First law of thermodynamics

The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two principal forms of energy transfer, heat and thermodynamic work. The law also defines the internal energy of a system, an extensive property for taking account of the balance of heat transfer, thermodynamic work, and matter transfer, into and out of the system. Energy cannot be created or destroyed, but it can be transformed from one form to another. In an externally isolated system, with internal changes, the sum of all forms of energy is constant.
An equivalent statement is that perpetual motion machines of the first kind are impossible; work done by a system on its surroundings requires that the system's internal energy be consumed, so that the amount of internal energy lost by that work must be resupplied as heat by an external energy source or as work by an external machine acting on the system to sustain the work of the system continuously.

Definition

For thermodynamic processes of energy transfer without transfer of matter, the first law of thermodynamics is often expressed by the algebraic sum of contributions to the internal energy, from all work, done on or by the system, and the quantity of heat, supplied to the system. With the sign convention of Rudolf Clausius, that heat supplied to the system is positive, but work done by the system is subtracted, a change in the internal energy, is written
Modern formulations, such as by Max Planck, and by IUPAC, often replace the subtraction with addition, and consider all net energy transfers to the system as positive and all net energy transfers from the system as negative, irrespective of the use of the system, for example as an engine.
When a system expands in an isobaric process, the thermodynamic work, done by the system on the surroundings is the product, of system pressure, and system volume change, whereas is said to be the thermodynamic work done on the system by the surroundings. The change in internal energy of the system is:
where denotes the quantity of heat supplied to the system from its surroundings.
Work and heat express physical processes of supply or removal of energy, while the internal energy is a mathematical abstraction that keeps account of the changes of energy that befall the system. The term is the quantity of energy added or removed as heat in the thermodynamic sense, not referring to a form of energy within the system. Likewise, denotes the quantity of energy gained or lost through thermodynamic work. Internal energy is a property of the system, while work and heat describe the process, not the system. Thus, a given internal energy change, can be achieved by different combinations of heat and work. Heat and work are said to be path dependent, while change in internal energy depends only on the initial and final states of the system, not on the path between. Thermodynamic work is measured by change in the system, and, because of friction, is not necessarily the same as work measured by forces and distances in the surroundings, though, ideally, such can sometimes be arranged; this distinction is noted in the term 'isochoric work', at constant system volume, with which is not a form of thermodynamic work.
For thermodynamic processes of energy transfer with transfer of matter, the extensive character of internal energy can be stated: for the otherwise isolated combination of two thermodynamic systems with internal energies and into a single system with internal energy

History

In the first half of the eighteenth century, French philosopher and mathematician Émilie du Châtelet made notable contributions to the emerging theoretical framework of energy, for example by emphasising Gottfried Wilhelm Leibniz's concept of vis viva, , as distinct from Isaac Newton's momentum,.
Empirical developments of the early ideas, in the century following, wrestled with contravening concepts such as the caloric theory of heat.
In the few years of his life after the 1824 publication of his book Reflections on the Motive Power of Fire, Sadi Carnot came to understand that the caloric theory of heat was restricted to mere calorimetry, and that heat and "motive power" are interconvertible. This is known only from his posthumously published notes. He wrote:
At that time, the concept of mechanical work had not been formulated. Carnot was aware that heat could be produced by friction and by percussion, as forms of dissipation of "motive power". As late as 1847, Lord Kelvin believed in the caloric theory of heat, being unaware of Carnot's notes.
In 1840, Germain Hess stated a conservation law for the heat of reaction during chemical transformations. This law was later recognized as a consequence of the first law of thermodynamics, but Hess's statement was not explicitly concerned with the relation between energy exchanges by heat and work.
In 1842, Julius Robert von Mayer made a statement that was rendered by Clifford Truesdell as "in a process at constant pressure, the heat used to produce expansion is universally interconvertible with work", but this is not a general statement of the first law, for it does not express the concept of the thermodynamic state variable, the internal energy. Also in 1842, Mayer measured a temperature rise caused by friction in a body of paper pulp. This was near the time of the 1842–1845 work of James Prescott Joule, measuring the mechanical equivalent of heat. In 1845, Joule published a paper entitled The Mechanical Equivalent of Heat, in which he specified a numerical value for the amount of mechanical work required to "produce a unit of heat", based on heat production by friction in the passage of electricity through a resistor and in the rotation of a paddle in a vat of water.
The first full statements of the law came in 1850 from Rudolf Clausius, and from William Rankine. Some scholars consider Rankine's statement less distinct than that of Clausius.

Original statements: the "thermodynamic approach"

The original 19th-century statements of the first law appeared in a conceptual framework in which transfer of energy as heat was taken as a primitive notion, defined by calorimetry. It was presupposed as logically prior to the theoretical development of thermodynamics. Jointly primitive with this notion of heat were the notions of empirical temperature and thermal equilibrium. This framework also took as primitive the notion of transfer of energy as work. This framework did not presume a concept of energy in general, but regarded it as derived or synthesized from the prior notions of heat and work. By one author, this framework has been called the "thermodynamic" approach.
The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850, referred to cyclic thermodynamic processes, and to the existence of a function of state of the system, the internal energy. He expressed it in terms of a differential equation for the increments of a thermodynamic process. This equation may be described as follows:
Reflecting the experimental work of Mayer and of Joule, Clausius wrote:
Because of its definition in terms of increments, the value of the internal energy of a system is not uniquely defined. It is defined only up to an arbitrary additive constant of integration, which can be adjusted to give arbitrary reference zero levels. This non-uniqueness is in keeping with the abstract mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system.
The concept of internal energy is considered by Bailyn to be of "enormous interest". Its quantity cannot be immediately measured, but can only be inferred, by differencing actual immediate measurements. Bailyn likens it to the energy states of an atom, that were revealed by Bohr's energy relation. In each case, an unmeasurable quantity is revealed by considering the difference of measured quantities.

Conceptual revision: the "mechanical approach"

In 1907, George H. Bryan wrote about systems between which there is no transfer of matter : "Definition. When energy flows from one system or part of a system to another otherwise than by the performance of mechanical work, the energy so transferred is called heat." This definition may be regarded as expressing a conceptual revision, as follows. This reinterpretation was systematically expounded in 1909 by Constantin Carathéodory, whose attention had been drawn to it by Max Born. Largely through Born's influence, this revised conceptual approach to the definition of heat came to be preferred by many twentieth-century writers. It might be called the "mechanical approach".
Energy can also be transferred from one thermodynamic system to another in association with transfer of matter. Born points out that in general such energy transfer is not resolvable uniquely into work and heat moieties. In general, when there is transfer of energy associated with matter transfer, work and heat transfers can be distinguished only when they pass through walls physically separate from those for matter transfer.
The "mechanical" approach postulates the law of conservation of energy. It also postulates that energy can be transferred from one thermodynamic system to another adiabatically as work, and that energy can be held as the internal energy of a thermodynamic system. It also postulates that energy can be transferred from one thermodynamic system to another by a path that is non-adiabatic, and is unaccompanied by matter transfer. Initially, it "cleverly" refrains from labelling as 'heat' such non-adiabatic, unaccompanied transfer of energy. It rests on the primitive notion of walls, especially adiabatic walls and non-adiabatic walls, defined as follows. Temporarily, only for purpose of this definition, one can prohibit transfer of energy as work across a wall of interest. Then walls of interest fall into two classes, those such that arbitrary systems separated by them remain independently in their own previously established respective states of internal thermodynamic equilibrium; they are defined as adiabatic; and those without such independence; they are defined as non-adiabatic.
This approach derives the notions of transfer of energy as heat, and of temperature, as theoretical developments, not taking them as primitives. It regards calorimetry as a derived theory. It has an early origin in the nineteenth century, for example in the work of Hermann von Helmholtz, but also in the work of many others.