low temperatures according to the distribution of fluctuations of the observer’s frame of reference: 0 and 3R at T = 0 K for square-wave and sawtooth-wave fluctuations, respectively, where R is the gas constant.
Einstein Solids, Specific Heat, Harmonic Oscillators, Fluctuations, Observer Effect, Thermodynamic Law
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Yun-Sok Shin, The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference, American Journal of Physics and Applications. Vol. 7, No. 1, 2019, pp. 21-26. doi: 10.11648/j.ajpa.20190701.14
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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