温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.

Influence of the heat reservoir boundary on the performance of Brownian heat engine

In this paper we study the thermodynamic performance of a Brownian heat engine, which is driven by temperature difference. Brownian particles move in a periodic single-barrier sawtooth potential under the action of an external load force, and contact an alternating hot and cold reservoir. The kinetic energy change of the Brownian particles and the heat leak between hot and cold reservoir are considered simultaneously. The dynamics of the Brownian particle is governed by the Smoluchowski equation. The expressions for heat flow, power output and efficiency are derived analytically. The influences of the height of barrier, the external load force and the heat reservoir boundary on efficiency and power output are discussed by numerical calculation. It is shown that the Brownian heat engine is irreversible when the irreversible heat flow caused by the kinetic energy change and the heat leak exist. The curve of the power output versus the efficiency is a loop-shaped one. When the barrier boundary coincides with the heat reservoir boundary, the heat engine has a maximum power output. The efficiency of the heat engine is enhanced, but the power output is reduced when the heat reservoir boundary is changed.
Keywords： Brownian heat engine heat leak thermodynamic performance irreversibility