# 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 LaTex / jpg Equal signs Robert Recorde 1557 $= \,$ Inequality signs Thomas Harriot c.1600 (jpg)(jpg)$> \,$ Momentum René Descartes c.1640 $\text{p} = m v \,$ Boyle’s lawMariotte’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 relationEuler 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 workPotential energy Sadi Carnot 1824 W = mghW = 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 principleFirst law of thermodynamics Rudolf Clausius 1865 $dU=dQ-dW\,$ Clausius inequality Rudolf Clausius 1865 $\oint \frac{dQ}{T} \leq 0$ Energy of the systemInternal energy Rudolf Clausius 1875 $U = T_v + J_e \,$ Maxwell internal energy relationSee: Maxwell’s relations James Maxwell c.1871 $dU = T dS - P dV \,$$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V \qquad$ Maxwell enthalpy relationSee: Maxwell’s relations James Maxwell c.1871 $dH = T dS + V dP \,$$\left(\frac{\partial T}{\partial P}\right)_S = \left(\frac{\partial V}{\partial S}\right)_P \qquad$ Maxwell-Helmholtz energy relationSee: Maxwell’s relations James Maxwell c.1871 $dF = -P dV - S dT \,$$\left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial S}{\partial V}\right)_T$ Maxwell-Gibbs energy relationSee: Maxwell’s relations James Maxwell c.1871 $dG = dH - S dT \,$$\left(\frac{\partial V}{\partial T}\right)_P = -\left(\frac{\partial S}{\partial P}\right)_T$ Affinity-free energy equation Hermann Helmholtz 1882 Reversible reactionEquilibrium 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 = nRTPV = 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 entropyBoltzmann-Planck entropy Max Planck 1903 S = k ln WS = k ln W $S = k \ln W \,$ Heat theoremThird 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 = mc²E = mc² $E = mc^2 \,$ New work done by chemical reaction Gilbert Lewis Lewis inequality for natural processes Gilbert Lewis 1923 ΔG < 0ΔG < 0 (jpg) Lewis inequality for unnatural processes Gilbert Lewis ΔG > 0 (jpg) 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 – TΔSΔH – TΔS $\Delta H - T \Delta S \,$ Standard free energy of formation Gilbert Lewis 1923 ΔG° = –RT ln KΔG° = –RT ln K Electric workGalvanic free energy change Gilbert Lewis 1923 ΔG = –nFEΔG = –nFE Gilbert Lewis 1923 A = –ΔGA = –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 – ΔHA = TΔS – ΔH $A = T \Delta S - \Delta H \,$ Alley equation The Alley c.2012 $\text{no job} = \text{no *****} \,$

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.

 Henry Adams (1838-1918) William Thayer (1859-1923)

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".

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.

Equation – Wikipedia.