Gerstenmaier York Christian
Technische Universität München, D-80333 Munich, Germany.
Phys Rev E. 2021 Mar;103(3-1):032141. doi: 10.1103/PhysRevE.103.032141.
Heat engines performing finite time Carnot cycles are described by positive irreversible entropy functions added to the ideal reversible entropy part. The model applies for macroscopic and microscopic (quantum mechanical) engines. The mathematical and physical conditions for the solution of the power maximization problem are discussed. For entropy models which have no reversible limit, the usual "linear response regime" is not mathematically feasible; i.e., the efficiency at maximum power cannot be expanded in powers of the Carnot efficiency. Instead, a physically less intuitive expansion in powers of the ratio of heat-reservoir temperatures holds under conditions that will be inferred. Exact solutions for generalized entropy models are presented, and results are compared. For entropy generation in endoreversible models, it is proved for all heat transfer laws with general temperature-dependent heat resistances, that minimum entropy production is achieved when the temperature of the working substance remains constant in the isothermal processes. For isothermal transition time t, entropy production then is of the form a/[tf(t)±c] and not just equal to a/t for the low-dissipation limit. The cold side endoreversible entropy as a function of transition times inevitably experiences singularities. For Newtonian heat transfer with temperature-independent heat conductances, the Curzon-Ahlborn efficiency is exactly confirmed, which-only in this unique case-shows "universality" in the sense of independence from dissipation ratios of the hot and cold sides with coinciding lower and upper efficiency bounds for opposite dissipation ratios. Extended exact solutions for inclusion of adiabatic transition times are presented.
执行有限时间卡诺循环的热机由添加到理想可逆熵部分的正不可逆熵函数描述。该模型适用于宏观和微观（量子力学）发动机。讨论了功率最大化问题解的数学和物理条件。对于没有可逆极限的熵模型，通常的“线性响应区域”在数学上是不可行的；即，最大功率下的效率不能以卡诺效率的幂次展开。相反，在将推断出的条件下，以热库温度比的幂次进行的物理上不太直观的展开成立。给出了广义熵模型的精确解，并对结果进行了比较。对于内可逆模型中的熵产生，对于所有具有一般温度依赖热阻的热传递定律，证明了当工作物质的温度在等温过程中保持恒定时，实现了最小熵产生。对于等温转变时间t，熵产生的形式为a/[tf(t)±c]，而不仅仅等于低耗散极限下的a/t。冷侧内可逆熵作为转变时间的函数不可避免地会出现奇点。对于具有与温度无关的热导率的牛顿热传递，精确证实了柯曾 - 阿尔伯恩效率，仅在这种独特情况下，它在与相反耗散比的热侧和冷侧的耗散比无关的意义上显示出“普遍性”，且具有重合的上下效率界限。给出了包含绝热转变时间的扩展精确解。
