Equations

In science, an equation is a formula that sets one or more numbers or mathematical symbols equal or unequal to another set of set of one or more numbers or mathematical symbols whose operation is governed by specific rules.

Table of equations
The table to the right lists hmolscience relevant equations, in text (some linked) and LaTex format, although a few of the latter are in jpg format, indicated by (jpg) bracket, due to some kind of wiki page save error issue (seems to have something to do with "<" in LaTex), and each equation shown in modern symbol notation with main theorist behind the formulation of each: [2]

Equation name	Formulator	Date	Text	.jpg	LaTex

Equal signs	Robert Recorde	1557			$= \,$
Inequality signs	Thomas Harriot	c.1600			(jpg) (jpg) $> \,$
Momentum	René Descartes	c.1640			$\text{p} = m v \,$
Boyle’s law Mariotte’s law	Robert Boyle	1662			$PV = k \,$
Gravity	Robert Hooke	1679			$\mbox{gravity} \ \propto \ \frac{1}{\mbox{distance}^2} \,$
Second law of motion	Isaac Newton	1686	F = ma		$F = ma \,$
Pressure	Daniel Bernoulli	1738			$P = \frac{F}{A} \,$
Reciprocity relation Euler reciprocity relation	Leonhard Euler	c.1739
Chemical equation	William Cullen	1757
Combination reaction	Torbern Bergman	1775			$A + B \rightarrow AB \,$
Legendre transform	Adrien-Marie Legendre	c.1786
Charles’ law	Jacques Charles	c.1787			$V = kT \,$
Gay-Lussac’s law	Joseph Gay-Lussac	1802			$P = kT \,$
Truncated Pfaffian	Johann Pfaff	c.1805			$dW = YdZ \,$
Pfaffian form	Johann Pfaff	c.1805			$dU = \sum_{i=1}^k X_i dx_i$
Vis viva	Joseph Lagrange	1811			$T = \tfrac12 m v^2 \,\! \,$
Principle of the transmission of work	Gustave Coriolis	1821	W = Fd		$W = Fd \,$
Gravitational work Potential energy	Sadi Carnot	1824	W = mgh W = mgh		$W = mgh \,$
Pressure-volume work	Emile Clapeyron	1834			$W = \int_{V_1}^{V_2} PdV \,$
Mechanical equivalent of heat	James Joule	1843			$J = \frac{W}{Q} \,$
	Rudolf Clausius	1850			$A = \frac{\text{heat consumed}}{\text{work done}} \,$
Equivalence value of all uncompensated transformations	Rudolf Clausius	1856			$N = - \int \frac{dQ}{T} \,$
Entropy	Rudolf Clausius	1862			$S = \frac{Q}{T} \,$
First main principle First law of thermodynamics	Rudolf Clausius	1865			$dU=dQ-dW\,$
Clausius inequality	Rudolf Clausius	1865			$\oint \frac{dQ}{T} \leq 0$
Energy of the system Internal energy	Rudolf Clausius	1875			$U = T_v + J_e \,$
Maxwell internal energy relation See: Maxwell’s relations	James Maxwell	c.1871			$dU = T dS - P dV \,$ $\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V \qquad$
Maxwell enthalpy relation See: Maxwell’s relations	James Maxwell	c.1871			$dH = T dS + V dP \,$ $\left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P \qquad$
Maxwell-Helmholtz energy relation See: Maxwell’s relations	James Maxwell	c.1871			$dF = -P dV - S dT \,$ $\left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial S}{\partial V}\right)_T$
Maxwell-Gibbs energy relation See: Maxwell’s relations	James Maxwell	c.1871			$dG = dH - S dT \,$ $\left(\frac{\partial V}{\partial T}\right)_P = -\left(\frac{\partial S}{\partial P}\right)_T$
Affinity-free energy equation	Hermann Helmholtz	1882
Reversible reaction Equilibrium reaction	Jacobus van't Hoff	1884			$x A + y B \rightleftharpoons z C + w D$
Equilibrium constant	Jacobus van't Hoff	1884			$K = \frac{[C]^z [D]^w} {[A]^x [B]^y} \,$
	Jacobus van't Hoff	1884			$\Delta G^\circ = -RT \ln K \,$
Ideal gas law	Walther Nernst	1893	PV = nRT PV = nRT		$PV = nRT \,$
	Max Planck	1899			$k_{B} = \frac{R}{N_{\rm A}}\,$
Lewis dot structure	Gilbert Lewis	1900			$\text{H:H} \rightleftharpoons H + H \,$
	Max Planck [?]	c.1900
Boltzmann entropy Boltzmann-Planck entropy	Max Planck	1903	S = k ln W S = k ln W		$S = k \ln W \,$
Heat theorem Third law of thermodynamics		1906			$\lim_{T \to 0} \Delta S = 0$
	Walther Nernst	1906	A = –ΔU		$A = - \Delta U \,$
Mass-energy equivalence	Albert Einstein	1905	E = mc² E = mc²		$E = mc^2 \,$
New work done by chemical reaction	Gilbert Lewis
Lewis inequality for natural processes	Gilbert Lewis	1923	ΔG < 0 ΔG < 0		(Latex errors page code)
Lewis inequality for unnatural processes	Gilbert Lewis		ΔG > 0		(Latex errors page code)
Driving force of chemical reaction	Gilbert Lewis		A = –ΔG		$A = - \Delta G \,$
			ΔG = ΔU + PΔV – TΔS ΔG = ΔU + PΔV – TΔS		$\Delta G = \Delta U + P \Delta V - T \Delta S \,$
	Gilbert Lewis	1923			$\Delta G = \Delta H - T \Delta S \,$
			ΔH – TΔS ΔH – TΔS		$\Delta H - T \Delta S \,$
Standard free energy of formation	Gilbert Lewis	1923	ΔG° = –RT ln K ΔG° = –RT ln K
Electric work Galvanic free energy change	Gilbert Lewis	1923	ΔG = –nFE ΔG = –nFE
	Gilbert Lewis	1923	A = –ΔG A = –ΔG
		?			$A = \frac{1}{J} \,$
	James Partington	1924			$J = \frac{A}{Q} \,$
Affinity-free energy equation per extent of reaction	Theophile de Donder	1936			$A=-\left(\frac{\partial G}{\partial \xi}\right)_{p,T}$
	Pierre Perrot	1998			$A^{\circ} = \sum_{i=1}^k - \nu_i \mu^{\circ}_i \,$
	Libb Thims	c.2010	A = TΔS – ΔH A = TΔS – ΔH		$A = T \Delta S - \Delta H \,$
Alley equation	The Alley	c.2012			no job = no sex
	Ben Biddle	2013	heat = passion
Lipmann coupling inequality

Latex issues
Some LaTex equations, e.g. ΔG < 0, particularly when put into tables, on in some cases pasted into page, the code won't hold for some reason, and the page will not save.

Discussion
In 1918, American historian William Thayer, in commentary on the previous work of American physical historian Henry Adams, posited the future would see the arrival of a “common formula” that would unite history and thermodynamics: [1]

“The time may come when human affairs may be described no longer by words and sentences, but by a system of symbols or notation similar to those used in algebra or chemistry … then it may be possible to invent a common formula for thermodynamics and history.”

The best candidate for this common formula, to note, as things currently stand, is the 1882 affinity-free energy equation (Goethe-Helmholtz equation), such as elaborated on in American chemical thermodynamicist Frederick Rossini's 1971 "Chemical Thermodynamics in the Real World" Priestly Medal address, the the full ramifications of this, as Adams concluded after nearly working on the problem for 50-years, will require the aid of "another Newton".

See also
● Equation of love
● Equation of state
● Equation overlay method
● Bridgman’s thermodynamic equations

References
1. Thayer, William R. (1921). “Vagaries of Historians”. Annual Report of the American Historical Association (pgs. 77-88, esp. pgs. 80-84). G.P.O.

External links
● Equation – Wikipedia.

● Pv=nrt calculator – EngineeringUnits.com.

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