Irreversible Brownian Heat Engine

Abstract

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. It is shown that the efficiency of such Brownian heat engine is far from Carnot efficiency even at quaistatic limit. At quasistatic limit, the efficiency of the heat engine approaches the efficiency of endoreversible engine η = 1 − Tc/T h [23]. On the other hand, the maximum power efficiency of the engine approaches. Moreover, the dependence of the current as well as the efficiency on the model parameters is explored analytically by omitting the heat exchange via the kinetic energy. In this case we show that the optimized efficiency always lies between the efficiently at quaistatic limit and the efficiency at maximum power. On the other hand, the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If one includes the heat exchange at the boundary of the heat baths, the efficiency of the engine becomes much smaller than the Carnot efficiency. In addition, the dependence for the coefficient of performance of the refrigerator on the model parameters is explored by including the heat exchange via the potential and kinetic energy. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t as well as the external load dictate the direction of the particle velocity. Moreover the performance of the heat engine improves with time. At large t (steady state),the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value.

Success versus failure: Efficient heat devices in thermodynamics

“…There is no physical inconsistency in the fact that some experimental values could attain values below the obtained lower bounds (as can be seen, for example, in Refs. [29,[39][40][41]); this only shows that, according to the meaning of , these plants should be qualified as thermodynamically inefficient heat devices. Let us recall that, in this work, while theoretical results have been obtained under strong assumptions by balancing reversibility and irreversibilities, experimental results account for quite different and more intricate arrangements where the design does not necessarily fit the theoretical balance of irreversibilities.…”

Optimal work in a harmonic trap with bounded stiffness

“…To begin with, we would like to discern when κ * u (t) becomes negative. Looking at (28), it is readily seen that the first term on its rhs becomes smaller than the second one for large enough y 1 , and y 1,u (t) increases linearly in time. Therefore, the value of the final time t f below which the unbounded solution ceases to be valid is determined by the condition κu (t f ) = 0, i.e.…”

“…These drawbacks are important for the optimisation of irreversible heat engines, a field of research that has become quite active in the last few years [24][25][26][27][28][29]. In fact, Brownian particles trapped by optical tweezers have been recently employed to build stochastic heat engines, both theoretically and experimentally [11,26,30], for a review see [23].…”

Exact time-dependent analytical solutions for entropy production rate for a system that operates in a heat bath where its temperature varies linearly in space

“…For a linearly decreasing temperature case, we show that the efficiency of such a Brownian heat engine is far less than Carnot's efficiency even at the quasistatic limit. At quasistatic limit, the efficiency of the heat engine approaches the efficiency of endoreversible engine η = 1 − T c /T h [30]. Moreover, the dependence of the current, as well as the efficiency on the model parameters, is explored analytically.…”