Handouts

## History

Thermal physics is among the older scientific disciplines, having roots in the speculations of Greek philosophers and other ancient peoples. The first reaction turbine was built as a curiosity by Hero of Alexandria (AD c. 120) and consisted of a pivoted copper sphere with two bent nozzles and partially filled with water. It was heated by a fire and rotated.

The rebirth of scientific activity in Europe in the 16th century and beyond brought new enthusiasm to the study of thermal phenomena and the technology that depended on heat for alchemical, chemical, or motive purposes. The three most important problems before about 1870 were 1) explaining the behavior of ideal gases, 2) understanding the nature of heat (was it a substance or a kind of motion?), and 3) determining how to harness the "motive power of fire" with optimal efficiency.

From a modern perspective, it is most remarkable that the term energy does not become widely applied in its modern sense until the 1840s, and it was in that decade that several scientists expressed the notion of the conservation of energy. Below is a very cursory overview of the significant conceptual and technological developments on the path to understanding how to build efficient heat engines and refrigerators.

Phlogiston
In the late 17th century, the change of a material upon combustion was explained as the departure of a material substance called phlogiston on burning.
Caloric
In 1789, Antoine Lavoisier thermally decomposed mercuric oxide, disproving the phlogiston theory. He replaced it with the caloric theory of heat. Caloric was a fluid surrounding the atoms of substances that could be removed during a reaction. Heat flow from warm to cold occurs because caloric particles repel one another.
Steam Engine
Thomas Savery developed a steam-operated pump, which was developed further by Thomas Newcomen into a piston engine in 1712. In 1769 James Watt produced an improved steam-powered piston engine (that operated at higher temperatures and pressures).
Converting Work into Heat
One of the first American scientific heroes, Sir Benjamin Thompson, also known as Count Rumford, whilst serving as minister of war in Bavaria (!) in 1798, and thereby overseeing the boring of cannon, noted that an apparently \emph{inexhaustible} supply of heat came out of the cannon. This appeared inconsistent with the caloric hypothesis. He further remarked that on boring underwater, the water always took the same amount of time to boil. Thus, he reasoned, work was being converted into heat. However, the issue was hardly settled by his observations.
Carnot
Sadi Carnot's analysis of heat engines in La puissance motrice du feu (1824) suggested that the maximum efficiency of a device operating in steady state or cyclically to convert heat into mechanical work was independent of the working substance and depended only on the temperature of the heat reservoirs involved.
Clapeyron
In 1834, the French engineer B. P. Emile Clapeyron carried out studies on liquids and gases, which were later refined by Clausius. The relationship between the equilibrium vapor pressures of a liquid, its temperature, and its molar heat of vaporization is called the Clausius-Clapeyron equation.

Clapeyron also "borrowed" a technical development of Watt's, which helped determine the work performed by an engine in one cycle.

Equivalence of Work and Heat
Julius L. Mayer suggested in 1842 (as had many before him) that heat is simply a result of molecular motions, but added the insight that combustion (oxidation) was responsible for the generation of heat in animals. He also suggested the mechanical equivalent of heat by noting that as a vat of paper pulp was stirred through an appropriate linkage by a horse, that the temperature of the pulp increased.

James Joule, a brewer and amateur scientist, showed in 1843 that mechanical work done by stirring water was converted into heat energy and obtained in 1849 the conversion between mechanical work and calories. He also demonstrated the equivalence of electrical work and thermal energy using resistors (Joule heating).

Announcing in 1843 (1849?) the result of his studies, he wrote: The work done by the weight of one pound through 772 feet in Manchester will, if spent in producing heat by friction of water, raise the temperature of one pound of water by one degree Fahrenheit.''

Entropy
Following Carnot's and Clapeyron's insights, Rudolf Clausius showed that the quotient of the heat transferred and the absolute (ideal gas) temperature was an important quantity (1854), which he named \emph{entropy} after the Greek in a paper of 1865. Ludwig Boltzmann first related entropy to disorder at the molecular level.

Clausius, William Thomson (later Lord Kelvin), and others developed obscure'' expressions of the Second Law of Thermodynamics such as \emph{It is impossible for a self-acting machine, unaided by external agency, to convey heat from a body at one temperature to another body at a higher temperature} and \emph{it is impossible by a cyclic process to take heat from a reservoir and convert it into work without, in the same operation, transferring heat from a hot to a cold reservoir.}

Kinetic Theory
The kinetic theory of gases was developed largely by Ludwig Boltzmann and James C. Maxwell in the 1870s. It provided a means to derive the ideal gas law from simple assumptions, accounted for the heat capacities of monatomic gases, lent powerful support to the atomic theory of matter, and suggested a very profound failure of classical physics in the heat capacity of diatomic gases. Maxwell recognized very clearly the problem, pronounced it fundamental, and speculated that the answer would require some great new insight in mechanics. The answer would require more than fifty years.
Gibbs
In a series of papers published between 1875 and 1878 in the Journal of the Connecticut Academy, Josiah Willard Gibbs invented statistical mechanics by postulating that the "proper" way to count states in phase space is equally with respect to positions and momenta (not energy). Maxwell champions Gibbs's work, which was translated into German in 1892.
Studies of the radiation produced by heated bodies led to the recognition that all bodies that absorbed all the radiation incident on them produced identical spectra, irrespective of composition. In 1879 Josef Stefan found that the radiation emitted by a heated body was proportional to {$T^{4}$}, a result that was derived five years later by Boltzmann. The classical theory of thermal radiation was worked out by Rayleigh and Jeans; it predicted $u(\lambda) = 8 \pi \kb T \lambda^{-4}$, which is indeed observed for large wavelengths. However, it also prediced a divergent energy at short wavelengths (the ultraviolet catastrophe).
Planck derived the correct expression for the spectral density of thermal radiation by focusing on the entropy in the radiation field. He introduced an ad hoc assumption into the classical statistical mechanics of Boltzmann: he assumed that energy could only be exchanged between the walls of the blackbody cavity and the electromagnetic (radiation) field in units which were proportional to the frequency. This quantum hypothesis solved the short-wavelength divergence by cutting off the infinity of high-energy modes at energies greater than {$k_B T$}.