EquationsThis is a featured page

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
TextLaTex / jpg

Equal signsRobert Recorde1557
 = \,
Inequality signs Thomas Harriot c.1600
greater than(jpg)
less than(jpg)
 > \,
MomentumRené Descartesc.1640
 \text{p} = m v \,
Boyle’s law
Mariotte’s law
Robert Boyle1662
 PV = k \,
GravityRobert Hooke1679
\mbox{gravity} \ \propto \ \frac{1}{\mbox{distance}^2} \,
Second law of motionIsaac Newton1686F = ma F = ma \,
PressureDaniel Bernoulli1738
 P = \frac{F}{A} \,
Reciprocity relation
Euler reciprocity relation
Leonhard Eulerc.1739
Euler reciprocity relation
Chemical equationWilliam Cullen1757
Cullen's reaction diagram (modern view)
Combination reactionTorbern Bergman1775
 A + B \rightarrow AB \,
Legendre transformAdrien-Marie Legendrec.1786
Legendre transform relations
Charles’ lawJacques Charlesc.1787
 V = kT \,
Gay-Lussac’s lawJoseph Gay-Lussac 1802
 P = kT \,
Truncated PfaffianJohann Pfaffc.1805
 dW = YdZ \,
Pfaffian form Johann Pfaffc.1805
 dU = \sum_{i=1}^k X_i dx_i
Vis vivaJoseph Lagrange1811
 T = \tfrac12 m v^2 \,\! \,
Principle of the transmission of workGustave Coriolis1821W = Fd W = Fd \,
Gravitational work
Potential energy
Sadi Carnot1824W = mgh
W = mgh
 W = mgh \,
Pressure-volume workEmile Clapeyron1834
 W = \int_{V_1}^{V_2} PdV \,
Mechanical equivalent of heatJames Joule1843
 J = \frac{W}{Q} \,

Rudolf Clausius1850
 A = \frac{\text{heat consumed}}{\text{work done}} \,
Equivalence value of all uncompensated transformationsRudolf Clausius1856
 N = - \int \frac{dQ}{T} \,
EntropyRudolf Clausius1862
S = \frac{Q}{T} \,
First main principle
First law of thermodynamics
Rudolf Clausius1865
Clausius inequalityRudolf Clausius1865
\oint \frac{dQ}{T} \leq 0
Energy of the system
Internal energy
Rudolf Clausius1875
 U = T_v + J_e \,
Maxwell internal energy relation
See: Maxwell’s relations
James Maxwellc.1871
 dU = T dS - P dV  \,
Up-down arrow (white top boarder)
\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 Maxwellc.1871
 dH = T dS + V dP  \,
Up-down arrow (white top boarder)
\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 Maxwellc.1871
 dF = -P dV - S dT  \,
Up-down arrow (white top boarder)
\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 Maxwellc.1871
 dG = dH - S dT \,
Up-down arrow (white top boarder)
\left(\frac{\partial V}{\partial T}\right)_P = -\left(\frac{\partial S}{\partial P}\right)_T
Affinity-free energy equationHermann Helmholtz1882
Helmholtz free energy equation (1882)
Reversible reaction
Equilibrium reaction
Jacobus van't Hoff1884
x A  + y B \rightleftharpoons z C + w D
Equilibrium constantJacobus van't Hoff1884
K = \frac{[C]^z [D]^w} {[A]^x [B]^y} \,

Jacobus van't Hoff1884
 \Delta G^\circ = -RT \ln K \,
Ideal gas lawWalther Nernst1893PV = nRT
PV = nRT
PV = nRT \,

Max Planck1899
k_{B} = \frac{R}{N_{\rm A}}\,
Lewis dot structureGilbert Lewis1900
 \text{H:H} \rightleftharpoons H + H \,

Max Planck [?]c.1900
PV equals N k sub B T
Boltzmann entropy
Boltzmann-Planck entropy
Max Planck1903S = k ln W
S = k ln W
 S = k \ln W \,
Heat theorem
Third law of thermodynamics

 \lim_{T \to 0} \Delta S = 0

Walther Nernst1906A = –ΔU A = - \Delta U  \,
Mass-energy equivalenceAlbert Einstein1905E = mc²
E = mc²
 E = mc^2 \,
New work done by chemical reactionGilbert Lewis

Lewis inequality for natural processesGilbert Lewis1923 ΔG < 0
ΔG < 0
DG lz c (jpg)
Lewis inequality for unnatural processesGilbert Lewis
ΔG > 0 E DG gz(jpg)
Driving force of chemical reactionGilbert Lewis
A = –ΔG A = - \Delta G \,

 \Delta G = \Delta U + P \Delta V - T \Delta S \,

Gilbert Lewis1923
 \Delta G = \Delta H - T \Delta S \,

 \Delta H - T \Delta S \,
Standard free energy of formationGilbert Lewis1923ΔG° = –RT ln K
ΔG° = –RT ln K

Electric work
Galvanic free energy change
Gilbert Lewis1923ΔG = –nFE
ΔG = –nFE

Gilbert Lewis1923A = –ΔG
A = –ΔG

 A = \frac{1}{J} \,

James Partington1924
 J = \frac{A}{Q} \,
Affinity-free energy equation per extent of reactionTheophile de Donder1936
A=-\left(\frac{\partial G}{\partial \xi}\right)_{p,T}

Pierre Perrot1998
 A^{\circ} = \sum_{i=1}^k - \nu_i \mu^{\circ}_i \,

Libb Thimsc.2010A = TΔS – ΔH
A = TΔS – ΔH
 A = T \Delta S - \Delta H \,
Alley equationThe AlleyExternal link icon (c)c.2012
no job = no sex

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 nsWilliam Roscow Thayer (1920)
Henry Adams
William Thayer

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

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.

EoHT symbol

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