# The Entropy and Energy for Non-Mechanical Work at the Bose–Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method

## TL;DR

This paper studies energy transfer during Bose-Einstein condensation in trapped rubidium gas, using an empirical model to explore its potential for quantum thermal engines.

## Contribution

The study introduces an empirical equation of state model to analyze the BEC transition and its thermodynamic properties for non-mechanical work.

## Key findings

- Entropy remains constant during the BEC transition, confirming it is isentropic.
- Enthalpy at BEC increases linearly with the number of atoms at fixed volume.
- A linear fit reveals specific enthalpy and intrinsic enthalpic loss during BEC.

## Abstract

Quantum thermal engines have received 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 in terms of temperature, and six technical coefficients, functions of the volume parameter and the number of atoms. By using standard thermodynamic relations, we determine the system’s entropy, shown to be constant at the BEC transition, as expected. Being isentropic makes the BEC transition an energy source for non-mechanical work. Hence, we observed that the enthalpy at the BEC transition, at fixed values of the volume parameter, grows fairly linearly with the number of atoms. We fitted a linear function to that data, finding the specific enthalpy of the BEC transformation and the intrinsic enthalpic loss for BEC. We deem this study to be a step closer to practical quantum-based engines.