### Dynamics of an irreversible cooling cycle

#### Abstract

A local stability analysis of an irreversible energy converter working in several optimum regimes, is presented. The energy converter in the present work is a cooling cycle that exchanges heat with the heat reservoirs at $T_{1}$ and $T_{2}$ ($T_{1}>T_{2}$) through a couple of thermal conductors, with the same conductance value ($\beta$). The working fluid has a constant heat capacity ($C$) in the two isothermal branches of the cycle. From the local stability analysis at the maximum COP and maximum ecological function regimes, we observe thermodynamic and dynamical properties similar to those found for other thermal cycles studied by several authors. The most important thermodynamic property that we find is that this converter also has optimal points of operation (maximum COP and maximum ecological function). On the other hand, with respect to the dynamic properties we find that under small perturbations this converter shows a robust behavior, i.e. the converter returns quickly to the steady state corresponding to one of the optimal points of operation. In the case of maximum COP the relaxation times are independent of the external temperatures of the cooling cycle but not of the internal irreversibilities, whereas in the case of maximum ecological function these times depend as much on the external temperatures as of the internal irreversibilities. We conclude from the assertions in the previous paragraph that the energetic properties of the energy converter at the maximum ecological function regime worsen as $\eta_{C}$ (Carnot efficiency) decreases. Moreover, since both relaxation times decrease as $\eta_{C}$ decreases, the decrements of $\eta_{C}$ improve the system stability and deteriorate its thermodynamic properties. Finally we can say that, $\eta_{C}$ drives a trade-off between stronger stability (dynamic robustness) and better thermodynamic properties like cooling power and COP.

#### Keywords

Non-equilibrium, irreversible thermodynamics; Performance characteristics of energy conversion systems; figure of merit

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**Revista Mexicana de Física S**

**ISSN: In Process**

Non periodical electronic journal published by Sociedad Sociedad Mexicana de Física, A.C

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