A branch of physics that assumed major stature during the 19th century was thermodynamics. It began by disentangling the previously confused concepts of heat and temperature, by arriving at meaningful definitions, and by showing how they could be related to the heretofore purely mechanical concepts of work and energy
Heat and Temperature
A different sensation is experienced when a hot or a cold body is touched, leading to the qualitative and subjective concept of temperature. The addition of heat to a body leads to an increase in temperature (as long as no melting or boiling occurs), and in the case of two bodies at different temperatures brought into contact, heat flows from one to the other until their temperatures become the same and thermal equilibrium is reached. To arrive at a scientific measure of temperature, scientists used the observation that the addition or subtraction of heat produced a change in at least one well-defined property of a body. The addition of heat, for example, to a column of liquid maintained at constant pressure increased the length of the column, while the heating of a gas confined in a container raised its pressure. Temperature, therefore, can invariably be measured by one other physical property, as in the length of the mercury column in an ordinary thermometer, provided the other relevant properties remain unchanged. The mathematical relationship between the relevant physical properties of a body or system and its temperature is known as the equation of state. Thus, for an ideal gas, a simple relationship exists between the pressure, p, volume V, number of moles n, and the absolute temperature T, given by pV = nRT, where R is the same constant for all ideal gases. Boyle's law, named after the British physicist and chemist Robert Boyle, and Gay-Lussac's law or Charles's law, named after the French physicists and chemists Joseph Louis Gay-Lussac and Jacques Alexandre César Charles, are both contained in this equation of state (see Gases).
Until well into the 19th century, heat was considered a massless fluid called caloric, contained in matter and capable of being squeezed out of or into it. Although the so-called caloric theory answered most early questions on thermometry and calorimetry, it failed to provide a sound explanation of many early 19th-century observations. The first true connection between heat and other forms of energy was observed in 1798 by the Anglo-American physicist and statesman Benjamin Thompson who noted that the heat produced in the boring of cannon was roughly proportional to the amount of work done. In mechanics, work is the product of a force on a body and the distance through which the body moves during its application
The First Law of Thermodynamics
The equivalence of heat and work was explained by the German physicist Hermann Ludwig Ferdinand von Helmholtz and the British mathematician and physicist William Thomson, 1st Baron Kelvin, by the middle of the 19th century. Equivalence means that doing work on a system can produce exactly the same effect as adding heat; thus the same temperature rise can be achieved in a gas contained in a vessel by adding heat or by doing an appropriate amount of work through a paddle wheel sticking into the container where the paddle is actuated by falling weights. The numerical value of this equivalent was first demonstrated by the British physicist James Prescott Joule in several heating and paddle-wheel experiments between 1840 and 1849.
That performing work or adding heat to a system were both means of transferring energy to it was thus recognized. Therefore, the amount of energy added by heat or work had to increase the internal energy of the system, which in turn determined the temperature. If the internal energy remains unchanged, the amount of work done on a system must equal the heat given up by it. This is the first law of thermodynamics, a statement of the conservation of energy. Not until the action of molecules in a system was better understood by the development of the kinetic theory could this internal energy be related to the sum of the kinetic energies of all the molecules making up the system.
The Second Law of Thermodynamics
While the first law indicates that energy must be conserved in any interactions between a system and its surroundings, it gives no indication whether all forms of mechanical and thermal energy exchange are possible. That overall changes in energy proceed in one direction was first formulated by the French physicist and military engineer Nicolas Léonard Sadi Carnot, who in 1824 pointed out that a heat engine (a device that can produce work continuously while only exchanging heat with its surroundings) requires both a hot body as a source of heat and a cold body to absorb heat that must be discharged. When the engine performs work, heat must be transferred from the hotter to the colder body; to have the inverse take place requires the expenditure of mechanical (or electrical) work. Thus, in a continuously working refrigerator, the absorption of heat from the low temperature source (the cold space) requires the addition of work (usually as electrical power), and the discharge of heat (usually via fanned coils in the rear) to the surroundings (see Refrigeration). These ideas, based on Carnot's concepts, were eventually formulated rigorously as the second law of thermodynamics by the German mathematical physicist Rudolf Julius Emanuel Clausius and by Lord Kelvin in various alternate, although equivalent, ways. One such formulation is that heat cannot flow from a colder to a hotter body without the expenditure of work.
From the second law, it follows that in an isolated system (one that has no interactions with the surroundings) internal portions at different temperatures will always adjust to a single uniform temperature and thus produce equilibrium. This can also be applied to other internal properties that may be different initially. If milk is poured into a cup of coffee, for example, the two substances will continue to mix until they are inseparable and can no longer be differentiated. Thus, an initial separate or ordered state is turned into a mixed or disordered state. These ideas can be expressed by a thermodynamic property, called the entropy (first formulated by Clausius), which serves as a measure of how close a system is to equilibrium—that is, to perfect internal disorder. The entropy of an isolated system, and of the universe as a whole, can only increase, and when equilibrium is eventually reached, no more internal change of any form is possible. Applied to the universe as a whole, this principle suggests that eventually all temperature in space becomes uniform, resulting in the so-called heat death of the universe.
Locally, the entropy can be lowered by external action. This applies to machines, such as a refrigerator, where the entropy in the cold chamber is being reduced, and to living organisms. This local increase in order is, however, only possible at the expense of an entropy increase in the surroundings; here more disorder must be created.
This continued increase in entropy is related to the observed nonreversibility of macroscopic processes. If a process were spontaneously reversible—that is, if, after undergoing a process, both it and all the surroundings could be brought back to their initial state—the entropy would remain constant in violation of the second law. While this is true for macroscopic processes, and therefore corresponds to daily experience, it does not apply to microscopic processes, which are believed to be reversible. Thus, chemical reactions between individual molecules are not governed by the second law, which applies only to macroscopic ensembles.
From the promulgation of the second law, thermodynamics went on to other advances and applications in physics, chemistry, and engineering. Most chemical engineering, all power-plant engineering, and air-conditioning and low-temperature physics are just a few of the fields that owe their theoretical basis to thermodynamics and to the subsequent achievements of such scientists as Maxwell, the American physicist Willard Gibbs, the German physical chemist Walther Hermann Nernst, and the Norwegian-born American chemist Lars Onsager.