ABSTRACT
The measure of efficiency of steam-engines, the 'duty', was developed during the eighteenth century. There, a large number of similar engines were doing the same job under the same conditions, with economy at a premium and with active co-operation between the responsible engineers. In 1854 Rankine published a seminal paper 'On the Geometrical Representation of the Expansive Action of Heat, and the Theory of Thermodynamic Engines'. Five years later, in his book The steam engine and other prime movers, Rankine gave another statement of his second law: 'If the total actual heat of a homogeneous and uniformly hot substance be conceived to be divided into any number of equal parts the effects of those parts in causing work to be performed are equal.' In 1865 Clausius defined the entropy. The analytical thermodynamics founded by Clausius and Thomson began to diverge from the geometrical thermodynamics of Rankine and the engineers.
