# First law of thermodynamics

 The basic model of the heat engine (Carnot engine), upon which the first law (or first main principle) is based.
In thermodynamics, the first law of thermodynamics is the principle of the conservation of energy applied to any thermodynamic system. [1] In short, the first law defines the equivalent relationship, between the heat input Q to a thermodynamics system to that of the change in internal energy U of that system and the work output W produced by the system.

History
The first mention of what eventually became the famed “first law" of thermodynamics was German physicist Rudolf Clausius’ 1850 equation (IIa), as described in his first memoir, as shown below:

$dQ = dU + AR \frac{a + t}{v} dv \,$

where dQ is a differential unit of heat, dU is the internal energy of the body, A is the mechanical equivalent of heat, R is the gas constant, at is an arbitrary constant related to nature of the gas used in his derivation, t is temperature of the body, v is volume, and dv is a differential unit of volume. [4] The next version of what would eventually become the first law, was the following equation:

$dQ = AW \,$

described in detail in both his forth memoir (1854) and fifth memoir (1856), in the latter of which he classifies it along side the following expression:

$\int \frac{dQ}{T} = -N \,$

where T is the absolute temperature and N is the equivalence value of all uncompensated transformations, as the "two fundamental theorems". The finalized and now commonly-known version of the first law was presented in Clausius' ninth memoir (1865), wherein he introduces what he labels as the "first fundamental equation, as follows:

$dQ = dU + AdW \,$
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Then he references the reader to his Appendix A to his sixth memoir, wherein he defined the quantity AW as being the exterior ergon. He then states that, for the sake of brevity, we can denote the exterior ergon by a simple letter:

$w = AW \,$

which which the former version of the first fundamental equation can be re-written as:

$dQ = dU + dw \,$

which he eventually goes on to re-write as:

$dQ = dU - dw \,$

signifying that "dw" in this version is the work done by the body on the surroundings. All of these would again be polished off and revised to some extent when Clausius re-wrote his nine memoirs into the 1875 second edition textbook version of his Mechanical Theory of Heat.

In overview, the basic outline of the first law states that, according to Boerhaave’s law, a unit of heat is added to a body, it will cause the body to expand, where the expansion can be quantified as the body pushing out a region of new volume V against the weight or pressure P of the atoms and molecules of the surrounding atmosphere of the earth, and that the change in the energy of the body dU will be amount of heat added less the work one:

$dU=dQ-dW\,$

This is always the basic starting point of the first law. Other terms are added on as system analysis becomes more detailed or involved. Knowing, for instance, that W is pressure-volume work PdV, with substitution we have:

$dU=dQ-PdV\,$

To note, after circa 1875, through the work of German mathematician Carl Neumann, differentials which are inexact, or path-dependent, such as heat Q or work W, began to be signified using the small Greek delta δ or the d-hat đ symbol, among others.

Carnot cycle model of Earth
Each day, due to the configuration of the solar system, biospheric portions of the earth's surface, during its rotation, are put in contact diurnally with a hot body (the sun) and cold body (the night sky) on an alternating basis, according to which heat Q flows through various partitioned off human social systems, e.g. one small city, that each function as "working bodies", i.e. any partitioned off system through which heat may flow, of molecular species (e.g. a set of human species). In the human point of view, during each cycle, work-output is produced cyclically through the operation of economic, socially-mediated, substrate-attached, human molecular interactions in the form of multiple coupled social heat engines. [2]

Clausius notes
In the words of German physicist Rudolf Clausius, "whenever an indefinitely small quantity of heat dQ is imparted to this body, the question arises what becomes of it, and what effect it produces?" [3] It may serve in part, according to Clausius, "to increase the amount of heat actually existing in the body; in part also, if in consequence of the imparting of this heat the body changes its condition, and that change includes the overcoming of some force, it may be absorbed in the work done thereby." If we denote, according to Clausius, "the total heat existing in the body, or more briefly the quantity of heat in the body, by H, and the indefinitely small increment of this quantity by dH, and if we put dL for the indefinitely small quantity of work done (by the body)", then we can write:

$dQ = dH + dL \,$

The forces against which the work is done by the working body (e.g. a system of people, who each may be considered as individual human molecules), according to Clausius, "may be divided into two classes: (1) those which the molecules of the body exert among themselves, and which are therefore dependent on the nature of the body itself, and (2) those which arise from external influences, to which the body is subjected. According to these two classes of forces, which have to be overcome, the work is divided into internal and external work." If we denote these two quantities by dJ and dW, we may put:

$dL = dJ + dW \,$

and the foregoing equation becomes:

$dQ = dH + dJ + dW \,$

This outlines the essential first law analysis for any working body, in the words of Clausius, which thus serves as the starting basis for the thermodynamic analysis of human life.

References
1. 30+ Variations of the First Law of Thermodynamics - Institute of Human Thermodynamics, Chicago
2. Thims, Libb. (2007). Human Chemistry (Volume Two). Morrisville, NC: LuLu.
3. Clausius, Rudolf. (1879). The Mechanical Theory of Heat, London: Macmillan & Co. (second edition), original.
4. Clausius, Rudolf. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies (“first fundamental principle”, 4+ pgs). trans. Thomas Hirst, 1867. London: John van Voorst.
5. (a) First law of thermodynamics handstamped necklace (sterling silver) – Etsy.com.
(b) First law handstamped necklace –Blog.NewsArama.com.