Thermodynamics in finite time

Until the 19th century, technology was essentially the domain of skilled artisans and constructors who relied on practical experience to design and build their machines. One of the first efforts to use physical theory to study the functioning of machines was undertaken by the French engineer Sadi Carnot. Motivated by the concern of the French about the superiority of British steam engines, he undertook a systematic study of the physical processes governing steam engines, resulting in his remarkable paper Reflexions sur la puissance motrice du feu (On the Motive Power of Heat) published in 1826. Among the earliest successes of this new science, thermodynamics, was the formulation of criteria describing how well real processes perform in comparison with an ideal model. Carnot showed that any engine, using heat from a hot reservoir at temperature $Th$ to do work, has to transfer some heat to a reservoir at lower temperature $T1,$ and that no engine could convert into work more of the heat taken in at $Th$ than the fraction known as the Carnot efficiency.