从活塞中移除重物能获得多少功？
How much work can you get by removing weights from a piston?
AI总结：
该研究通过绝热气缸内带分块负载的无摩擦活塞模型，证明固定总负载下最大块质量趋于零时气体做功趋近可逆极限，还确定固定N时最优分步膨胀对应平衡压力几何级数，解决了相关猜想。
AI中文摘要：
在热力学中，可逆绝热膨胀可被理解为分步不可逆过程的极限。我们通过研究绝热气缸内的理想气体来将这一思想具体化，该气缸带有支撑着被分为N个块的负载的无摩擦活塞。若一次移除一个块，由此产生的膨胀是分步不可逆过程，但我们证明，对于固定的总负载，当最大块质量趋于零时，气体做的功趋近于可逆极限。在趋近该极限的过程中，有限N时会出现一个有趣的功优化问题：气体做的功如何依赖于被移除块的顺序和大小？在适合高年级本科生的数值实验的引导下，我们提出并证明了这些问题的一般答案。我们的主要有限N结果证明，对于固定N，最优分步膨胀对应于平衡压力的几何级数，解决了Andresen、Berry、Nitzan和Salamon此前提出的一个猜想。
英文摘要：
In thermodynamics, reversible adiabatic expansion can be understood as a limit of stepwise irreversible processes. We make this idea concrete by studying an ideal gas in an insulating cylinder with a frictionless piston supporting a load divided into $N$ blocks. If blocks are removed one at a time, the resulting expansion is a stepwise, irreversible process, but we prove that for a fixed total load, the work done by the gas approaches the reversible limit as the largest block mass tends to zero. On the way to this limit, an interesting work optimization question arises at finite $N$: how does the work done by the gas depend on the order and sizes of the removed blocks? Guided by numerical experiments accessible to advanced undergraduates, we motivate and then prove general answers to these questions. Our main finite-$N$ result proves that for fixed $N$, the optimal stepwise expansion corresponds to a geometric progression of equilibrium pressures, settling a conjecture previously made by Andresen, Berry, Nitzan, and Salamon.
