The first law of thermodynamics, formalized based on the heat-friction experiments of James Joule in 1843, deals with the concept of energy, which is conserved in all processes; the first law, however, is unable to quantify the effects of friction and dissipation.
The analysis which led to the concept of entropy began with the work of French mathematician Lazare Carnot who in his 1803 paper Fundamental Principles of Equilibrium and Movement proposed that in any machine the accelerations and shocks of the moving parts represent losses of moment of activity. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire which posited that in all heat-engines whenever "caloric", or what is now known as heat, falls through a temperature difference, work or motive power can be produced from the actions of the "fall of caloric" between a hot and cold body. This was an early insight into the second law of thermodynamics.
Carnot based his views of heat partially on the early 18th century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on the contemporary views of Count Rumford who showed (1789) that heat could be created by friction as when cannon bores are machined. Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state (temperature and pressure) at the end of a complete engine cycle, that "no change occurs in the condition of the working body". This latter comment was amended in his foot notes, and it was this comment that led to the development of entropy.
In the 1850s and 1860s, German physicist Rudolf Clausius objected to this supposition, i.e. that no change occurs in the working body, and gave this "change" a mathematical interpretation by questioning the nature of the inherent loss of usable heat when work is done, e.g. heat produced by friction. Clausius described entropy as the transformation-content, i.e. dissipative energy use, of a thermodynamic system or working body of chemical species during a change of state. This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass.
Later, scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, and James Clerk Maxwell gave entropy a statistical basis. In 1877 Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the logarithm of the number of microstates such a gas could occupy. Henceforth, the essential problem in statistical thermodynamics, i.e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems. Carathéodory linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability.
Read more about this topic: Entropy
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