Abstract
We use the general formulation of irreversible thermodynamics and study the minimally nonlinear irreversible model of heat engines operating between a time-varying hot heat source of finite size and a cold heat reservoir of infinite size. We find the criterion under which the optimized efficiency obtained by this minimally nonlinear irreversible heat engine can reach the reversible efficiency under the tight coupling condition: a condition of no heat leakage between the system and the reservoirs. We assume the rate of heat transfer from the hot to the cold heat reservoir obeys Fourier’s law and discuss physical conditions under which one can obtain the reversible efficiency in a finite time with finite power. We also calculate the efficiency at maximum power for the minimally nonlinear irreversible heat engine under the nontight coupling condition.
Acknowledgment
I thank R. Arun for the critical reading of the manuscript. I also thank the anonymous referees for their critical comments and valuable suggestions.
Appendix I
We have
By using eqs. (23)–(50) one can calculate
For optimization eq. (28) can be rewritten in terms of T(t) as
By using eqs. (51)–(54) in the above equation one can obtain
Since
and
eq. (56) can be rewritten as
where
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