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.
Published in | American Journal of Physics and Applications (Volume 7, Issue 1) |
DOI | 10.11648/j.ajpa.20190701.14 |
Page(s) | 21-26 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Einstein Solids, Specific Heat, Harmonic Oscillators, Fluctuations, Observer Effect, Thermodynamic Law
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APA Style
Yun-Sok Shin. (2019). 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, 7(1), 21-26. https://doi.org/10.11648/j.ajpa.20190701.14
ACS Style
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. Am. J. Phys. Appl. 2019, 7(1), 21-26. doi: 10.11648/j.ajpa.20190701.14
AMA Style
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. Am J Phys Appl. 2019;7(1):21-26. doi: 10.11648/j.ajpa.20190701.14
@article{10.11648/j.ajpa.20190701.14, author = {Yun-Sok Shin}, title = {The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference}, journal = {American Journal of Physics and Applications}, volume = {7}, number = {1}, pages = {21-26}, doi = {10.11648/j.ajpa.20190701.14}, url = {https://doi.org/10.11648/j.ajpa.20190701.14}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20190701.14}, abstract = {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.}, year = {2019} }
TY - JOUR T1 - The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference AU - Yun-Sok Shin Y1 - 2019/02/22 PY - 2019 N1 - https://doi.org/10.11648/j.ajpa.20190701.14 DO - 10.11648/j.ajpa.20190701.14 T2 - American Journal of Physics and Applications JF - American Journal of Physics and Applications JO - American Journal of Physics and Applications SP - 21 EP - 26 PB - Science Publishing Group SN - 2330-4308 UR - https://doi.org/10.11648/j.ajpa.20190701.14 AB - 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. VL - 7 IS - 1 ER -