A History of Thermodynamics: The Missing Manual.

We present a history of thermodynamics. Part 1 discusses definitions, a pre-history of heat and temperature, and steam engine efficiency, which motivated thermodynamics. Part 2 considers in detail three heat conservation-based foundational papers by Carnot, Clapeyron, and Thomson. For a reversible Carnot cycle operating between thermal reservoirs with Celsius temperatures and t + d t , heat from the hot reservoir, and net work , Clapeyron derived W / Q = d t / C ( t ) , with C ( t ) material-independent. Thomson used μ = 1 / C ( t ) to define an absolute temperature but, unaware that an additional criterion was needed, he first proposed a logarithmic function of the ideal gas temperature T g . Part 3, following a discussion of conservation of energy, considers in detail a number of energy conservation-based papers by Clausius and Thomson. As noted by Gibbs, in 1850, Clausius established the first modern form of thermodynamics, followed by Thomson's 1851 rephrasing of what he called the Second Law. In 1854, Clausius theoretically established for a simple Carnot cycle the condition Q 1 / T 1 + Q 2 / T 2 = 0 . He generalized it to ∑ i Q i / T g , i = 0 , and then ∮ d Q / T g = 0 . This both implied a new thermodynamic state function and, with appropriate integration factor 1 / T , the thermodynamic temperature. In 1865, Clausius named this new state function the entropy .