A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium), the principles of which were first elaborated by J. Willard Gibbs in the mid-19th century. It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. A system is a geometric section of the universe, whose boundaries may be fixed or varied, and that may contain matter or energy or both. The state of a system is a reproducible condition, defined by assigning fixed numerical values to the measurable attributes of the system. These attributes may be wholly reproduced as soon as a fraction of them has been reproduced. In this case the fractional number of attributes determines the state, and is referred to as the number of variables of state or the number of degrees of freedom of the system.The concept of temperature can be evolved as soon as a means is available for determining when a body is “hotter” or “colder.” Such means might involve the measurement of a physical parameter such as the volume of a given mass of the body. When a “hotter” body, A, is placed in contact with a “colder” body, B, it is observed that A becomes “colder” and B “hotter.” When no further changes occur, and the joint system involving the two bodies has come to equilibrium, the two bodies are said to have the same temperature. Thus temperature can only be measured at equilibrium. Therefore thermodynamics is a science of equilibrium, and a thermodynamic state is necessarily an equilibrium state. Thermodynamics is a macroscopic discipline, dealing only with the properties of matter and energy in bulk, and does not recognize atomic and molecular structure. Although severely limited in this respect, it has the advantage of being completely insensitive to any change in our ideas concerning molecular phenomena, so that its laws have broad and permanent generality. Its chief service is to provide mathematical relations among the measurable parameters of a system in equilibrium so that, for example, a variable like pressure may be computed when the temperature is known, and vice versa.
