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 Leibniz's concept of ' vis viva ', mv2, as distinct from Newton's momentum, mv.
[6][7] Empirical developments of the early ideas, in the century following, wrestled with contravening concepts such as the caloric theory of heat.
In 1842, Julius Robert von Mayer made a statement that was rendered by Clifford Truesdell (1980) 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.
[14] 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.
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.
The constant of proportionality is universal and independent of the system and in 1845 and 1847 was measured by James Joule, who described it as the mechanical equivalent of heat.
[15][31] For the thermodynamics of closed systems, the distinction between transfers of energy as work and as heat is central and is within the scope of the present article.
Carathéodory's 1909 version of the first law of thermodynamics was stated in an axiom which refrained from defining or mentioning temperature or quantity of heat transferred.
Such statements of the first law for closed systems assert the existence of internal energy as a function of state defined in terms of adiabatic work.
[28] Carathéodory's paper asserts that its statement of the first law corresponds exactly to Joule's experimental arrangement, regarded as an instance of adiabatic work.
It does not point out that Joule's experimental arrangement performed essentially irreversible work, through friction of paddles in a liquid, or passage of electric current through a resistance inside the system, driven by motion of a coil and inductive heating, or by an external current source, which can access the system only by the passage of electrons, and so is not strictly adiabatic, because electrons are a form of matter, which cannot penetrate adiabatic walls.
Heat supplied is then defined as the residual change in internal energy after work has been taken into account, in a non-adiabatic process.
[43] Another respected text defines heat exchange as determined by temperature difference, but also mentions that the Born (1921) version is "completely rigorous".
The original discovery of the law was gradual over a period of perhaps half a century or more, and some early studies were in terms of cyclic processes.
If we isolate the tank thermally, and move the paddle wheel with a pulley and a weight, we can relate the increase in temperature with the distance descended by the mass.
Next, the system is returned to its initial state, isolated again, and the same amount of work is done on the tank using different devices (an electric motor, a chemical battery, a spring,...).
It is irrelevant if the work is electrical, mechanical, chemical,... or if done suddenly or slowly, as long as it is performed in an adiabatic way, that is to say, without heat transfer into or out of the system.
[46] This kind of evidence, of independence of sequence of stages, combined with the above-mentioned evidence, of independence of qualitative kind of work, would show the existence of an important state variable that corresponds with adiabatic work, but not that such a state variable represented a conserved quantity.
The fact of such irreversibility may be dealt with in two main ways, according to different points of view: The formula (1) above allows that to go by processes of quasi-static adiabatic work from the state
In particular, if no work is done on a thermally isolated closed system we have This is one aspect of the law of conservation of energy and can be stated: If, in a process of change of state of a closed system, the energy transfer is not under a practically zero temperature gradient, practically frictionless, and with nearly balanced forces, then the process is irreversible.
Then the heat and work transfers may be difficult to calculate with high accuracy, although the simple equations for reversible processes still hold to a good approximation in the absence of composition changes.
An experimental result that seems to violate the law may be assumed to be inaccurate or wrongly conceived, for example due to failure to account for an important physical factor.
In these terms, T, the system's temperature, and P, its pressure, are partial derivatives of U with respect to S and V. These variables are important throughout thermodynamics, though not necessary for the statement of the first law.
[60] Classical thermodynamics is initially focused on closed homogeneous systems (e.g. Planck 1897/1903[45]), which might be regarded as 'zero-dimensional' in the sense that they have no spatial variation.
If two of the kinds of wall are left unsealed, then energy transfer can be shared between them, so that the two remaining permitted terms do not correspond precisely.
[99] For fictive quasi-static transfers for which the chemical potentials in the connected surrounding subsystems are suitably controlled, these can be put into equation (4) to yield where
that are called internal variables have been introduced, which allows[102][103][104] to formulate for the general case Methods for study of non-equilibrium processes mostly deal with spatially continuous flow systems.
He considers a conceptual small cell in a situation of continuous-flow as a system defined in the so-called Lagrangian way, moving with the local center of mass.
[106] Apparently in a different frame of thinking from that of the above-mentioned paradoxical usage in the earlier sections of the historic 1947 work by Prigogine, about discrete systems, this usage of Gyarmati is consistent with the later sections of the same 1947 work by Prigogine, about continuous-flow systems, which use the term "heat flux" in just this way.
[109] This usage is described by Bailyn as stating the non-convective flow of internal energy, and is listed as his definition number 1, according to the first law of thermodynamics.