A Spin-half System As A Working Substance Of A Heat Engine Exploring Its Finite-time Thermodynamic Quantities

Three different model heat engines, two of which operate between two reservoirs atrninverse positive absolute temperatures and a third one that operates between two in-rnverse negative absolute temperatures are investigated. As a working substance of thernengines, a system of two-level spin-half particles, in the thermodynamic limit, subjectedrnto a time-dependent external magnetic field, is used. We investigate the heat enginesrnunder two schemes: the quasistatic and finite-time thermodynamic processes.rnIn the quasistatic process the system and the reservoirs essentially remain in ther-rnmal equilibrium and exchange energy in the form of heat and work. As they link thernisothermal processes, adiabatic changes are also basic components of the quasistaticrnprocesses. After setting the models, the expressions for net work done, net heat ab-rnsorbed and efficiency of each model are analytically derive. For parameter values ofrnenergy level spacing, occupation probability in the excited state and inverse tempera-rnture, the efficiencies coincide with the Carnot efficiency of each model.rnIn the finite-time process, the expressions for net work done, power and efficiency ofrnthe heat engines are derived. In all the three models, power versus period (τ ) initiallyrn(τ ≤ τmp -period at the maximum power) shows a rapid increase with period; then itrnshows a maximum value at mp before it decrease as period becomes longer and longer.rnIn the very long period limit, finite-time quantities including power, approach to theirrncorresponding quasistatic values.rnEmploying a unified criterion for energy converters, the model engines are effectivelyrnoptimized and found to yield optimum finite-time quantities. Efficiency-wise optimizedrnefficiencies are found to be better than efficiencies at maximum power; however, power-rnviiirnwise, the optimized power is smaller than its maximum power. The figure of merit ofrnmodel I, ψI , plotted against the quaistaitic efficiency, increases from its 1.12 to aboutrn1.3, as its quasistatic efficiency increases from zero to the maximum possible value. So,rnin the entire range of ηC , optimum working condition is an advantage for the model.rnHowever, the figure of merit of model III, ψIII , generally decreases from its peakrnvalue of 1.89 with an increase in ηC . Only in the small ηC 0.2 values, the optimumrnworking condition is preferred to the maximum power working condition. Else where,rnthe maximum working condition is better than the optimum working condition for thernmodel. In model II, the figure of merits, ψII , slightly decreases from its value of aboutrn1.15 to 1.1 as at ηC increases from zero to 0.57

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