Version 1
: Received: 17 June 2024 / Approved: 18 June 2024 / Online: 18 June 2024 (11:34:55 CEST)
How to cite:
Miotti, M.; Martins, E. B.; Hemmerling, M.; Dubessy, R.; Bagnato, V. S. Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method. Preprints2024, 2024061225. https://doi.org/10.20944/preprints202406.1225.v1
Miotti, M.; Martins, E. B.; Hemmerling, M.; Dubessy, R.; Bagnato, V. S. Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method. Preprints 2024, 2024061225. https://doi.org/10.20944/preprints202406.1225.v1
Miotti, M.; Martins, E. B.; Hemmerling, M.; Dubessy, R.; Bagnato, V. S. Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method. Preprints2024, 2024061225. https://doi.org/10.20944/preprints202406.1225.v1
APA Style
Miotti, M., Martins, E. B., Hemmerling, M., Dubessy, R., & Bagnato, V. S. (2024). Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method. Preprints. https://doi.org/10.20944/preprints202406.1225.v1
Chicago/Turabian Style
Miotti, M., Romain Dubessy and Vanderlei Salvador Bagnato. 2024 "Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method" Preprints. https://doi.org/10.20944/preprints202406.1225.v1
Abstract
Quantum thermal engines are receiving much attention in recent years, due to their potential applications.~For a candidate group, harmonically trapped gases under Bose-Einstein condensation (BEC), we see little investigation on the energy transference around that transition.~Therefore, we present an empirical study with rubidium-87 gas samples in a magnetic harmonic trap.~We developed an empirical Equation of State model to fit to our experimental dataset, expressing the pressure parameter ($\mathcal{P}$) in terms of temperature ($T$) and six technical coeffcients ($\{a_i\}_{0,\dots,4}$, $T_\mathrm{th}$), functions of volume parameter ($\mathcal{V}$) and number of atoms ($N$).~For weakly interacting gases, the internal energy is $U\cong3\mathcal{P}\mathcal{V}$, thus we determine the entropy with $U = TS - \mathcal{P}\mathcal{V}$ for fixed $N$.~As expected, we show that the entropy at the BEC transition ($S_c$) is constant for varying $\mathcal{V}$.~Being isentropic makes BEC transition an energy source for non-mechanical work.~Hence, we observed that the enthalpy at the BEC transition $H_c = E_c + \mathcal{P}_c\mathcal{V} = T_cS_c$, at fixed values of $\mathcal{V}$ and varying $N$, grows fairly linearly with $N$.~We fitted $H_c=\eta{N}-H_c^0$ to that data, being $\eta$ the specific enthalpy of BEC transformation and $H_c^0$ an intrinsic enthalpic loss.~We deem this study to be a step closer to practical quantum-based engines.
Copyright:
This 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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