The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference

Yun-Sok Shin

doi:doi:10.11648/j.ajpa.20190701.14

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The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference

Yun-Sok Shin

Published in American Journal of Physics and Applications (Volume 7, Issue 1)

Received: 15 December 2018 Accepted: 11 January 2019 Published: 22 February 2019

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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.

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

Keywords

Einstein Solids, Specific Heat, Harmonic Oscillators, Fluctuations, Observer Effect, Thermodynamic Law

References

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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

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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

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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

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@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}
}

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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
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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  -

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Author Information

Yun-Sok Shin

Sejong Academy of Science and Arts, Sejong, Republic of Korea

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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

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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

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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

Copy | Download

@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}
}

Copy | Download

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  -

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