量子卡诺循环

Quantum Mechnical Carnot Cycle

以经典理想气体为工质的卡诺热机循环由两个等温和两个绝热过程构成,热机可逆时,它的效率为最大。本文建立一种量子卡诺热机循环模型,该量子卡诺热机循环以一维无限深势阱中极端相对论粒子系统为工质。通过分析,发现该量子卡诺热机循环中的等温和绝热过程和经典卡诺热机的等温和绝热过程具有相似之处,它的效率表达式和经典热力学的可逆卡诺热机的效率表达式也类似,只是用系统的哈密顿量的期望值即系统的能量平均值代替经典热力学中的温度。

A cyclic thermodynamic heat engine,which combines adiabatic and isothermal processes and consists of classical ideal gas as working substance, runs most efficiently if it is reversible. In this paper,A new cyclic model of quantum Carnot heat engine whose working substance consists of non - interacting extreme relativistic particles confined to an infinite potential well, is set up. It is shown that the engine whose cycle consists of adiabatic and isothermal quantum processes are close analogues of the corresponding classical processes and that the efficiency of this engine is equal to the Carnot efficiency because quantum dynamics is reversible. Consequently, the expectation value of the Hanliltonian in the expression of the efficiency is similar to the temperature in that of the classical one.