Rankine studied the mechanics of the
heat engine. Though his theory of circulating streams of elastic vortices whose volumes spontaneously adapted to their environment sounds fanciful to scientists formed on a modern account, by 1849, he had succeeded in finding the relationship between
saturated vapour pressure and
temperature. The following year, he used his theory to establish relationships between the temperature,
pressure and
density of
gases, and expressions for the
latent heat of
evaporation of a
liquid. He accurately predicted the surprising fact that the apparent
specific heat of
saturated steam would be negative. Emboldened by his success, in 1851 he set out to calculate the efficiency of heat engines and used his theory as a basis to deduce the principle, that the maximum efficiency possible for any heat engine is a function only of the two temperatures between which it operates. Though a similar result had already been derived by
Rudolf Clausius and
William Thomson, Rankine claimed that his result rested upon his hypothesis of molecular vortices alone, rather than upon Carnot's theory or some other additional assumption. The work marked the first step on Rankine's journey to develop a more complete theory of heat. In 1853, he coined the term
potential energy. Rankine later recast the results of his molecular theories in terms of a macroscopic account of
energy and its transformations. He defined and distinguished between
actual energy which was lost in dynamic processes and
potential energy by which it was replaced. He assumed the sum of the two energies to be constant, an idea already, although surely not for very long, familiar in the law of
conservation of energy. From 1854, he made wide use of his
thermodynamic function which he later realised was identical to the
entropy of Clausius. By 1855, Rankine had formulated a
science of energetics which gave an account of dynamics in terms of energy and its transformations rather than
force and
motion. This article presents the first published definition of energy in terms of capacity for performing work, which quickly became the standard general definition of energy. The theory was very influential in the 1890s. In 1859 he proposed the
Rankine scale of temperature, an absolute or thermodynamic scale whose degree is equal to a
Fahrenheit degree. In 1862, Rankine expanded Lord Kelvin's theory of universal
heat death and, along with Kelvin himself, formulated the
heat death paradox, which disproves the possibility of an infinitely old universe. Energetics offered Rankine an alternative, and rather more mainstream, approach, to his science and, from the mid-1850s, he made rather less use of his molecular vortices. Yet he still claimed that Maxwell's work on electromagnetics was effectively an extension of his model. And, in 1864, he contended that the microscopic theories of heat proposed by Clausius and
James Clerk Maxwell, based on linear atomic motion, were inadequate. It was only in 1869 that Rankine admitted the success of these rival theories. By that time, his own model of the atom had become almost identical with that of Thomson. As was his constant aim, especially as a teacher of engineering, he used his own theories to develop a number of practical results and to elucidate their physical principles including: • The
Rankine–Hugoniot equation for propagation of
shock waves, governs the behaviour of shock waves normal to the oncoming flow. It is named after physicists Rankine and the French engineer
Pierre Henri Hugoniot; • The
Rankine cycle, an analysis of an ideal heat-engine with a condensor. Like other thermodynamic cycles, the maximum efficiency of the Rankine cycle is given by calculating the maximum efficiency of the
Carnot cycle; • Properties of steam, gases and vapours. The history of
rotordynamics is replete with the interplay of theory and practice. Rankine first performed an analysis of a
spinning shaft in 1869, but his model was not adequate and he predicted that supercritical speeds could not be attained. ==Fatigue studies==