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 (\aᵢ\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=N-Hc⁰ to that data, being 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.