Top (left): a 2009 time derivative dt version of the second law showing that positive values of entropy change dS will accrue in all natural cyclical processes (dS > 0) at temperatures above absolute zero (at which point dS=0) quantified by the inequality notation that the time derivative of entropy change is greater than or equal to (≥) zero; as tattooed on the upper back of a high school physics teacher named Alison. [6] Right: The precursor formulation of the Clausius inequality (1856), which states that for all natural processes the value of N will be greater than zero (N > 0) meaning that uncompensated transformations will accrue in the system at the end of one heat cycle, on the arm of a newly minted 2010 philosophy graduate student. [15] Bottom (left): the circle integral version of the Clausius inequality between a new and burnt match, indicative of the meaning that entropy is the arrow of time. |
a < b | a is less than b.
a ≤ b | a is less than or equal to b.
a ≪ b | a is much less than b.
a > b | a is greater than b.
a ≥ b | a is greater than or equal to b.
a ≫ b | a is much greater than or equal to b.
“The mark of the majority (signum majoritatis) as a > b, signifies a greater than b and the mark of the minority (signum minoritatis) to a < b signifies a lesser than b.”
“In non reversible processes, those in which uncompensated transformations necessarily arise, the magnitude of N has consequently a determinable and necessarily positive value.”
Inequality
(1876 notation)Inequality
(modern notation)Description For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations δ of the state of the system which do not alter its energy ε, the variation of its entropy η shall either vanish or be negative. For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations δ of the state of the system which do not alter its entropy η, the variation of its energy ε shall either vanish or be positive.
where
()
Where by letting psi ψ represent the available energy [free energy] of the system, expressed by the formula ψ = ε – tη, it is found that for the equilibrium of any isolated system it is necessary and sufficient that in all possible variations δ of the state of the system which do not alter its temperature t, the variation of its available energy ψ shall either vanish or be positive.
The difference in the two values of available energy ψ for two different states of the system which have the same temperature represents the work which would have to be expended in bringing the system from one state to another by a reversible process and without change of temperature.The reduced form of the second of equilibrium criterion for systems incapable of thermal changes, whereby we may regard the entropy as having the constant value of zero. The reduced form of the third equilibrium criterion for systems incapable of thermal changes, whereby we may regard the entropy as having the constant value of zero.
“The quantities ‘–ε’ (negative energy) and ‘–ψ’ (negative available energy), related to a system without sensible motion, may be regarded as a kind of force-function for the system.”
See main: Lewis inequalityIn 1923, American physical chemist Gilbert Lewis, starting with the foundation of Gibbs inequalities, which he says are applicable to "chemical processes which are in some way harnessed for the production of useful work", introduced a new inequality as follows:
Inequality (1923 notation) Inequality (modern notation) Description
where
()
where
()
Whereby "no actual isothermal process is possible unless it meets this condition", which applies to "the far more common case of a reaction which runs freely, like the combustion of a fuel, or the action of an acid upon a metal; or, in other words, a system which is subject to no external forces, except a constant pressure exerted by the environment."
“No actual natural process is possible unless it meets this inequality ΔG < 0 criterion.”
“We may think of the quantity ‘– ΔF ’ as the driving force of a reaction; where, in a thermodynamic sense, a system is stable when no process can occur with a diminution in free energy.”
Newton notation (1718) Lewis notation (1923) Partington notation (1924) Modern notation (1933)
The position of G1 is such that, in the words of Gilbert Lewis (1923), "no further process can occur with a diminution in free energy", and is thus representative of a state of maximal stability; whereas the position of G1 could decrease further in free energy, to the position of state one, and is thus not maximally stable. |
A tabulated view of the nature of the greater than > or less than < zero inequality aspects of the standard Gibbs free energy change ΔG° and equilibrium constant Keq quantification methods of reactions, expressed by the van’t Hoff equation, ΔG° = – RT ln Keq, for a generic reversible reaction, e.g. A + B ⇌ C + D, where a large positive equilibrium constant (ΔG ≪ 0) signifies a reaction that goes strongly, completely, and spontaneously in the forward direction towards the formation of products. [7] |
See main: Spontaneity criterionThe much greater than (a ≪ b) or much less than (a ≪ b) notations are sometimes used to depict levels of spontaneity in the quantification of chemical reactions, according to the following rule:
● The notation ΔG ≪ 0 (as compared to ΔG < 0) means that the free energy change for the process is much less than zero and will thus be greatly spontaneous.
● The notation ΔG ≫ 0 (as compared to ΔG > 0) means that the free energy change for the process is much greater than zero and will thus be greatly non-spontaneous.
A + B ⇌ AB
Sodium chloride NaCl put in contact with water H20 after which a solvation-type dissolution reaction occurs. |
2Na(s) + 2H20 (l) → 2NaOH(aq) + H2(g) 0 -237 kJ/mol -418k kJ/mol 0