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

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 (P) in terms of temperature (T) and six technical coeffcients (ᵢ\0,,4, Tₜh), functions of volume parameter (V) and number of atoms (N).~For weakly interacting gases, the internal energy is U3PV, thus we determine the entropy with U = TS - PV for fixed N.~As expected, we show that the entropy at the BEC transition (Sc) is constant for varying V.~Being isentropic makes BEC transition an energy source for non-mechanical work.~Hence, we observed that the enthalpy at the BEC transition Hc = Ec + PcV = TcSc, at fixed values of V and varying N, grows fairly linearly with N.~We fitted Hc=ηN-Hc⁰ to that data, being η the specific enthalpy of BEC transformation and Hc⁰ an intrinsic enthalpic loss.~We deem this study to be a step closer to practical quantum-based engines.